Fuzzy Set Theory—and Its Applications

2008

Context-awareness is a key to enabling intelligent adaptation in pervasive computing applications that need to cope with dynamic and uncertain environments. Addressing uncertainty is one of the major issues in context-based situation modeling and reasoning approaches. Uncertainty can be caused by inaccuracy, ambiguity or incompleteness of sensed context. However, there is another aspect of uncertainty that is associated with human concepts and real-world situations. In this paper we propose and validate a Fuzzy Situation Inference (FSI) technique that is able to represent uncertain situations and reflect delta changes of context in the situation inference results. The FSI model integrates fuzzy logic principles into the Context Spaces (CS) model, a formal and general context reasoning and modeling technique for pervasive computing environments. The strengths of fuzzy logic for modeling and reasoning of imperfect context and vague situations are combined with the CS model’s underlying theoretical basis for supporting context-aware pervasive computing scenarios. An implementation and evaluation of the FSI model are presented to highlight the benefits of the FSI technique for context reasoning under uncertainty.

Landslides, 2010

Statistical and deterministic methods are widely used in geographic information system based landslide susceptibility mapping. This paper compares the predictive capability of three different models, namely the Weight of Evidence, the Fuzzy Logic and SHALSTAB, for producing shallow earth slide susceptibility maps, to be included as informative layers in land use planning at a local level. The test site is an area of about 450 km2 in the northern Apennines of Italy where, in April 2004, rainfall combined with snowmelt triggered hundreds of shallow earth slides that damaged roads and other infrastructure. An inventory of the landslides triggered by the event was obtained from interpretation of aerial photos dating back to May 2004. The pre-existence of mapped landslides was then checked using earlier aerial photo coverage. All the predictive models were run on the same set of geo-environmental causal factors: soil type, soil thickness, land cover, possibility of deep drainage through the bedrock, slope angle, and upslope contributing area. Model performance was assessed using a threshold-independent approach (the ROC plot). Results show that global accuracy is as high as 0.77 for both statistical models, while it is only 0.56 for SHALSTAB. Besides the limited quality of input data over large areas, the relatively poorer performance of the deterministic model maybe also due to the simplified assumptions behind the hydrological component (steady-state slope parallel flow), which can be considered unsuitable for describing the hydrologic behavior of clay slopes, that are widespread in the study area.

International Journal of Systems Science, 2007

In real-world production/transportation planning decision (PTPD) problems in a supply chain, because of the conflicting nature of the multiple objectives and the vagueness in information regarding the environmental coefficients and related parameters, conventional deterministic methods are unsuitable for yielding an effective solution. This study presents a fuzzy goal programming approach for solving the integrated PTPD problems with fuzzy multiple goals in uncertain environments. The proposed model aims to simultaneously minimize the total distribution and production costs, the total number of rejected items, and the total delivery time with reference to available capacity, labor level and quota flexibility constraints at each source, as well as forecasting demand and warehouse space at each destination. The proposed approach adopts the piecewise linear membership functions to represent the fuzzy goals of the decision maker for the integrated PTPD problems in a supply chain, and achieves more flexible doctrines via an interactive decision-making process. The analytical results obtained by implementing an industrial case indicate that the proposed approach is practically applicable for the solving the integrated multi-objective PTPD problems in uncertain environments, and can effectively improve producer/distributor relationships in a supply chain.

2009

Geospatial data base creation for landslide-hazard mapping is often an almost inhibitive activity. This has been the reason that for quite some time landslide-hazard analysis was modeled on the basis of spatially related factors. This paper presents the use of fuzzy logic to landslide-hazard analysis in the Penang Island, Malaysia, using remote sensing data and a geographic information system (GIS). To achieve the goal, a data-derived model (frequency ratio) and a knowledge-derived model (fuzzy operator) were combined for landslide-hazard analysis. Landslide locations within the study areas were identified by interpreting aerial photographs, satellite images and field surveys. The nine factors that influence landslide occurrence were extracted from the database and the frequency ratio coefficient for each factor was computed. Using the factors and the identified landslide, the fuzzy membership values were calculated. Then fuzzy algebraic operators were applied to the fuzzy membership values for landslide-hazard mapping. Finally, the produced map was verified by comparing with existing landslide locations for calculating prediction accuracy. Among the fuzzy operators, in the case in which the gamma operator (λ = 0.8) showed the best accuracy (80%) while the case in which the fuzzy or operator was applied showed the worst accuracy (56%).

Sadhana-academy Proceedings in Engineering Sciences, 2005

Although information plays a major role in effective functioning of supply chain networks (SCNs), studies that deal specifically with the dynamics of supply chains are few. This problem is relatively new since fast communications and the means to employ it for effective management of supply chains did not exist till recently. In order to provide a vehicle for dynamic modelling and analysis of supply chain operations in vague and uncertain environments, we propose a fuzzy enhanced high level petri net (FEHLPN) model. The proposed model captures the capability of petri nets for graphical and analytical representation of dynamic SCNs with the management of uncertain information provided by fuzzy logic. The dynamics associated with two production planning and control policies are modelled, viz. make-to-stock and assemble-to-order in vague and ambiguous situations in electronic commerce environment. A fuzzy set and fuzzy truth-values are attached to an uncertain fuzzy token to model imprecision and uncertainty. The proposed FEHLPN incorporates essential aspects of rule-based systems, such as conservation of facts, refraction, and closed-world assumption.

Journal of Industrial Engineering International, 2015

The main research intent of this paper is to introduce the use of fault tree analysis (FTA) and failure mode and effects analysis (FMEA) in conjunction to analyse the risk and reliability of a complex mechatronic system in both qualitative and quantitative manner. The major focus is on handling imprecise and vague information with the help of fuzzy synthesis of information. A complex mechatronic system, i.e. modular automated production system (MAPS), composed of mechanical, electronic, and embedded software subsystems is considered to study the reliability aspects using hybrid FTA. From the results, it is found that the proposed approach models both subjective issues such as human errors along with hardware failures. The in-depth analysis and prioritizing of failure modes using a risk ranking approach based on fuzzy inference system and grey relation approach not only integrate expert judgment, experience, and expertise in more flexible and realistic manner, but also address the limitations associated with traditional procedure of FMEA.

Italian Journal of Animal Science, 2014

Intramammary infection affects the quality and quantity of dairy goat milk. Health status (HS) and milk quality can be monitored by electrical conductivity (EC). The aim of the study was to determine the detection potential of EC when measured on-line on a daily basis and compared with readings from previous milkings. Milk yields (MYs) were investigated with the same approach. To evaluate these relative traits, a multivariate model based on fuzzy logic technology -which provided interesting results in cows -was used. Two foremilk samples from 8 healthy Saanen goats were measured daily over the course of six months. Bacteriological tests and somatic cells counts were used to define the HS. On-line EC measurements for each gland and MYs were also considered. Predicted deviations of EC and MY were calculated using a moving-average model and entered in the fuzzy logic model. The reported accuracy has a sensitivity of 81% and a specificity of 69%. Conclusions show that fuzzy logic is an interesting approach for dairy goats, since it offered better accuracy than other methods previously published. Nevertheless, specificity was lower than in dairy cows, probably due to the lack of a significant decrease of MY in diseased glands. Still, results show that the detection of the HS characteristics with EC is improved, when measured on-line, daily and compared with the readings from previous milkings.

Lake and Reservoir Management, 2011

Limited water resources with uneven distribution and growing demands are the main challenges of water management in Iran. The government has planned several water resources development projects. The complex technical, socio-economical and environmental outcomes of these projects require a comprehensive evaluation. To select more adaptive and accountable projects, suitable group decision support systems are needed. In this research, 4 proposed routes of water transfer schemes to Urmia Lake in Iran, which is in danger of completely drying out, are evaluated with respect to different criteria. The criteria and weights were obtained from an organization responsible for major water infrastructures in the basin. By using an efficient multi-criteria decision making method of compromise programming, the 4 alternatives were ranked, and the most robust water transfer route was selected. This best alternative transfers about 300 million cubic meters per year from another basin in the north of the lake. Results show the importance of using decision support systems for participatory and effective lake management.

Earthquake Engineering & Structural Dynamics, 2005

Past earthquake experiences indicate that most buildings designed in accordance with modern seismic design codes could survive moderate-to-strong earthquakes; however, the ÿnancial loss due to repairing cost and the subsequent business interruption can be unacceptable. Designing building structures to meet desired performance targets has become a clear direction in future seismic design practice. As a matter of fact, the performance of buildings is a ected by structural as well as non-structural components, and involves numerous uncertainties. Therefore, appropriate probabilistic approach taking into account structural and non-structural damages is required. This paper presents a fuzzy-random model for the performance reliability analysis of RC framed structures considering both structural and non-structural damages. The limit state for each performance level is deÿned as an interval of inter-storey drift ratios concerning, respectively, the non-structural and structural damage with a membership function, while the relative importance of the two aspects is re ected through the use of an appropriate cost function. To illustrate the methodology, herein the non-structural damage is represented by inÿll masonry walls. The probabilistic drift limits for RC components and masonry walls from the associated studies are employed to facilitate the demonstration of the proposed model in an example case study. The results are compared with those obtained using classical reliability model based on single-threshold performance deÿnition. The proposed model provides a good basis for incorporating di erent aspects into the performance assessment of a building system.

2011

Product concept generation and evaluation in a product development environment has been identified as the two major activities needed for obtaining an optimal design scheme. Product conceptual design is of critical importance in design through customer involvement for the systematic and simultaneous consideration on the impact of design decisions on manufacturing and assembly leads to repeated and excessive changes in design and processes. This paper introduces a novel knowledge support approach for the organization and ranking of design feature knowledge towards an integrated product model that incorporates a feature-based representation scheme targeted to evaluate the impact of design on subsequent activities in the conceptual design phase, taking into account the presence of design information and user preferences. An uncertain linguistic multi-attribute decision-making evaluation model is proposed and discussed for obtaining an optimal design scheme during the evaluation and selection of product design alternatives in conceptual design. The focus of this paper is on the development of a knowledge-intensive support design scheme and a comprehensive systematic fuzzy evaluation methodology for product conceptual design generation, evaluation, and selection. A case study and the corresponding scenario of knowledge support for design alternatives generation, evaluation and selection are provided for illustration.

