Rough Sets

RSCTC'2010 Discovery Challenge was a special event of Rough Sets and Current Trends in Computing conference. The challenge was organized in the form of an interactive on-line competition, at TunedIT.org platform, in days between Dec 1, 2009 and Feb 28, 2010. The task was related to feature selection in analysis of DNA microarray data and classification of samples for the purpose of medical diagnosis or treatment. Prizes were awarded to the best solutions. This paper describes organization of the competition and the winning solutions.

This paper presents a framework of rule generation in Nondeterministic Inf ormation Systems (NISs), which follows rough sets based rule generation in Deterministic Inf ormation Systems (DISs). Our previous work about NISs coped with certain rules, minimal certain rules and possible rules. These rules are characterized by the concept of consistency. This paper relates possible rules to rules by the criteria support and accuracy in NISs. On the basis of the information incompleteness in NISs, it is possible to define new criteria, i.e., minimum support, maximum support, minimum accuracy and maximum accuracy. Then, two strategies of rule generation are proposed based on these criteria. The first strategy is Lower Approximation strategy, which defines rule generation under the worst condition. The second strategy is U pper Approximation strategy, which defines rule generation under the best condition. To implement these strategies, we extend Apriori algorithm in DISs to Apriori algorithm in NISs. A prototype system is implemented, and this system is applied to some data sets with incomplete information.

We have investigated rough set-based concepts for a given Non-deterministic Information System (N IS). In this paper, we consider generating a NIS from a Deterministic Information System (DIS) intentionally. A N IS Φ is seen as a diluted DIS ϕ, and we can hide the actual values in ϕ by using Φ. We name this way of hiding Information Dilution by non-deterministic information. This paper considers information dilution and its application to hiding the actual values in a table.

This study aims to identify significant risks and their relationship to the successful operation of the Trans-Sumatra toll road in Indonesia. The research utilizes the Delphi and DEMATEL methods, along with rough set analysis, to identify and evaluate 28 risks associated with toll road operations in Sumatra. The research identifies 13 dominant risks, including policy changes, government intervention, inflation, financial distress, fluctuation of interest rate, fluctuation of currency, high cost of maintenance, low volume of traffic, competitive routes, overloading vehicles, many infrastructure defects, and natural disasters. In this case, natural disasters, inflation, and vehicles with excessive loads are the most dominant cause factors because those risks have the highest cause value based on the cause-effect diagram. Furthermore, the prominence diagram reveals that income risk, policy changes, and financial distress have notable implications for operational activities. The study presents a MCDM risk assessment approach that incorporates rough set analysis, providing a comprehensive understanding of the critical risk relationship factors for toll road operations. By integrating rough set analysis, this research contributes to the field of toll road operations and risk assessment. The identified risks and their relationships serve as a foundation for developing effective strategies for toll road operational management.

This paper introduces a novel extension of soft rough fuzzy set so-called modified soft rough fuzzy set model in which new lower and upper approximation operators are presented together their related properties that are also investigated. Eventually it is shown that these new models of approximations are finer than previous ones developed by using soft rough fuzzy sets.

Triangular Model Every entity has an extent in time, such as the lifetime of an object or the duration of an event. These temporal extents are usually described by crisp time intervals bounded by a welldefined start and end. However, under some circumstances, the temporal extent of an entity is imperfect, and cannot be adequately modelled by a crisp time interval. On the one hand, some events may start or end gradually and therefore their start and end cannot be pinned to exact time stamps. For example, it is difficult to decide when the Industrial Revolution started and finished. Intervals of this kind of events are usually modelled by fuzzy sets through the quantification of the graded truth of whether a time point is in the interval, bring the concept of fuzzy time interval. On the other hand, in some other cases, it is only known that the start and end of a crisp interval are within certain ranges, but no extra information or assumptions about the distribution of the start and the end is available. Modelling this kind of imperfect time intervals with fuzzy sets would induce extra overhead and unnecessary complexity. In these cases, the alternative approach, i.e. rough sets , can excellently suit the modelling and handling of time intervals. Currently, a lot of disciplines are faced with the issue of imperfect time intervals, which is reflected in many contributions in modelling intervals by fuzzy sets (

