Reasonable properties for the ordering of fuzzy quantities (I)

2017

Since Lotfi A. Zadeh introduced the concept of fuzzy sets in 1965, many authors have devoted their efforts to the study of these new sets, both from a theoretical and applied point of view. Fuzzy sets were later extended in order to get more adequate and flexible models of inference processes, where uncertainty, imprecision or vagueness is present. Type 2 fuzzy sets comprise one of such extensions. In this paper, we introduce and study an extension of the fuzzy numbers (type 1), the type 2 generalized fuzzy numbers and type 2 fuzzy numbers. Moreover, we also define a partial order on these sets, which extends into these sets the usual order on real numbers, which undoubtedly becomes a new option to be taken into account in the existing total preorders for ranking interval type 2 fuzzy numbers, which are a subset of type 2 generalized fuzzy numbers.

Journal of Physics: Conference Series

We consider a fuzzy graph G ˜ ( V , E ˜ ) with a crisp vertex set V and a fuzzy edge set E ˜ . A fuzzy graph has some α-cut graphs for α ∈ [0, 1] which are crisp graphs. Coloring of a fuzzy graph could be transformed into classical coloring of the α-cut graphs. Let G ˜ 1 ( V 1 , E ˜ 1 ) and G ˜ 2 ( V 2 , E ˜ 2 ) be two fuzzy graphs with fuzzy chromatic numbers χ ˜ 1 ( G ˜ 1 ) = { ( k , v χ ¯ 1 ( k ) ) } and χ ˜ 2 ( G ˜ 2 ) = { ( k , v χ ¯ 2 ( k ) ) } , respectively. Let G ˜ = G ˜ 1 ∪ G ˜ 2 be a union of G ˜ 1 and G ˜ 2 . By coloring of the α-cut graphs, we get the result that membership function of fuzzy chromatic number of the union χ ˜ ( G ˜ ) = { ( k , v χ ¯ ( k ) ) } satisfies a property v χ ¯ ( k ) = max { v χ ¯ 1 ( k ) , v χ ¯ 2 ( k ) } for k ∈ {1, 2, 3, …, |V 1 ⋃ V 2|}. Furthermore, we also verify the connection between the fuzzy chromatic number χ ˜ ( G ˜ ) and max { χ ˜ 1 , χ ˜ 2 } through a defuzzification dependent at a decision level.

INTERNATIONAL CONFERENCE ON ADVANCES IN MATERIALS, COMPUTING AND COMMUNICATION TECHNOLOGIES: (ICAMCCT 2021)

Intuitionistic Fuzzy sets are used to solve problems with state of uncertainty due to many uncontrollable factors. Intuitionistic fuzzy sets are extension of fuzzy sets where they have a non-membership function along with membership function. The primary purpose is to generalize Odd IFN with their MFn and NMFn. The generalized value and generalised ambiguity definitions with alpha and beta cuts are defined. Generalized odd IFN which are defined are justified by evaluating a hendecagonal IFN problem based transportation.

Advances in Fuzzy Systems, 2016

Granular computing is an emerging computing theory and paradigm that deals with the processing of information granules, which are defined as a number of information entities grouped together due to their similarity, physical adjacency, or indistinguishability. In most aspects of human reasoning, these granules have an uncertain formation, so the concept of granularity of fuzzy information could be of special interest for the applications where fuzzy sets must be converted to crisp sets to avoid uncertainty. This paper proposes a novel method of defuzzification based on the mean value of statistical Beta distribution and an algorithm for ranking fuzzy numbers based on the crisp number ranking system on R. The proposed method is quite easy to use, but the main reason for following this approach is the equality of left spread, right spread, and mode of Beta distribution with their corresponding values in fuzzy numbers within(0,1)interval, in addition to the fact that the resulting meth...

Fuzzy Information and Engineering, 2010

Ranking of fuzzy numbers play an important role in decision making, optimization and forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples, it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as an RM approach. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (3): 375).