Journal of Decision Systems, 2007

Programs.

Lecture Notes in Computer Science, 2005

In this paper, a new fuzzy logic-based approach to production scheduling in the presence of uncertain disruptions is presented. The approach is applied to a real-life problem of a pottery company where the uncertain disruption considered is glaze shortage. This disruption is defined by two parameters that are specified imprecisely: number of glaze shortage occurrences and glaze delivery time. They are modelled and combined using standard fuzzy sets and level 2 fuzzy sets, respectively. A predictive schedule is generated in such a way as to absorb the impact of the fuzzy glaze shortage disruption. The schedule performance measure used is makespan. Two measures of predictability are defined: the average deviation and the standard deviation of the completion time of the last job produced on each machine. In order to analyse the performance of the predictive schedule, a new simulation tool FPSSIM is developed and implemented. Various tests carried out show that the predictive schedules have good performance in the presence of uncertain disruptions.

BMC Medical Informatics and Decision Making, 2007

The understanding of heterogeneities in disease transmission dynamics as far as malaria vectors are concerned is a big challenge. Many studies while tackling this problem don't find exact models to explain the malaria vectors propagation.

The International Journal of Advanced Manufacturing Technology, 2009

Decision making is the process of finding the best option among the feasible alternatives. In classical multiple criteria decision-making (MCDM) methods, the ratings and the weights of the criteria are known precisely. Owning to vagueness of the decision data, the crisp data are inadequate for real-life situations. Since human judgments including preferences are often vague and cannot be expressed by exact numerical values, the application of fuzzy concepts in decision making is deemed to be relevant. In this paper, we proposed the application of a fuzzy distance formula in order to compute a crisp value for the standard deviation of fuzzy data. Then, we use this crisp value of the standard deviation to normalize the fuzzy data using the distance formula again. In our normalization approach, we have enough flexibility to consider various types of fuzzy numbers (such as triangular, trapezoidal, and interval). Finally, we use the technique for order preference by similarity to an ideal solution to determine the ranking order of the alternatives. A numerical example from the literature is solved to demonstrate this applicability of the proposed model. We also compare our proposed approach with similar methods in the literature using some examples with known results and a number of randomly generated test problems. The results point to the applicability of our method and signify its effectiveness in identifying solutions.

Journal of the American Society for Information Science and Technology, 2007

The vector space model of information retrieval is one of the classical and widely applied retrieval models. Paradoxically, it has been characterized by a discrepancy between its formal framework and implementable form. The underlying concepts of the vector space model are mathematical terms: linear space, vector, and inner product. However, in the vector space model, the mathematical meaning of these concepts is not preserved. They are used as mere computational constructs or metaphors. Thus, the vector space model actually does not follow formally from the mathematical concepts on which it has been claimed to rest. This problem has been recognized for more than two decades, but no proper solution has emerged so far. The present article proposes a solution to this problem. First, the concept of retrieval is defined based on the mathematical measure theory. Then, retrieval is particularized using fuzzy set theory. As a result, the retrieval function is conceived as the cardinality of the intersection of two fuzzy sets. This view makes it possible to build a connection to linear spaces. It is shown that the classical and the generalized vector space models, as well as the latent semantic indexing model, gain a correct formal background with which they are consistent. At the same time it becomes clear that the inner product is not a necessary ingredient of the vector space model, and hence of Information Retrieval (IR). The Principle of Object Invariance is introduced to handle this situation. Moreover, this view makes it possible to consistently formulate new retrieval methods: in linear space with general basis, entropy-based, and probability-based. It is also shown that Information Retrieval may be viewed as integral calculus, and thus it gains a very compact and elegant mathematical way of writing. Also, Information Retrieval may thus be conceived as an application of mathematical measure theory.

Sustainable Development, 2006

The paper deals with the problem of the redevelopment of derelict buildings and abandoned sites as a complex issue that includes environmental, social and economic aspects. The objective of the research was to suggest a model for determining the rational revitalization of derelict immovable property from the perspective of sustainable development. The authors assume that a multi-criterion analysis is an appropriate technique to use to assure equilibrium among various domains of sustainability. When taking into account the uncertainty of a problem, calculations using the fuzzy version of the TOPSIS method were proposed. The development of a model for determining revitalization priorities of abandoned buildings was based on a case study of derelict rural buildings in Lithuania. A set of indicators was defined and used to perform the multi-criterion analysis of revitalization alternatives of the derelict buildings. Based on results from calculations, scientific recommendations for a rational revitalization of buildings and their sites were prepared.

Journal of Civil Engineering and Management, 2003

The problem of Lithuanian derelict and mismanaged rural buildings that have a negative influence on the economy and environment of the country is analysed in the paper. Revitalisation of unused rural buildings is analysed in a context of sustainable development. Factors determining distribution and revitalisation perspectives of unused buildings were established by using methods of mathematical statistics. It was estimated that the peculiarities of territorial distribution are different in various zones of different development activity, also they differ according to the uses of buildings. Analytical review of sustainability indicator systems was performed. The model of indicator system for revitalisation of derelict rural buildings is proposed in the paper. This indicator system was worked out according to the common principles of sustainable development and to local peculiarities, explored by analysing territorial distribution of objects. It is possible to rate the priorities of building revitalisation alternatives by using the proposed model of the system with the help of multiple criteria decision-making methods. Due to incomplete and inconsistent information regarding sustainable development, the author suggests to use fuzzy set theory.

International Journal of Information Technology & Decision Making, 2006

Discounted Cash Flow techniques are the generally accepted methods for valuing firms. Such methods do not provide explicit acknowledgment of the value determinants and overlook their interrelations. This paper proposes a different method of firm valuation based on fuzzy logic and expert systems. It does represent a conceptual transposition of Discounted Cash Flow techniques but, unlike the latter, it takes explicit account of quantitative and qualitative variables and their mutual integration. Financial, strategic and business aspects are considered by focusing on twenty-nine value drivers that are combined together via "if-then" rules. The output of the system is a real number in the interval [0,1], which represents the value-creation power of the firm. To corroborate the model a sensitivity analysis is conducted. The system may be used for rating and ranking firms as well as for assessing the impact of managers' decisions on value creation and as a tool of corporate governance.

Quality & Quantity, 2005

Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2014

Inherent safety is a proactive approach for loss or elimination of hazard values and risk management. Expansion of safety relating to process and production in a supply chain in an uncertain environment has a critical effect on the competitive advantage of each food industrial organization. In this article, the fuzzy rating weights of each pair of the considered hazards and uncertain hazard values are described by linguistic expressions modelled by triangular fuzzy numbers. The fuzzy extent approach for the synthetic extent values of the pairwise comparison for handling fuzzy analytic hierarchical process is used to calculate the weight vector. The proposed fuzzy model is arranged in a hierarchical structure, so that the output of one interference system is used as an input for the second interference step. In the first of interference steps, the total hazard value for each identified process is calculated using the fuzzy algebra rules. In the second interference step, the inherent safety index for each process is determined on the basis of total hazard value, using the IF-THEN fuzzy logic rules. It is shown that the proposed fuzzy model is highly suitable as a decision making tool for making decisions about the inherent safety index of food industrial processes.

Studies in Fuzziness and Soft Computing, 2006

A rational approach toward decision-making should take into account human subjectivity, rather than employing only objective probability measures. This attitude towards the uncertainty of human behavior led to the study of a relatively new decision analysis field: Fuzzy decision-making. Fuzzy systems are suitable for uncertain or approximate reasoning, especially for the system with a mathematical model that is difficult to derive. Fuzzy logic allows decision-making with estimated values under incomplete or uncertain information. A major contribution of fuzzy set theory is its capability of representing vague data. Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in industrial engineering (IE) when the dynamics of the decision environment limit the specification of model objectives, constraints and the precise measurement of model parameters. This chapter provides a survey of the applications of fuzzy set theory in IE.

Simulation Methods for Reliability and Availability of Complex Systems, 2010

Computer Applications in Engineering Education, 2004

In this study, an educational tool has been presented to teach fuzzy logic controller (FLC) and classical controllers to undergraduate and graduate level students, so that students could establish a thorough understanding and be able to compare FLC with classical controllers. The tool has flexible structure and user-friendly graphical interface. Direct current (DC) motor speed control has been presented to help students learn and compare the FLC and classical controllers. Students practice on both controller, interpret and draw conclusions related to system parameters by changing parameters of FLC and classical controller with various working conditions. ß

Lecture Notes in Computer Science, 2010

With the emergence of ubiquitous data mining and recent advances in mobile communications, there is a need for visualization techniques to enhance the user-interactions, real-time decision making and comprehension of the results of mining algorithms. In this paper we propose a novel architecture for situation-aware adaptive visualization that applies intelligent visualization techniques to data stream mining of sensory data. The proposed architecture incorporates fuzzy logic principles for modeling and reasoning about context/situations and performs gradual adaptation of data mining and visualization parameters according to the occurring situations. A prototype of the architecture is implemented and described in the paper through a real-world scenario in the area of healthcare monitoring.

Soft Computing, 2010

The reference point method is an interactive technique for multiple criteria optimization problems. It is based on the optimization of the scalarizing achievement function built as the augmented max-min aggregation of individual outcomes with respect to the given reference levels. Actually, the worst individual achievement is optimized, but regularized with the term representing the average achievement. In order to avoid inconsistencies caused by the regularization, we apply the ordered weighted averages (OWA) with monotonic weights to combine all the individual achievements. Further, following the concept of the weighted OWA (WOWA), we incorporate the importance weighting of several achievements into the RPM. We show that the resulting WOWA RPM can be quite effectively implemented as an extension of the original constraints and criteria with simple linear inequalities.

Annals of Operations Research, 2008

In this paper, a new predictive-reactive approach to a parallel machine scheduling problem in the presence of uncertain disruptions is presented. The approach developed is based on generating a predictive parallel machine scheduling in such a way as to absorb the effects of possible uncertain disruptions through adding idle times to the job processing times. The uncertain disruption considered is material shortage and it is described using two parameters: number of disruption occurrences and disruption repair period. These parameters are specified imprecisely based on managerial subjective judgement and they are modelled and combined using fuzzy sets. If the impact of a disruption is too high to be absorbed by the predictive schedule, a rescheduling action is needed. In this new approach two rescheduling methods are applied, namely Left shift rescheduling and Building new schedules. The approach developed has been applied to solving a real-life scheduling problem of a pottery company. The results obtained have been satisfactory and showed the flexibility of the predictive-reactive approach.