In this paper, fuzzy lower approximation-based fuzzy rough set is used for selection of features. A distributed sampling (DS)-based initialization method is introduced to pick better seed population, in particle swarm optimization (PSO) and intelligent dynamic swarm (IDS). PSO and IDS are used for simultaneously selecting the appropriate feature subset. Fitness function for these computations is fuzzy rough dependency measure. Using the proposed initialization, while using PSO and IDS, improvement in size of selected subset of features with improved classification accuracy is also demonstrated.

In this special issue on "Fuzzy Expert Systems," six papers cover a wide range of concerns--from theory to applications including: (1) a rule base reorganization, (2) a linear interpolation, (3) a neuro-fuzzy approach to pairwise comparison, (4) properties of reduction, in transitive matrices, (5) a consistency checking procedure, and (6) a context dependency model. We present a brief review of these papers next. In "Rule Base Reorganization and Search with a Fuzzy Cluster Analysis," Tiirksen and Jiang proposes a fuzzy cluster analysis for the purpose of restructuring a knowledge base where rules are either S-or R-implication types. The proposed algorithm can be implemented either with a compositional or an analogical tolerance relation. It is shown that analogical tolerance relation is more efficient in a rule base restructuring and a rule firing schema, under the proposed search scheme. In "Approximate Reasoning by Linear Rule Interpolation and General Approximation," K6czy and Hirota investigate the problem of sparse fuzzy rule bases. They review various methods of analogical reasoning available in current literature. They discuss concepts of graduality, measurability, distance, and similarity in the fuzzy sense. The fundamental equation of rule interpolation is introduced with a-cuts and resolution principle. The method is extended to multi-dimensional spaces. In "Neuro-Fuzzy Approach to Data Analysis of Pairwise Comparisons," Ichihashi and Tiirksen propose an artificial neural network model with an iterative on-line learning scheme. Two quantification methods of pairwise comparisons are presented in order to derive the associated weights. The proposed approach can also be implemented even when we have access to incomplete pairwise comparisons. The proposed approach is compared with Guttman's method and Saaty's AHP. In "On Reduction of Transitive Fuzzy Matrices and Its Applications," Di Nola, Kolodziejczjk, and Sessa show that the class of s-trarisitive (w-transitive) fuzzy matrices properly contain the class of max-min transitive fuzzy matrices. It is also shown that the basic properties of the reduction models remain valid also for s-transitive fuzzy matrices.

This paper presents the application of a rough-set based neuro-fuzzy system (RNFS) in volatility forecasting by synergizing the information extraction of popular generalized auto-regressive conditional heteroscedasticity (GARCH) models with the human like interpretable RNFS. Additional intraday volatility indicators such as realized power variation (RPV) are proposed to further boost volatility forecasts in the hybrid model. Experiments are performed on real-life data (Citigroup and J.P Morgan price series) to compare the volatility forecast and interpretability of the hybrid model against the commonly used GARCH, Exponential GARCH (EGARCH) and Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) models and other soft computing methods. The results show that the accuracy of the proposed hybrid system can match or outperform the GARCH models and other soft computing methods. It also yields improved interpretability in terms of number of if-then fuzzy rules compared against other soft computing methods.

In the paper is discussed the truncated nondeterministic rules and their role in an evaluation of classification model. The nondeterministic rules are created as the result of shorting deterministic rules in accordance with the principle of minimum description length (MDL). As deterministic rules in database we treat the full objects description in a meaning of descriptors conjunction. The nondeterministic rules are calculated in polynomial time by using greedy strategy. The classification model is composed in two steps process. In the first step deterministic and nondeterministic rules are constructed. Next these rules are used for classifier evaluation. The evaluation results are compared with classifiers only based on deterministic rules creating by different algorithms. The experiments shows that such nondeterministic rules could be treat as an extra knowledge about data. This knowledge is able to improve the classification quality. It should be pointed out that classification process requires tuning some of their parameters relative to analyzed data.