Frontiers of Computer Science, 2014

In this paper, we propose some distance measures between type-2 fuzzy sets, and also a new family of utmost distance measures are presented. Several properties of different proposed distance measures have been introduced. Also, we have introduced a new ranking method for the ordering of type-2 fuzzy sets based on the proposed distance measure. The proposed ranking method satisfies the reasonable properties for the ordering of fuzzy quantities. Some properties such as robustness, order relation have been presented. Limitations of existing ranking methods have been studied. Further for practical use, a new method for selecting the best alternative, for group decision making problems is proposed. This method is illustrated with a numerical example.

Journal of Control, Automation and Electrical Systems, 2020

Ranking of intuitionistic fuzzy numbers is an engrossing and very difficult task among the several researchers. The present studies introduce a new ranking method for intuitionistic fuzzy numbers (IFN) by using the concept of distance minimizer between two intuitionistic fuzzy numbers, with the help of their defined membership and non-membership functions. The proposed ranking method for intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. Further, we have applied the developed ranking method to solve fully intuitionistic fuzzy transportation problems in which cost, supplies and requirements all are in term of intuitionistic fuzzy numbers. The developed method has been illustrated by an example, and the result obtained by the proposed method shows a superior performance compared with some existing methods available in the literature.

Fuzzy Optimization and Decision Making, 2016

The aim of this work is to extend the notion of stochastic order to the pairwise comparison of fuzzy random variables. We consider the three most important stochastic orders in the literature: expected utility, stochastic dominance and statistical preference, which are related to the comparisons of the expectations, distribution functions and medians of the underlying variables. We discuss how to generalize these notions to the fuzzy case, when an epistemic interpretation is given to the fuzzy random variables. In passing, we investigate to which extent the earlier extensions of stochastic dominance and expected utility to the comparison of sets of random variables can be useful as fuzzy rankings. Finally, we illustrate our results in a decision making problem.

Complexity, 2020

In this study, a new parametric method is proposed to rank intuitionistic fuzzy numbers in a general form. One of the advantages of the proposed method is that the decision maker’s idea is taken into account by selecting appropriate amounts of decision level and hesitation degree parameters. In some illustrative examples, the superiority of the proposed method over some other approaches is demonstrated. Furthermore, to show the ability of the method to solve intuitionistic fuzzy optimization problems, the proposed method is applied to solve intuitionistic fuzzy network data envelopment analysis (IFNDEA) problems. Also, in three appropriate examples, the validity of the suggested method and its capacity to solve real-world problems are illustrated.

International Journal of Green Energy, 2020

The energy consumed around the world and especially in Morocco is dominated by oil products. The latter; whether in the global or the national context; are mainly due to diesel, whose climate impacts are well established, suggesting the search for a greener alternative. Despite its virtues, biodiesel is struggling to impose itself for purely economic reasons. Thus, in order to offer a sustainable solution, while keeping in mind the unpredictable fluctuations (price, demand. . .). This work proposes a generalization of fuzzy goal programming into fully fuzzy goal programming and a relative application, where the aim is to have a final product at a competitive price.

Fuzzy Sets and Systems, 2003

In a continuous-time fuzzy stochastic system, a stopping model with fuzzy stopping times is presented. The optimal fuzzy stopping times are given under an assumption of regularity for stopping rules. Also, the optimal fuzzy reward is characterized as a unique solution of an optimality equation under a differentiability condition. An example in the Markov models is discussed.