BMC Medical Informatics and Decision Making, 2010

Background: Decision curve analysis (DCA) has been proposed as an alternative method for evaluation of diagnostic tests, prediction models, and molecular markers. However, DCA is based on expected utility theory, which has been routinely violated by decision makers. Decision-making is governed by intuition (system 1), and analytical, deliberative process (system 2), thus, rational decision-making should reflect both formal principles of rationality and intuition about good decisions. We use the cognitive emotion of regret to serve as a link between systems 1 and 2 and to reformulate DCA. Methods: First, we analysed a classic decision tree describing three decision alternatives: treat, do not treat, and treat or no treat based on a predictive model. We then computed the expected regret for each of these alternatives as the difference between the utility of the action taken and the utility of the action that, in retrospect, should have been taken. For any pair of strategies, we measure the difference in net expected regret. Finally, we employ the concept of acceptable regret to identify the circumstances under which a potentially wrong strategy is tolerable to a decision-maker. Results: We developed a novel dual visual analog scale to describe the relationship between regret associated with "omissions" (e.g. failure to treat) vs. "commissions" (e.g. treating unnecessary) and decision maker's preferences as expressed in terms of threshold probability. We then proved that the Net Expected Regret Difference, first presented in this paper, is equivalent to net benefits as described in the original DCA. Based on the concept of acceptable regret we identified the circumstances under which a decision maker tolerates a potentially wrong decision and expressed it in terms of probability of disease. Conclusions: We present a novel method for eliciting decision maker's preferences and an alternative derivation of DCA based on regret theory. Our approach may be intuitively more appealing to a decision-maker, particularly in those clinical situations when the best management option is the one associated with the least amount of regret (e.g. diagnosis and treatment of advanced cancer, etc).

BMC Medical Informatics and Decision Making, 2012

Background: Dual processing theory of human cognition postulates that reasoning and decision-making can be described as a function of both an intuitive, experiential, affective system (system I) and/or an analytical, deliberative (system II) processing system. To date no formal descriptive model of medical decision-making based on dual processing theory has been developed. Here we postulate such a model and apply it to a common clinical situation: whether treatment should be administered to the patient who may or may not have a disease.

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2003

Proceedings ACS/IEEE International Conference on Computer Systems and Applications, 2000

Cybernetics and Systems Analysis, 1999

The prediction of the number of diseases of some type or other at the level of a city, district, or region is a necessary element of organization of medical-preventive measures. From a formal viewpoint, this problem is related to a wide class of problems of predicting discrete sequences (collections of values at some fixed time points [1 ]) originating not only in medicine but also in physics, engineering, economics, sociology, and other domains.

Cybernetics and Systems Analysis, 1998

Geomatics, Natural Hazards and Risk, 2013

Search Methodologies, 2005

Quality & Quantity, 2007

This paper through a real illustrative example and a power test shows that designing a fuzzy control chart for process average of a continuous (variable) quality characteristic with a warning line is a better alternative to ShewhartX chart in many respects, like providing better neural view to inspectors, offering different strategic options for company to choose, detecting the desire shifts more quickly, and more sensibility to small shifts without any complexity augmentation to the chart.

Transportation Planning and Technology, 2011

This paper presents a discrete choice model for evaluating parking users' behaviour. In order, to explicitly take into account imprecision and uncertainty lying in user's choice process, the proposed model has been developed within the framework of Possibility Theory. This approach is an alternative way to represent imperfect knowledge (uncertainty) of users about both parking and transportation system status, as well the natural approximate reasoning of the human decision maker (imprecision). The resulting model is a quantitative soft computing tool that could support traffic analysts in planning parking policies and Advanced Travellers Information System (ATIS). In fact, effects of information on user choice can be incorporated in the model itself. Thus, we consider the parking user be a decision-maker that assumes a certain choice set (set of perceived parking alternatives); the user has some information about parking supply system and he/she associates to each parking alternatives an approximate perceived cost/utility that is represented by a possibility distribution; finally, user chooses the alternative which minimise/maximise his/her perceived parking cost/utility. The results have shown how the model is able to represent the effect of various parking policies on users behaviour and how the single component of the parking policy affects the decision-process.

Iranian Journal of Science and Technology, Transactions of Civil Engineering, 2021

In carrying out stability analysis of rock slopes, it is inevitable to deal with the geometrical and geomechanical parameters that are approximate in nature. The geometrical parameters, namely dips and dip directions of discontinuities, are conventionally selected by drawing the density contours on stereonet and then picking the point with the highest density. The density contours in itself clearly show the approximation inherent in the geometrical parameters. Moreover, inexactness involved in expressing the geomechanical parameters such as cohesion and friction angle of the rock mass or the rock joints must also be considered in the analyses. The theory of fuzzy sets capable of dealing with vague and inexact parameters is an ideal tool for this kind of problem. In this study, an algorithm is proposed based on the theory of fuzzy sets to assess the stability analysis of rock slopes. To this end, a 3-D membership function is proposed to represent the approximate nature of discontinuities. Incorporating the proposed fuzzy sets for the discontinuities together with the suitable fuzzy sets assigned to the geomechanical parameters, the final fuzzy safety factor is determined accordingly. Finally, practical applications of the proposed method are illustrated using actual field records.

Geoenvironmental Disasters, 2015

Background: Sikkim Himalaya is under consistent distress due to landslides. Abrupt thrust on infrastructure development in the valley regions of Sikkim Himalaya has led to a need for a prior planning to face landslide hazard. A comprehensive study for the identification of landslide hazard zones using landslide frequency ratio and fuzzy logic in GIS environment has been presented for the Lachung valley, Sikkim, India, where a number of hydroelectric projects are proposed. Temporal remote sensing data was used to generate significant landslide causative factors in addition to landslide inventory. Primary topographic attributes namely slope, aspect and relative relief were derived from digital elevation model. Landslide frequency ratio approach was adopted to correlate landslide causal factors with landslide incidences. Further, fuzzy logic method was used for the integration of landslide causative factors in order to delineate the landslide hazard zones. Fuzzy memberships were derived from the landslide frequency ratio values. Different gamma values were used in fuzzy gamma integration process, which resulted different landslide hazard index maps. Receiver operating characteristic curves were prepared to analyze consistency of the resulting landslide hazard index maps. Results: Landslide frequency ratio values have emphasised the importance of factors/classes in landsliding. High slope angle (35°-45°), very high slope category (>45°), High and very high relative relief categories; south, southeast and southwest aspects; drainage and lineaments buffer range of 0-50m, 50-100m and 100 to 150m; quartzite/ garnet schist and migmatite type of lithology; Sandy loam and Rock/loam classes of soils; fallow land and sparse vegetation classes of land use/land cover were found to be associated with landsliding. Five landslide hazard zonation maps with each comprising five relative landslide hazard zones namely; very low, low, moderate, high and very high hazard zones were prepared by using five fuzzy gamma operators. Maps indicated that steep talus slopes, close proximity to drainages, ridges and spars fall under high hazard zones. Settlement areas were observed in low to moderate hazard zones. Very high hazard zones were observed in steep slopes, cliffs and cut slopes excavated for the roads. Low hazard zones were observed in agricultural terraces and permafrost areas. Conclusions: Hence it can be concluded that landslide causative factor's integration using fuzzy logic has yielded good results for Lachung valley. Frequency ratio method for determination of fuzzy membership value has reduced subjectivity in the model. The final LHZ map (γ = 0.92) can be used for the planning of future infrastructure, settlement and ecological development in Lachung region.

International journal of occupational safety and ergonomics : JOSE, 2012

Managing occupational safety in any kind of industry, especially in processing, is very important and complex. This paper develops a new method for occupational risk assessment in the presence of uncertainties. Uncertain values of hazardous factors and consequence frequencies are described with linguistic expressions defined by a safety management team. They are modeled with fuzzy sets. Consequence severities depend on current hazardous factors, and their values are calculated with the proposed procedure. The proposed model is tested with real-life data from fruit processing firms in Central Serbia.

International journal of occupational safety and ergonomics : JOSE, 2012

Risk and safety management are very important issues in healthcare systems. Those are complex systems with many entities, hazards and uncertainties. In such an environment, it is very hard to introduce a system for evaluating and simulating significant hazards. In this paper, we analyzed different types of hazards in healthcare systems and we introduced a new fuzzy model for evaluating and ranking hazards. Finally, we presented a developed software solution, based on the suggested fuzzy model for evaluating and monitoring risk.

Journal of Intelligent Manufacturing, 2011

In a competitive business environment, the textile industrialists intend to propose diversified products according to consumers preference. For this purpose, the integration of sensory attributes in the process parameters choice seems to be a useful alternative. This paper provides fuzzy and neural models for the prediction of sensory properties from production parameters of knitted fabrics. The prediction accuracy of these models was evaluated using both the root mean square error (RMSE) and mean relative percent error (MRPE). The results revealed the models ability to predict tactile sensory attributes based on the production parameters. The comparison of the prediction performances showed that the neural models are slightly powerful than the fuzzy models.

Mathematical Sciences, 2015

In this work, the fuzzy Boussinesq equation is considered to solve via the homotopy analysis method (HAM). For this purpose, a theorem is proved to illustrate the convergence of the proposed method. Also, two sample examples are solved by applying the HAM to verify the efficiency and importance of the method.

Annals of Operations Research, 2012

In this paper we present an application of Tabu Search (TS) to the exams timetabling problem. One of the drawback of this meta-heuristic is related to the necessity of tuning some parameter (like tabu tenure) whose choice affects the performance of the algorithm. The importance of developing an automatic procedure is clear considering that most of the users of timetabling software, like university and school staff, do not have the expertise to conduct such tuning. The goal of this paper is to present a method to automatically manage the memory in the TS using a Decision Expert System. More precisely a Fuzzy Inference Rule Based System (FIRBS) was implemented to handle the tabu tenure based on two concepts "frequency" and "inactivity". These concepts are related to the number of times a move was attempt and the last time it was called. Computational results show that the implemented FIRBS handles well the tuning of the tabu status duration improving as well the performance of Tabu Search.

International Journal of Modern Physics C, 2007

A theoretical measure of the ionicity based on different mathematical concepts is presented in this research. Considering the distribution of valence electrons on each atom in a bond, we assume that the chemical properties of the atom can be expressed by means of probability. Using the introduced probability, different probabilistic models such as classical, fuzzy and information theoretical models have been employed to introduce new descriptors of bond ionicity. The ionicities were calculated for 12 heterodiatomic molecules and the bonds were classified in terms of covalency vs. ionicity. It was found that our proposed ionicity descriptors correlate well with the partial ionic character of the bonds.

Analytical and Bioanalytical Chemistry, 2008

We discuss the clustering of 234 environmental samples resulting from an extensive monitoring program concerning soil lead content, plant lead content, traffic density, and distance from the road at different sampling locations in former East Germany. Considering the structure of data and the unsatisfactory results obtained applying classical clustering and principal component analysis, it appeared evident that fuzzy clustering could be one of the best solutions. In the following order we used different fuzzy clustering algorithms, namely, the fuzzy c-means (FCM) algorithm, the Gustafson-Kessel (GK) algorithm, which may detect clusters of ellipsoidal shapes in data by introducing an adaptive distance norm for each cluster, and the fuzzy c-varieties (FCV) algorithm, which was developed for recognition of r-dimensional linear varieties in high-dimensional data (lines, planes or hyperplanes). Fuzzy clustering with convex combination of point prototypes and different multidimensional linear prototypes is also discussed and applied for the first time in analytical chemistry (environmetrics). The results obtained in this study show the advantages of the FCV and GK algorithms over the FCM algorithm. The performance of each algorithm is illustrated by graphs and evaluated by the values of some conventional cluster validity indices. The values of the validity indices are in very good agreement with the quality of the clustering results.

Journal of Intelligent Manufacturing, 2011

In this study, we utilize analytic network process (ANP), a more general form of AHP, for justifying standalone machine tools out of available alternatives in market due to the fact that AHP cannot accommodate the variety of interactions, dependencies and feedback between higher and lower level elements. However, due to the vagueness and uncertainty on judgments of a decision-maker, the crisp pair wise comparison in the conventional ANP seems to be insufficient and imprecise to capture the right judgments of the decision-maker. That is why, also in this paper, fuzzy number logic is introduced in the pair wise comparison of ANP to make up for this deficiency in the ANP. In short, here, an intelligent approach to machine tool selection (MTS) problem through fuzzy ANP is proposed to improve the imprecise ranking of company's requirements which is based on the conventional ANP. In order to reach to final solution, a preference ratio (PR) analysis is done by using the results of the fuzzy ANP, and investment costs of alternatives. In addition, a numerical example is presented to illustrate the proposed approach.

Journal of Economics Zeitschrift f�r National�konomie, 2000

The theory of fuzzy sets is applied to the output decisions of a price-taking firm facing imprecise information about expected future prices. Accepting risk resulting from the randomness of prices, the manager is interested in expected profits only. Since the set of possible expected-price vectors is fuzzy, a suitable defuzzification strategy is defined in analogy to the pessimism-optimism index proposed by L. Hurwicz. It depends on the manager's willingness to accept "surprises" resulting from a deviation of the true expected prices from the values that guided output decisions. Despite a linear cost function, well specified solutions to the optimization problem are possible without resorting to capacity constraints.

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2007

This paper describes an approach to pointwise construction of general aggregation operators, based on monotone Lipschitz approximation. The aggregation operators are constructed from a set of desired values at certain points, or from empirically collected data. It establishes tight upper and lower bounds on Lipschitz aggregation operators with a number of different properties, as well as the optimal aggregation operator, consistent with the given values. We consider conjunctive, disjunctive and idempotent n-ary aggregation operators; p-stable aggregation operators; various choices of the neutral element and annihilator; diagonal, opposite diagonal and marginal sections; bipolar and double aggregation operators. In all cases we provide either explicit formulas or deterministic numerical procedures to determine the bounds. The findings of this paper are useful for construction of aggregation operators with specified properties, especially using interpolation schemata.

International Transactions in Operational Research, 2004

A model is presented that develops the Quality Function Deployment (QFD) House of Quality tool into a fuzzy-set based multi-criteria decision-making process to determine the distributions of effort directed toward technical changes. When customers are polled for desired product-specific attributes, the responses are typically defined by linguistic variables that represent a fuzzy set distribution. Fuzzy sets also define customer perceptions of the product attributes and technical expert opinions about product design criteria relative to marketplace competitors. Therefore, for each technical criterion, the following factors have an effect on the decision to implement change(s): (1) fuzzy sets providing evidence of customer need for attributes; (2) motivation to change to satisfy desired customer attributes; (3) motivation for technical criterion change; and (4) the strength of the relationships between the attributes and the technical criterion. Priority rankings are linked to the distributions of effort to apply in fulfilling continuous product improvement.

International Journal of Management Science and Engineering Management

This paper presents a fuzzy decision-making approach to deal with a clustering supplier problem in a supply chain system. During recent years, determining suitable suppliers in the supply chain has become a key strategic consideration. However, the nature of these decisions is usually complex and unstructured. In general, many quantitative and qualitative factors, such as quality, price, and flexibility and delivery performance, should be considered in order to determine suitable suppliers. The aim of this paper is to present a new approach for a particle swarm optimization (PSO) algorithm to clustering suppliers under fuzzy environments into manageable smaller groups with similar characteristics. Our numerical analysis indicates that the proposed PSO improves the performance of the fuzzy c-means (FCM) algorithm.

Advances in Fuzzy Systems

Cloud computing can be considered as one of the leading-edge technological advances in the current IT industry. Cloud computing or simply cloud is attributed to the Service Oriented Architecture. Every organization is trying to utilize the benefit of cloud not only to reduce the cost overhead in infrastructure, network, hardware, software, etc., but also to provide seamless service to end users with the benefit of scalability. The concept of multitenancy assists cloud service providers to leverage the costs by providing services to multiple users/companies at the same time via shared resource. There are several cloud service providers currently in the market and they are rapidly changing and reorienting themselves as per market demand. In order to gain market share, the cloud service providers are trying to provide the latest technology to end users/customers with the reduction of costs. In such scenario, it becomes extremely difficult for cloud customers to select the best service ...

Research in Engineering Design, 2012

Consensus can be used for working out an agreement during design conflict resolution. This paper introduces an approach for consensus modelling in collaborative and distributed design. Consensus is represented by a formal model based on the fuzzy set theory. Defining a design cluster as a fuzzy evaluation relationship between a group of functional requirements and a group of conjecture regions allows the concept of consensus as a problem of the overlapping of design clusters of different perspectives to be introduced. To measure consensus, two key concepts are suggested: the intraconsensus design coefficient and the interconsensus design coefficient. Using the concept of consensus and its properties, the actors can more easily move towards consensus improvement or towards ideal consensus. From our observation, the result of interactions during collaborative and distributed design shows that a solution is a set of consensual design clusters. The concept of consensus is used (1) to evaluate design solution, (2) to assist the collaborative designing of a group of conjecture regions according to consensual functional requirements and finally (3) to capitalize on and share the know-how of the different actors.

International Journal of Intelligent Systems, 2012

This paper proposes a mathematical model to deal with project scheduling problem under vagueness and a framework of a heuristic approach to fuzzy resource-constrained project scheduling problem (F-RCPSP) using heuristic and metaheuristic scheduling methods. Our approach is very simple to apply, and it does not require knowing the explicit form of the membership functions of the fuzzy activity times. We first identify two typical activity priority rules, namely, resource over time and minimum slack priority rules. They are used in the F-RCPS problem and in the initial solution of Taboo search (TS) method. We improved the TS algorithm method for the solution of F-RCPSP. Our objective is to check the performance of these rules and metaheuristic method in minimizing the project completion time for the F-RCPS problems. In our study, we use trapezoidal fuzzy numbers (TraFNs) for activity times and activity-on-nodes (AON) representation and compute several project characteristics such as earliest, latest, and slack times in terms of TraFNs. The computational experiment shows that the performance of the proposed TS is better than the evaluation and light beam search algorithms in the literature.

Security and Communication Networks, 2015

CAPTCHA is a security technique to allow a computer application to distinguish between computer and human access. Most of now a day CAPTCHA words have their characters connected together which makes them very difficult to be segmented and recognized. In this paper we present an efficient technique that first benefits from the intersections between characters in a word and then segment it based on the recognition of each segmented character. Edge corners (ECs) are used in both segmentation and recognition phases. A novel fuzzy logic-based scheme is proposed to match characters using their ECs. Experimental results show the efficiency of the proposed scheme in terms of success rate using a large set of CAPTCHA's words.

Critical Reviews in Plant Sciences, 2004

The International Journal of Advanced Manufacturing Technology, 2013

Data envelopment analysis (DEA) is a linear programming method for assessing the efficiency and productivity of organizational units called decisionmaking units (DMUs). We propose a new network DEA (NDEA) model for measuring the performance of agility in supply chains. The uncertainty of the input and output data is modeled with linguistic terms parameterized with fuzzy sets. The proposed fuzzy NDEA model is linear and independent of the α-cut variables. The linear feature allows for a quick identification of the global optimum solution and the α-cut independency feature allows for a significant reduction in the computational efforts. We show that our model always generate solutions within a bounded feasible region. Our model also eliminates the potential for conflict by producing unique interval efficiency scores for each DMU. The proposed model is used to measure the performance of agility in a real-life case study in the dairy industry.

Communications in Computer and Information Science, 2018

Our research here suggests a fortified Offspring fuzzy neural networks (FOFNN) classifier developed with the aid of Fuzzy C-Means (FCM). The objective of this study concerns the selection of preprocessing techniques for the dimensionality reduction of input space. Principal component analysis (PCA) algorithm presents a pre-processing phase to the network to shape the low-dimensional input variables. Subsequently, the effectual step to handle uncertain information by type-2 fuzzy sets using Fuzzy C-Means (FCM) clustering. The proposition (condition) phase of the rules is formed by two FCM clustering algorithms, which are appealed by spending distinct values of the fuzzification coefficient successively resulting in valued type-2 membership functions. The simultaneous parametric optimization of the network by the evolutionary algorithm is finalized. The suggested classifier is applied to some machine learning datasets, and the results are compared with those provided by other classifi...