International Journal of Fuzzy Systems, 2019

The final values of alternatives usually are fuzzy numbers in most decision making problems under uncertain environment. These fuzzy numbers need to be defuzzified by a ranking method to assist in decision making. Chen proposed ranking fuzzy numbers with maximizing set and minimizing set as an improvement on Jain's maximizing set method. Liou and Wang indicated that ranking of any two fuzzy numbers by Chen's method may be altered when x max , x min and k are changed. To solve this problem, Liou and Wang proposed ranking fuzzy numbers with integral value. However, the problem of Chen's method remains. This work proposes relative maximizing and minimizing sets to improve upon Chen's method. Comparative examples are provided to demonstrate advantages of the proposed ranking method, and an experiment is conducted to show its robustness. The proposed ranking method is applied to a fuzzy multiple criteria decision making (MCDM) model to present its applicability. Ranking procedure can be clearly displayed to enhance execution efficiency of the suggested fuzzy MCDM model. A numerical example is used to display feasibility of the proposed model. Finally, an experiment is investigated to show that the proposed ranking method improves upon Chen's method in consistently ranking the final fuzzy numbers in the suggested fuzzy MCDM model.

SeMA journal, 2017

In this study, a quasi-Newton method is developed to obtain efficient solutions of interval optimization problems. The idea of generalized Hukuhara differentiability for multivariable interval-valued functions is employed to derive the quasi-Newton method. Through an inverse-Hessian approximation with rank-two modification, the proposed technique sidesteps the high computational cost for the computation of inverse-Hessian in Newton method for interval optimization problems. The rank-two modification of inverse-Hessian approximation is applied to generate the iterative points in the quasi-Newton technique. A sequential algorithm and the convergence result of the derived method are also presented. It is obtained that the sequence in the proposed method has superlinear convergence rate. The method is also found to have quadratic termination property. Two numerical examples are provided to illustrate the developed technique.

Soft Computing, 2020

The decision-making under several uncertainties is a major concern to choose the best alternative among the several separate alternatives. This paper deals with the uncertainty of using a complete ranking classification of generalized trapezoidal fuzzy numbers (GTrFNs). In the view of that several measures such as mode, spread, midpoint the score, radius, left and right fuzziness score and linguistic expression are considered to compute the ranking order of GTrFN. Using the proposed complete ranking of GTrFN, this paper presents a method for solving fuzzy multi-criteria decision-making problems. The comparative analysis of existing methods with our proposed method is also described.

Entropy, 2019

In this paper, a new method for the solution of distribution problem in a fuzzy setting is presented. It consists of two phases. In the first of them, the problem is formulated as the classical, fully fuzzy transportation problem. A new, straightforward numerical method for solving this problem is proposed. This method is implemented using the α -cut approximation of fuzzy values and the probability approach to interval comparison. The method allows us to provide the straightforward fuzzy extension of a simplex method. It is important that the results are fuzzy values. To validate our approach, these results were compared with those obtained using the competing method and those we got using the Monte–Carlo method. In the second phase, the results obtained in the first one (the fuzzy profit) are used as the natural constraints on the parameters of multiobjective task. In our approach to the solution of distribution problem, the fuzzy local criteria based on the overall profit and con...

Complexity, 2017

Fuzzy set theory, extensively applied in abundant disciplines, has been recognized as a plausible tool in dealing with uncertain and vague information due to its prowess in mathematically manipulating the knowledge of imprecision. In fuzzy-data comparisons, exploring the general ranking measure that is capable of consistently differentiating the magnitude of fuzzy numbers has widely captivated academics’ attention. To date, numerous indices have been established; however, counterintuition, less discrimination, and/or inconsistency on their fuzzy-number rating outcomes have prohibited their comprehensive implementation. To ameliorate their manifested ranking weaknesses, this paper proposes a unified index that multiplies weighted-mean and weighted-area discriminatory components of a fuzzy number, respectively, called centroid value and attitude-incorporated left-and-right area. From theoretical proof of consistency property and comparative studies for triangular, triangular-and-trape...

Mathematical Sciences, 2016

Ranking of intuitionistic fuzzy numbers is a difficult task. Many methods have been proposed for ranking of intuitionistic fuzzy numbers. In this paper we have ranked both trapezoidal intuitionistic fuzzy numbers and triangular intuitionistic fuzzy numbers using the centroid concept. Some of the properties of the ranking function have been studied. Also, comparative examples are given to show the effectiveness of the proposed method.