Complex & Intelligent Systems, 2021

In this paper, a fuzzy fractional two-stage transshipment problem where all the parameters are represented by fuzzy numbers is studied. The problem uses the ratio of costs divided by benefits as the objective function. A solution method which employs the extension principle is used to find the fuzzy objective value of the problem. For this purpose, the fuzzy fractional two-stage transshipment problem is decomposed into two sub-problems where each of them is tackled individually using various $$\alpha$$ α levels to obtain the fuzzy objective function value and its associated membership function. To deal with the nonlinearity of the objective function the Charnes–Cooper transformation method is embedded to the proposed approach. The superior efficiency of the presented formulation and the proposed solution method is examined over a numerical example as well as a case study comparing to the literature.

Advances in Intelligent Networking and Collaborative Systems

In this paper, we propose a new Fuzzy-based Simulation System for Driver Risk Management in Vehicular Ad hoc Networks (VANETs). The proposed system considers Driver's Health Condition (DHC), Vehicle's Environment Condition (VEC), Weather Condition (WC), Road Condition (RC) and Vehicle Speed (VS) to assess the risk level. The proposed system is composed of two Fuzzy Logic Controllers (FLCs): FLC1 and FLC2. FLC1 has the following inputs: WC, RC and VS and its output, together with VEC and DHC, serve as input parameters for FLC2. The input parameters' data can come from different sources, such as on-board and on-road sensors and cameras, sensors and cameras in the infrastructure and from the communications between the vehicles. Based on the system's output i.e., driving risk level, a smart box informs the driver for a potential risk/danger and provides assistance. We show through simulations the effect of the considered parameters on the determination of the driving risk and demonstrate a few actions that can be performed accordingly.

Information Technology and Management, 2012

One strategy for alleviating excess latency (delay) in the Internet is the caching of web content at multiple locations. This reduces the number of hops necessary to reach the desired content. This strategy is used for web content such as html pages, images, streaming video, and Internet radio. The network of servers which store this content, and the collections of objects stored on each server, is called a content distribution network (CDN). In order to optimally design a CDN, given a network topology with available server storage capacity at various points in the network, one must decide which object collections to place on each server in order to achieve performance or cost objectives. The placements must be within the storage limits of the servers and must reflect the request patterns for each collection of objects to be cached. Researchers have suggested formulations for the CDN problem which address performance by minimizing latency (the average number of hops is a commonly accepted measure of latency) from client to content, or formulations that focus on minimizing cost of storage and/or bandwidth. In this research, we develop a model which allows for the simultaneous treatment of performance and cost, present examples to illustrate the application of the model and perform a detailed designed experiment to gain insights into cost/hops tradeoff for a variety of network parameters.

2018

Wang and Chin (Expert Syst Appl, 38:11678–11685, 2011 [25]) proposed an optimistic as well as pessimistic fuzzy CCR data envelopment analysis (DEA) model and an approach for solving it to evaluate the best relative fuzzy efficiency as well as worst relative fuzzy efficiency and hence, relative geometric crisp efficiency of decision making units (DMUs). In this chapter, it is shown that the fuzzy CCR models, proposed by Wang and Chin, are not valid and hence cannot be used to evaluate the best relative fuzzy efficiency as well as worst relative fuzzy efficiency and hence, relative geometric crisp efficiency of DMUs. To resolve the flaws of the fuzzy CCR DEA models, proposed by Wang and Chin, new fuzzy CCR DEA models are proposed. Also, a new approach is proposed to solve the proposed fuzzy CCR DEA models for evaluating the relative geometric crisp efficiency of DMUs.

Canadian Journal of Administrative Sciences / Revue Canadienne des Sciences de l'Administration, 2012

The job classification literature has been dominated by a micro-level orientation reflective of the needs of specialists in human resources. In contrast, we take a multidisciplinary approach involving both micro-and macro-level variables to propose a relatively simple system comprised of four job classes. Our model isintended to inform management as to the type and mix of controls (e.g., centralization, formalization, and various human resources policies) that could be applied to different job types to optimally promote the overall goals of the organization. Fuzzy numbers analysis is employed to illustrate the application of the system using four jobs in a car dealership in Spain.

SN Applied Sciences

This paper suggests a hybrid NSGA-II based decision-making method in a fuzzy multi-objective reliability optimization problem. Multi-objective evolutionary algorithms (MOEAs) are popular techniques to be solved various kinds of multiobjective optimization problems efficiently. NSGA-II is one of the elitist MOEAs, which is largely used in engineering design problems. The reliability-based system design problem comprises various kinds of uncertainties such as expert's information character, qualitative statements, vagueness, incompleteness, unclear system boundaries, etc. Fuzzy optimization techniques can be useful during the initial stage of the conceptual design of a system. In many complex problems, it is not possible to produce the entire Pareto-optimal set in one simulation run. Apart from this, getting a well diverse solution set is another important phenomenon in this field. The proposed approach finds the optimal system design by resolving these issues in a fuzzy multi-objective reliability optimization problem. A numerical example of the overspeed protection system consisting of three mutually conflicting objectives such as system reliability, system cost, and system weight is considered with several design constraints to illustrate the method. Finally, the results obtained by the proposed approach are discussed with the existing approach.

Production & Manufacturing Research

With the advancement in material science and engineering, hard as well as difficult to cut materials are coming to the fore on regular basis. Machining such advanced materials with higher geometrical accuracy by conventional means is almost impossible. Thus, demand for higher accuracy with desired surface finish leads us to a large pool of non-traditional machining (NTM) processes. However, zeroing-in for a particular NTM process, for a particular operation and for a case-specific machining, is a cumbersome task. In order to make this task simpler for a decision-maker, the present research uses, fuzzy analytic hierarchy process to calculate the relative importance of various NTM processes taking product and process characteristics as the comparison basis. Finally, an overall score of various NTM processes have been obtained using quality function deployment methodology based on various shape features and work material combination. Also, the variations in the process capability features have been taken into consideration. Analysis of the present research study shows that electrochemical machining process has an edge over the other NTM processes with respect to surface finish, corner radii, minimum surface damage depth, and production time.

2020

This paper introduces fuzzy Challenge Response Framework, designed to understand the relationship between the model of a real-world situation and some real observations, based on scaled fuzzy Implicators between them. This general framework is applied to a particular case in recommender systems: the prediction of on-line performance given off-line evaluation results. We perform an empirical evaluation with real data from a Czech travel agency, comparing different recommender algorithms, different metrics for on-line and offline evaluations, and different implication operators.

Transportation Planning and Technology, 2009

Soft Computing, 2013

Hypothesis testing is one of the most significant facets of statistical inference, which like other situations in the real world is definitely affected by uncertain conditions. The aim of this paper is to develop hypothesis testing based on likelihood ratio test in fuzzy environment, where it is supposed that both hypotheses under study and sample data are fuzzy. The main idea is to employ Zadeh's extension principle. In this regard, a pair of non-linear programming problems is exploited toward obtaining membership function of likelihood ratio test statistic. Afterwards, the membership function is compared with critical value of the test in order to assess acceptability of the fuzzy null hypothesis under consideration. In this step, two distinct procedures are applied. In the first procedure, a ranking method for fuzzy numbers is utilized to make an absolute decision about acceptability of fuzzy null hypothesis. From a different point of view, in the second procedure, membership degrees of fuzzy null hypothesis acceptance and rejection are first derived using resolution identity and then, a relative decision is made on fuzzy null hypothesis acceptance or rejection based on some arbitrary decision rules. Flexibility of the proposed approach in testing fuzzy hypothesis with vague data is presented using some numerical examples.

IFIP Advances in Information and Communication Technology, 2019

SMEs are considered to be the spine of the Indian economic structure which has on a continuous basis proved to be the bulwark of the country"s economy, providing it the resilience to ward of economic shocks and the sustaining capacity in many financial adversities and calamities. These have relentlessly contributed to the overall growth of national GDP and also has generated employment to millions and export to the worldwide economy. While, SMEs are the engines of development in the current scenario, their growth is hindered by factors like low capital basis, availability of low-cost credit, poor technology, lack of quality and sufficiency in material and human resources, infrastructural constraints, lack of market awareness, globalization of trade, increasing competition and timely restructuring when stressed. The motive of this research paper is to analyze and understand the impediments in the growth of SMEs in the Indian context and to suggest solutions to overcome them. The paper also seeks to explore the impact of the growth of these SMEs at a global juncture.

International Journal of Applied and Computational Mathematics, 2021

Carbon emissions are a big concern for both the current business market and global warming. Most countries have focused on reducing the environmental effects of business with long time financial profits. This study demonstrates a green inventory model for non-instantaneous substitutable deteriorating items under joint ordering policy with carbon emission. The study discusses all possible cases: when an item is entirely used up due to demand and deterioration, the demand of that item is partially met by other item and all unsatisfied demand goes to lost sale. In this model rate of deterioration and demand rate are assumed as deterministic, constant and triangular fuzzy numbers. The objective of this model is to find optimal ordering quantity and optimize the total cost function with carbon emission. This paper introduces the solution approach and includes a numerical example to demonstrate the implementation of the model. Sensitivity analysis is given to get the impact of parameters ...

Structure and Infrastructure Engineering, 2018

The energy consumption of field-programmable gate arrays (FPGA) is dominated by leakage currents and dynamic energy associated with programmable interconnect. An FPGA built entirely from nanoelectromechanical (NEM) relays can effectively eliminate leakage energy losses, reduce the interconnect dynamic energy, operate at temperatures >225 • C and tolerate radiation doses in excess of 100 Mrad, while hybrid FPGAs comprising both complementary metal-oxide-semiconductor (CMOS) transistors and NEM relays (NEM-CMOS) have the potential to realize improvements in performance and energy efficiency. Large-scale integration of NEM relays, however, poses a significant engineering challenge due to the presence of moving parts. We discuss the design of FPGAs utilizing NEM relays based on a heterogeneous 3-D integration scheme, and carry out a scaling study to quantify key metrics related to performance and energy efficiency in both NEM-only and NEM-CMOS FPGAs. We show how the integration scheme has a profound effect on these metrics by changing the length of global wires. The scaling regime beyond which net performance and energy benefits is seen in NEM-CMOS over a baseline 90 nm CMOS technology is defined by an effective relay beam length of 0.5 µm, on-resistance of 200 k , and a via pitch of 0.4 µm, all achievable with existing process technology. For ultra-low energy applications that are not performance critical, NEM-only FPGAs can provide close to 15× improvement in energy efficiency.

Soft Computing, 2019

In hospital management, it is often observed that each decision making unit is under different and uncontrollable conditions. Consequently, comparing the units to each other cannot necessarily identify ineffectiveness of the units. This paper suggests the manager of a hospital to implement self-assessment technique for measuring the efficiency. The objective of this paper is to measure the efficiency of parallel system in intuitionistic fuzzy environment by introducing self-assessment technique which is the best type of evaluation where the maximum stability of the conditions is considered. The proposed model evaluates the performance of system and processes and determines the reasons of inefficiency in order to reduce the risk of lack of information about decision and deal with vague and complex conditions in real world. Keywords Self-assessment Á Parallel network systems Á Intuitionistic fuzzy parallel DEA Communicated by V. Loia.

Technological and Economic Development of Economy, 2018

This paper aims to introduce a quantitative method to builders for the most appropriate material selections based on multiple attributes and integrate decision group member opinions throughout bidding process. In this respect, a new model used together with the Analytic Hierarchy Process (AHP) and fuzzy Multi-Objective Optimization on the Basis of Ratio Analysis (MOORA), multi-criteria decision methods are proposed. In a real decision process, there are many uncertainties and ambiguities. In fact decision makers cannot always provide practical guidelines and especially precise judgments due to time limitations. The intelligent model proposed demonstrates that the AHP and fuzzy MOORA approach can not only be used easily to imitate the decision duration in the material selection but also the results obtained from this work provide contractors valuable insight into the material selection problem. At the same time, the quantitative analysis method based on the appropriately raised floor...

Water Resources Management, 2009

In this paper, the operation of a complex system of multireservoirs with multiple objectives is being demonstrated. The multireservoir system includes uncertainties of inflows, demands to the large extent. Fuzzy set theory has been proved as a robust theory where these kinds of uncertainties have major role. In this study, the fuzzy linear programming method is used to get the better policy for the system operation with the uncertainty in various parameters i.e. resources, technological coefficients, objective function coefficients. A four reservoir system (a compound parallel and series) is taken as a case study and the fuzzification of all parameters is tried on the system. The effect of fluctuations in irrigation demand and release, power demand and release and available storage volume are considered. The consequences on the objectives i.e. maximization of returns from irrigation release, maximization of returns from power releases are also examined. The operation policies thus evolved give a better understanding of the problem and the intricate complexities associated and there effects. With this the policy makers (a decision maker) can have a wide range of options at his disposal for suitable action.

International Journal of Enterprise Information Systems, 2019

One of the major problems that most companies face with during the implementation of an ERP system is to determine the best satisfying ERP software based on their needs and expectations. Because an improperly selected ERP software might lead to time loss and increased costs, and in the long run, a loss of market share. Therefore, the ERP evaluation process for companies becomes to a vital point. On the other hand, evaluating ERP software alternatives under a set of criteria leads us to a multiple-criteria decision making (MCDM) problem, and needs to use proper MCDM methods. In the current literature, a number of the MCDM methods have been proposed to solve these kinds of problems, both of which are the analytic network process (ANP) of Saaty, and grey relational analysis (GRA) which has been widely used in solving MCDM selection problems in various fields. Moreover, in this article, the authors used the fuzzy extension of the ANP method to reflect the uncertainty and ambiguity of de...

The Journal of The Textile Institute, 2017

In this paper, the mechanical and physical properties of rotorcraft compact spinning yarns were evaluated. For this aim, the filament pre-tension, yarn count and type of sheath fibers were selected as the controllable factors, and the effect of them on the elongation and hairiness was investigated statistically and the obtained results indicated that controllable factors have significant effect on the measured properties. In the next step, the relation between factors and measured properties was modeled by fuzzy interface system and genetic algorithm was used to optimize the number of membership function and its kind. It was observed that the accuracy of obtained models for both elongation and hairiness is acceptable (correlation coefficient for both models was: 0.99). Finally, to find a set of controllable factors to produce a yarn with high elongation and low hairiness, multi objective optimization was applied by means of nondominated sorting genetic algorithm and a set of trade off solutions obtained so that each solution can be accepted as a response.

Water Resources Management, 2013

Multiobjective fuzzy methodology is applied to a case study of Khadakwasla complex irrigation project located near Pune city of Maharashtra State, India. Three objectives, namely, maximization of net benefits, crop production and labour employment are considered. Effect of reuse of wastewater on the planning scenario is also studied. Three membership functions, namely, nonlinear, hyperbolic and exponential are analyzed for multiobjective fuzzy optimization. In the present study, objective functions are considered as fuzzy in nature whereas inflows are considered as dependable. It is concluded that exponential and hyperbolic membership functions provided similar cropping pattern for most of the situations whereas nonlinear membership functions provided different cropping pattern. However, in all the three cases, irrigation intensities are more than the existing irrigation intensity.

Journal of Intelligent & Fuzzy Systems, 2017

In this paper, we study semi-analytical methods entitled fuzzy fractional differential transform method to solve fuzzy impulsive fractional differential equations using Caupto fractional derivative. At the end first of all fuzzy differential transform method in fractional case is defined and its properties are considered completely. Then existence and uniquness theorem for the solution are proved and convergence of the proposed method is considered in details. Some examples indicate that this method can be easily applied to many linear and nonlinear problems.

Computational and Applied Mathematics, 2020

The aim of this paper is to use the combination of Reproducing kernel Hilbert space method (RKHSM) and fractional differential transform method (FDTM) to solve the linear and nonlinear fuzzy impulsive fractional differential equations. Finding the numerical solutions of this class of equations are a difficult topic to analyze. In this study, convergence analysis, estimations error and bounds errors are discussed in detail under some hypotheses which provide the theoretical basis of the proposed algorithm. Some numerical examples indicate that this method is an efficient one to solve the mentioned equations.

Soft Computing, 2015

The fractional transportation problem (FTP) plays an important role in logistics and supply management for reducing cost and improving service. In the real world, however, the parameters in the models are seldom known exactly and have to be estimated. This paper investigates the FTP where the cost coefficients and right-hand sides are represented by fuzzy parameters. Intuitively, when the parameters in the FTP are fuzzy numbers, the derived objective value should be also a fuzzy number. Based on Zadeh's extension principle, a pair of two-level mathematical programs is formulated to calculate the fuzzy objective value of the FTP with fuzzy parameters. By applying the dual formulation of linear fractional programming and variable substitution techniques, the two-level mathematical programs are transformed into ordinary one-level linear programs to solve. At a specific α-cut, solving the pair of linear programs produces the bounds of the objective value of the fuzzy FTP. By collecting the bounds from different α levels, one can depict the shape of the membership function. An example illustrates how to apply the concept of this paper to solve the fuzzy FTP problem.

2021

Received: September 24, 2020 Receive in Revised Form: October 31, 2020 Accepted: November 12, 2020 The present fuel cell technology is under considerations as a potential power source for Unmanned Aerial Vehicles. Fuel cells are an electrochemical power plant that takes hydrogen and oxygen as inputs and produces electricity, water and heat as outputs. Most of the global hydrogen production is from non-renewable fossil fuels. Therefore, this paper investigates how to save hydrogen fuel consumption and operate at high efficiency in the fuel cell/battery hybrid system to power a small Aircraft. We achieved that by working on the power management of the fuel cell/battery hybrid propulsion system for small UAV by using the fuzzy logic controller and charging up the batteries. The hybrid propulsion system consists of a 1.2kW PEM fuel cell, three 12V batteries, DC/DC converters, and an electric engine. The fuzzy logic controls the batteries' output powers through the bidirectional DC/D...

Health and Technology, 2022

COVID-19 disease is an outbreak that seriously affected the whole world, occurred in December 2019, and thus was declared a global epidemic by WHO (World Health Organization). To reduce the impact of the epidemic on humans, it is important to detect the symptoms of the disease in a timely and accurate manner. Recently, several new variants of COVID-19 have been identified in the United Kingdom (UK), South Africa, Brazil and India, and preliminary findings have been suggested that these mutations increase the transmissibility of the virus. Therefore, the aim of this study is to construct a support system based on fuzzy logic for experts to help detect of COVID-19 infection risk in a timely and accurate manner and to get a numerical output on symptoms of the virus from every person. The decision support system consists of three different sub and one main Mamdani type fuzzy inference systems (FIS). Subsystems are Common- Serious symptoms (First), Rare Symptoms (Second) and Personal Inf...

Value of Information and Flexibility, 2021

Выполнение хирургических вмешательств у больных тяжелой формой гемофилии А, получающих с профилактической целью эмицизумаб, требует выработки протокола ведения периоперационного периода. Цель: представить первый опыт выполнения лапароскопической герниопластики, гемостатической терапии и лабораторного контроля у пациента, страдающего тяжелой формой гемофилии А, получающего профилактическое лечение препаратом эмицизумаб. Трансперитонеальная герниопластика была выполнена пациенту 31 года, страдающему тяжелой формой гемофилии А, находящемуся на профилактической терапии эмицизумабом. Гемостатическая терапия рекомбинантным FVIII проводилась в течение 5 сут. Лабораторный контроль (определение FVIII хромогенным и клоттинговым методами, тромбоэластография, определение активированного частичного тромбопластинового времени и титра ингибитора) осуществляли на протяжении 8 сут. Для осуществления полноценного послеоперационного гемостаза потребовалось значительно меньшее количество концентрата FVIII за счет меньшей кратности введений по сравнению с аналогичными хирургическими вмешательствами у пациентов с тяжелой формой гемофилии А, не получающих профилактическую терапию эмицизумабом. По данным тромбоэластрографии ни одного эпизода гиперкоагуляции зарегистрировано не было. Эмицизумаб в монотерапии может обеспечить адекватный гемостаз при хирургических вмешательствах, сопряженных с потенциально низким риском периоперационного кровотечения у больных гемофилией А. В иных ситуациях применение стандартных доз концентрата FVIII на фоне эмицизумаба позволяет контролировать гемостаз в послеоперационном периоде без риска тромботических осложнений. Пациент подписал согласие на использование информации, в том числе фотографий, в научных исследованиях и публикациях.

Natural Hazards, 2016

The Hyogo Framework for Action was conceived to help nations build resilience against disasters. This framework was negotiated and approved by the United Nations at the World Conference on Disaster Reduction, held in Hyogo, Japan, in 2005. Disaster risk reductions systems are multi-agency integrated environment needing clear goals and ways to assess their evolution for planning purposes. The assessment of risk reduction maturity levels in countries/cities is difficult due to the large amount of data that must be collected and integrated to assess what is being done within each action indicated by the Hyogo Framework. Most indicators dependent on human perception are used in this assessment, making it highly dependent on the evaluators' perceptions. The objective of this work is to propose a participatory fuzzy model able to assess the maturity level of disaster risk reduction using indicators in line with the Hyogo Framework. We apply the model and the evaluation method in an exploratory study in the city of Rio de Janeiro where there are several communities at risk of landslides due heavy rains.

Journal of Engineering Design, 2017

The problem of decision-making in an uncertain environment during early design stages has found paramount importance in recent years. A novel method based on soft set theory is developed and proposed here, for concept selection during the early phase of product design. The advantage of soft set theory to describe the features of an object through any approximations is used in the proposed method to incorporate qualitative judgements of decision-makers. Bijective soft sets are used in the proposed work to depict mapping between customer requirements and generated design concepts. The method proposes the construction of a correlation table from a bijective soft set in a parametric sense. Correlation table helps the designers to identify the effect of conflicting requirements of different customers. The union and intersection operations are then performed on the correlation table which are called here as Row Union (RUnion), Row Intersection (RIntersection), Column Union (CUnion), and Column Intersection (CIntersection). A RUnion and CUnion operation on correlation table helps the designer to identify all the potential concepts which are suboptimal choices based on customer requirements. After performing RUnion and CUnion operations, RIntersection and CIntersection are performed to identify optimal choice(s) which could meet maximum conflicting requirements of customers.

International Journal of Management Science and Engineering Management, 2020

In the recent times, remanufacturing and recycling processes have been widespread because of hard environmental legislations. The significance of green factors such as uncertainty of return rates in supply networks has been extensively acknowledged in presented studies. A revenue sharing contract improves the performance of green supply chain and has a significant role in the profitability of total supply chain. There are few quantitative studies on revenue sharing contract in green supply chains. In this study, we propose coordination subject matters of a green supply chain with recycling perishable goods, involving suppliers, manufacturers, retailers, together with collection and disposal centers, in a multi-product, multi-period and multi-level basis under Fuzzy conditions. The consequences indicate that in dairy industries, appropriate collected returned products could be used as raw material for another product, which increases the supply chain profits and reduces waste; and also, since perishable goods have a limited shelf life, they can be reusable if they are collected before reaching to a critical time. Furthermore, the proposed revenue sharing contract can share benefits between supply network members and gain coordination of channel.

International Journal of Fuzzy System Applications, 2019

Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. One approach to optimize a multi-objective mathematical model is to employ utility functions for the objectives. Recent studies on utility-based multi-objective optimization concentrates on considering just one utility function for each objective. But, in reality, it is not reasonable to have a unique utility function corresponding to each objective function. Here, a constrained multi-objective mathematical model is considered in which several utility functions are associated for each objective. All of these utility functions are uncertain and in fuzzy form, so a fuzzy probabilistic approach is incorporated to investigate the uncertainty of the utility functions for each objective. Meanwhile, the total utility function of the problem will be a fuzzy no...

Journal of the American Society for Information Science and Technology, 2003

Sequential patterns refer to the frequently occurring patterns related to time or other sequences, and have been widely applied to solving decision problems. For example, they can help managers determine which items were bought after some items had been bought. However, since fuzzy sequential patterns described by natural language are one type of fuzzy knowledge representation, they are helpful in building a prototype fuzzy knowledge base in a business. Moreover, each fuzzy sequential pattern consisting of several fuzzy sets described by the natural language is well suited for the thinking of human subjects and will help to increase the flexibility for users in making decisions. Additionally, since the comprehensibility of fuzzy representation by human users is a criterion in designing a fuzzy system, the simple fuzzy partition method is preferable. In this method, each attribute is partitioned by its various fuzzy sets with pre-specified membership functions. The advantage of the simple fuzzy partition method is that the linguistic interpretation of each fuzzy set is easily obtained. The main aim of this paper is exactly to propose a fuzzy data mining technique to discover fuzzy sequential patterns by using the simple partition method. Two numerical examples are utilized to demonstrate the usefulness of the proposed method. ͑r͒ ϭ ͑t p1 ͑r͒ , t p2 ͑r͒ , …, t pd ͑r͒), and 1 Յ p Յ ␣ r ; L j , j-th frequent fuzzy grid, where 1 Յ jՅ ␤.

International Journal of Fuzzy Systems, 2020

The present paper proposes a number of models for calculating the average efficiency of two-stage networks using DEA and DEAR with fuzzy data. If the input, intermediate, and output parameters are available in a twostage network, DEA and DEAR models can be used to compute the efficiency. When evaluating decision-making units (DMUs) in two-stage network DEA, the respective programming models are fractional. Meanwhile, in DEAR , the proposed programming models are linear. Although, it is necessary that the output-to-input ratios (output-orientation) or vice versa (input orientation) be defined and available. Furthermore, DEAR models can also evaluate DMUs with a network structure when only ratio data are available. Generally, using fuzzy data is necessary for an accurate evaluation of organizations with a two-stage network structure. Therefore, in the present article, using the a-cut approach, an average efficiency model is proposed for the first and second stages of a network structure. At the end, a comparison is made between the mean efficiency scores of a number of airlines by considering fuzzy data in two-stage network DEA and DEAR .

Journal of Physics: Conference Series, 2017

There are an abnormal electric activities or irregular interference in brain of epilepsy patient. Then a sensor will be put in patient's scalp to measure and records all electric activities in brain. The result of the records known as Electroencephalography (EEG). The EEG has been transfer to flat EEG because it's easier to analyze. In this study, the uncertainty in flat EEG data will be considered as fuzzy digital space. The purpose of this research is to show that the flat EEG is fuzzy topological digital space. Therefore, the main focus for this research is to introduce fuzzy topological digital space concepts with their properties such as neighbourhood, interior and closure by using fuzzy set digital concept and Chang's fuzzy topology approach. The product fuzzy topology digital also will be shown. By introduce this concept, the data in flat EEG can considering having fuzzy topology digital properties and can identify the area in fuzzy digital space that has been affected by epilepsy seizure in epileptic patient's brain.

Foundations of Science

Local hidden-variable model of singlet-state correlations discussed in (Czachor, 2021a) is shown to be a particular case of an infinite hierarchy of local hidden-variable models based on an infinite hierarchy of calculi. Violation of Bell-type inequalities can be interpreted as a 'confusion of languages' problem, a result of mixing different but neighboring levels of the hierarchy. Mixing of nonneighboring levels results in violations beyond the Tsirelson bounds.

OPSEARCH, 2015

The aim of this research is to study the stochastic behaviour of a PGU (power generating unit) of a medium size coal fired thermal power plant using fuzzy methodology (FM). The PN approach was used to depict series and parallel configurations of the subsystems constituting the PGU. To study the failure dynamics of the considered system, various reliability parameters such as failure rate, repair time, MTBF, ENOF, availability and reliability of the system were computed using fuzzy λ-τ approach. RCA was conducted to determine the failure causes of various subsystems of the PGU. FMEA was carried out to determine the RPN scores of the various failure causes of different components. On the basis of these RPN scores, critical components were identified and ranked on the basis of criticality. Further, the limitations of the traditional FMEA approach were overcome by introducing a Fuzzy decision support system (FDSS). Findings of this study would be communicated to field engineers/system analysts of the considered system to help them understand and anticipate system behavior, and implement appropriate and effective maintenance policies for improving system availability.

Neural Computing and Applications, 2016

Credit score is a creditworthiness index, which enables the lender (bank and credit card companies) to evaluate its own risk exposure toward a particular potential customer. There are several credit scoring methods available in the literature, but one that is widely used is the FICO method. This method provides a score ranging from 300 to 850 as a fast filter for high-volume complex credit decisions. However, it falls short in the aspect of a decision support system where revised scoring can be achieved to reflect the borrower's strength and weakness in each scoring dimension, as well as the possible trade-offs made to maintain one's lending risk. Hence, this study discusses and develops a decision support tool for credit score model based on multi-criteria decision-making principles. In the proposed methodology, criteria weights are generated by fuzzy AHP. Fuzzy linguistic theory is applied in AHP to describe the uncertainties and vagueness arising from human subjectivity in decision making. Finally, drawing from the risk distance function, TOPSIS is used to rank the alternatives based on the least risk exposure. A sensitivity analysis is also demonstrated by the proposed fuzzy AHP-TOPSIS method.

Sustainability

The adoption of blockchain technology (BCT) in a supply chain holds great potential for textile industries by executing transactions among stakeholders in a most reliable and verifiable way. Textile industries in emerging economies, like Pakistan, confront severe economic pressures and uncertain environment and strive to achieve sustainable supply chain excellence through blockchain implementation. This study is an initiative to analyze the key barriers in adopting BCT-related practices within the textile industry. This study conducts an extensive review of the literature using fuzzy Delphi approach for finalizing the barriers and applied fuzzy analytical hierarchy process (AHP) for prioritizing the barriers under uncertain environment. Based on the extensive review of the literature and panel discussions with experts, a total of five main barriers and 21 sub-barriers were categorized and ranked. The results and findings prioritize technological and system-related barriers (TSB) fir...

Journal of Earth System Science, 2015

A comprehensive study for the identification of landslide susceptible zones using landslide frequency ratio and fuzzy logic in GIS environment is presented for Tehri reservoir rim region (Uttarakhand, India). Temporal remote sensing data was used to prepare important landslide causative factor layers and landslide inventory. Primary and secondary topographic attributes namely slope, aspect, relative relief, profile curvature, topographic wetness index, and stream power index, were derived from digital elevation model. Landslide frequency ratio technique was adopted to correlate factors with landslides. Further, fuzzy logic method was applied for the integration of factors (causative factor) to map landslide susceptible zones. Normalized landslide frequency ratio value was used for the fuzzy membership function and different fuzzy operators were considered for the preparation of landslide susceptibility/hazard index map. The factors considered in this study were found to be carrying a wide range of information. Accordingly, a methodology was evolved to integrate the factors using combined fuzzy gamma and fuzzy OR operation. Fuzzy gamma integration was performed for six different gamma values (range: 0-1). Gamma value of 0.95 was selected for the preparation of final susceptibility map. Landslide susceptibility index map was divided into the following five hazard zones-very low, low, moderate, high, and very highon the basis of natural break classification. Validation of the model was performed by using cumulative percentage curve technique. Area under curve value of cumulative percentage curve of proposed landslide susceptibility map (gamma = 0.95) was found to be 0.834 and it can be said that 83.4% accuracy was achieved by applying combined fuzzy logic and landslide frequency ratio method.

Fuzzy Set and Its Extension, 2019

In this paper we have firstly examined the properties of α and β cuts of intuitionistic fuzzy numbers in R n with the help of well-known Stacking and Characterization theorems in fuzzy set theory. Then, we have studied the generalized Hukuhara difference in intuitionistic fuzzy environment by using the properties of α and β cuts and support function. Finally, we have extended the strongly generalized differentiability concept from fuzzy set theory to intuitionistic fuzzy environment and proved the related theorems with this concept.

Journal of Intelligent Manufacturing, 2011

Product modelling is an essential issue in the configurable product design. Many attempts have been made for modelling the configurable products. However, most of conducted research considers the configurable product modelling as an arrangement problem of a predefined set of components into a valid product structure. This paper considers configuration not only as a structural problem but also as a collaborative design problem. Product configuration must consider explicitly different actors and their perspectives influencing simultaneously the design of configurable products. Solving product configuration problems requires collaboration of actors from multiple distributed views. Therefore, from process and product point of views, engineering design of configurable products can be assisted by multi-agents systems. Following up this consideration, this paper proposes a Fuzzy Configuration Grammar based agents to assist collaborative and distributed design for configuration. Based on the distributed fuzzy models, fuzziness of interactions during the collaborative and distributed design for configuration, a computational approach for product configuration is developed. Modelling and implementation of an agent-based system, called G-APIC (Grammars based Agents for Product Integrated Configuration), is presented.

IOP Conference Series: Earth and Environmental Science, 2019

The use of solar energy using solar panels began to be encouraged. Solar panels utilize solar radiation and convert it into clean and renewable energy. The problems of the accuracy of the panel facing right towards radiation are a challenge in the development of a driving system. Solar panels have limited motion, which is a maximum of phi, so that wind disturbances are very dangerous for motor drives and solar panels. This paper aims to eliminate wind disturbances in solar panel drive systems. The fuzzy logic control is used to determine the amount of power given to the driving motor to direct the panel towards solar radiation. Inputs and outputs of fuzzy controllers are arranged by dividing into each of the five members. Simulation results show that the position error of solar panels without wind disturbances reaches 0.3325° in zonal and 0.5210° in meridional. By using wind disturbances, this system managed to maintain errors smaller than 0.4285° in zonal and 0.6116° in meridional. After modifying the rule base and membership function, systems show decreasing of error half of recent trial.

Mathematical Optimization Theory and Operations Research, 2019

In the class of decision-making problems with fuzzy information concerning criterion values, the problem of comparing fuzzy numbers is relevant. There are various approaches to solving it. They are determined by the specific character of the problem under consideration. This paper proposes one approach to comparing fuzzy numbers. The proposed approach is as follows. At first, a rule is constructed for comparing a real number with a level set of a fuzzy number. Then, with the help of a procedure for constructing the exact lower approximation for the collection of sets, a fuzzy set is constructed. This fuzzy set determine the rule for comparing a real number with a fuzzy number. Using this rule and the approach based on separating two fuzzy numbers with a real number, the procedure is chosen for comparing two fuzzy numbers. As an example, fuzzy numbers with trapezoidal membership functions are considered, and the geometric interpretation of the results being given.

Journal of Model Based Research

This paper considers an EOQ inventory model with varying demand and holding costs. It suggests minimizing the total cost in a fuzzy related environment. The optimal policy for the nonlinear problem is determined by both Lagrangian and Kuhn-tucker methods and compared with varying price-dependent coefficient. All the input parameters related to inventory are fuzzified by using trapezoidal numbers. In the end, a numerical example discussed with sensitivity analysis is done to justify the solution procedure. This paper primarily focuses on the aspect of Economic Order Quantity (EOQ) for variable demand using Lagrangian, Kuhn-Tucker and fuzzy logic analysis. Comparative analysis of there methods are evaluated in this paper and the results showed the efficiency of fuzzy logic over the conventional methods. Here in this research trapezoidal fuzzy numbers are incorporated to study the price dependent coefficients with variable demand and unit purchase cost over variable demand. The results...

Synthesis Lectures on Mathematics and Statistics, 2020

Uncertainty is an inseparable component of almost every measurement and occurrence when dealing with real-world problems. Finding solutions to real-life problems in an uncertain environment is a difficult and challenging task. As such, this book addresses the solution of uncertain static and dynamic problems based on affine arithmetic approaches. Affine arithmetic is one of the recent developments designed to handle such uncertainties in a different manner which may be useful for overcoming the dependency problem and may compute better enclosures of the solutions. Further, uncertain static and dynamic problems turn into interval and/or fuzzy linear/nonlinear systems of equations and eigenvalue problems, respectively. Accordingly, this book includes newly developed efficient methods to handle the said problems based on the affine and interval/fuzzy approach. Various illustrative examples concerning static and dynamic problems of structures have been investigated in order to show the reliability and efficacy of the developed approaches.

Journal of Information and Optimization Sciences, 2018

Linear Programming problems and System of Linear equations have many applications in various science and engineering problems like network analysis, operations research etc. In general Linear Programming Problem (LPP) and the system of linear equations contain crisp parameters that is real numbers or complex numbers as their coefficients and constants, but in real life applications, LPP and system of equations may contain the constrains or the parameters as uncertain. These uncertain values are not the exact real numbers but vary within some range of values, the values may vary within an interval or can be considered as fuzzy number. In this paper, we have developed a new Ranking function (which converts the fuzzy number into crisp) to solve a fully fuzzy LPP and System of equations. Unlike the previous ranking functions, the proposed ranking function uses fuzzy number itself improving the accuracy of the solution. The ranking function is derived by replacing the non-parallel sides of the trapezoidal fuzzy number with non-linear functions. Various numerical examples are included and compared with the pre-existing methods.

Methods for Handling Imperfect Spatial Information, 2010

This chapter explores the phenomenon of vagueness as it relates to spatial information. It will be seen that many semantic subtleties and representational difficulties arise when spatial information is affected by vagueness. Moreover, since vagueness is particularly pervasive in spatial terminology, these problems have a significant bearing on the development of computational systems to provide functionality involving high-level manipulation of spatial data. The paper begins by considering various foundational issues regarding the nature and semantics of vagueness. Overviews are then given of several approaches to spatial vagueness that have been proposed in the literature. Following this, a more detailed presentation is given of the relatively recently developed standpoint theory of vagueness and how it can be applied to spatial concepts and relations. This theory is based on the identification of parameters of variability in the meaning of vague concepts. A standpoint is a choice of threshold values determining the range of variation over which a vague predicate is judged to be applicable. The chapter concludes with an examination a number of particularly significant vague spatial properties and relations and how they can be represented.

Engineering Management Journal, 2018

It is the nature of problems in quality management to contain elements of uncertainty. The uncertainty of input data is the result of a subjective approach to the interpretation of imprecise information. The aim of this article is to present the application of an effective fuzzification instrument in dealing with different kinds of uncertainty and also the application of natural language to model decision making in quality management. The article shows how the integration of fuzzy logic can assist with the planning of a particular product. First, the traditional Quality Function Deployment (QFD) method was used for the purpose of achieving quality improvement in a boiler (house electric water heater). Second, the QFD method combined with fuzzy logic was used for the same purpose. The preferred quality characteristics were defined using both traditional and fuzzy QFD methods, and results obtained were compared and discussed. The implications of the research for practice and future research are outlined.

Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2019

Amidst numerous factors affecting the quality of the environment especially the availability of conventional sources of energy, development of sustainable technologies to benefit the natural ecosystem can be cited as the primary need of the hour. Solar vehicles, with no emissions of greenhouse gases and its renewable-energy-based working can be considered a substitute to modern-day automobiles in this genre. However, the power obtained from solar energy in a running car is limited and for proper functioning of the car, its energy efficiency is a necessity. Selection of appropriate material for the manufacture of the car design is often associated with energy saving and emission reduction in a car. The selection of the material, however is an issue involving multiple characteristics associated with the performance of the material, including physical, mechanical, and environmental properties. This study presents a systematic structure for selection of the optimum material using a hierarchy of 14 different properties of 19 different feasible materials taken into account, using a hybrid Multi-Criteria Decision Making (MCDM) analogy, the Fuzzy Complex Proportional Assessment (COPRAS) model. A Sensitivity Analysis was conducted to account for the robustness of the solution obtained. The results prove the effectivity of this approach toward selection of optimum material for manufacture of a solar car.

Central European Journal of Operations Research, 2018

Two-stage data envelopment analysis (TsDEA) models evaluate the performance of a set of production systems in which each system includes two operational stages. Taking into account the internal structures is commonly found in many situations such as seller-buyer supply chain, health care provision and environmental management. Contrary to conventional DEA models as a black-box structure, TsDEA provides further insight into sources of inefficiencies and a more informative basis for multi-stage evaluation. In addition, ignoring the qualitative and imprecise data leads to distorted evaluations, both for the subunits and the system efficiency. We present the fuzzy input and output-oriented TsDEA models to calculate the global and pure technical efficiencies of a system and sub-processes when some data are fuzzy. To this end, we propose a possibilistic programming problem and then convert it into a deterministic interval programming problem using the α-level based method. The proposed method preserves the link between two stages in the sense that the total efficiency of the system is equal to the product of the efficiencies derived from two stages. In addition to the study of technical efficiency, this research includes two further contributions to ancillary literature; firstly, we minutely discuss the efficiency decompositions to indicate the sources of inefficiency and secondly, we present a method for ranking the efficient units in a fuzzy environment. An empirical illustration is also utilized to show the applicability of the proposed technique. Please see the attachments.

Economics of Innovation and New Technology, 2017