In this paper a new approach of rough set features selection has been proposed. Feature selection has been used for several reasons a) decrease time of prediction b) feature possibly is not found c) present of feature case bad prediction. Rough set has been used to select most significant features. The proposed rough set has been applied on heart diseases data sets. The main problem is how to predict patient has heart disease or not depend on given features. The problem is challenge, because it cannot determine decision directly .Rough set has been modified to get attributes for prediction by ignored unnecessary and bad features. Bayes net has been used for classified method. 10-fold cross validation is used for evaluation. The Correct Classified Instances were 82.17, 83.49, and 74.58 when use full, 12, 7 length of attributes respectively. Traditional rough set has been applied, the minimum Correct Classified Instances were 58.41 and 81.51 when use 2 length of attributes respectively

In their novel “The Difference Engine”, William Gibson and Bruce Sterling accomplish the feat of imagining that computer science developed from the investigations of Charles Babbage, Ada Lovelace, and from the formalisms that followed those achievements. All of this is implicit in the Babbage text that the authors place at the end of the book (“The Language of Signs” inspired by Lord Charles Babbage, “Passages from the Life of a Philosopher”, 1864.)
But the period that inspired Gibson and Sterling's fiction, was extraordinarily influential in multiple domains of science. In mathematics, it led to the intense development of operator theory, and it was within this framework that George Boole produced his revolutionary algebraic theory of logic between 1847 and 1854. Shortly thereafter, Cayley created the theory of matrices and Peirce had the vision of using this theory to deal with some aspects of logic.
However, the use of matrix algebra in logic came to a halt. The emergence of Frege's formalisms and that of Whitehead and Russell transformed logic into a virtual instrument for investigating the foundations of mathematics, and the enormous achievements of this line of research, which perhaps culminates in the enormous contributions of Gödel and Turing, need not be emphasized. But since the beginning of the 21st century, vigorous developments in quantum computing research have taken up matrix algebra as one of its basic techniques.
The research reported in this monograph is based on a matrix formalism of logic originating in neural models developed in the late 1980s. Matrix algebra provides a surprisingly simple procedure for addressing relevant topics in basic logic and, in particular, in many-valued logics. Here we investigate the relationships among three relevant systems of three-valued logics, postulated in different contexts by their authors. These are: Lukasiewicz's logic, which combines philosophical roots with the technical search for mathematical formalisms for modalities; Kleene's logic, inspired by decidability problems in formal systems; and Heyting's logic, which succeeded in defining a three-valued logic that encompasses the fundamental properties of intuitionistic logic. We will show how the translation of these systems to matrix algebra produces unexpected and new results.

Border Gateway Protocol (BGP) is the core component of the Internet's routing infrastructure. Abnormal routing behavior impairs global Internet connectivity and stability. Hence, designing and implementing anomaly detection algorithms is important for improving performance of routing protocols. While various machine learning techniques may be employed to detect BGP anomalies, their performance strongly depends on the employed learning algorithms. These techniques have multiple variants that often work well for detecting a particular anomaly. In this paper, we use the decision tree and fuzzy rough set methods for feature selection. Decision tree and extreme learning machine classification techniques are then used to maximize the accuracy of detecting BGP anomalies. The proposed techniques are tested using Internet traffic traces.

Feature selection based on fuzzy rough sets is an effective approach to select a compact feature subset that optimally predicts a given decision label. Despite being studied extensively, most existing methods of fuzzy rough set based feature selection are restricted to computing the whole data set in batch, which is often costly or even intractable for large data sets. To improve the time efficiency, we investigate the incremental perspective for fuzzy rough set based feature selection assuming data can be presented in sample subsets one after another. The key challenge for the incremental perspective is how to add and delete features with the subsequent arrival of sample subsets. We tackle this challenge with strategies of adding and deleting features based on the relative discernibility relations that are updated as subsets arrive sequentially. Two incremental algorithms for fuzzy rough set based feature selection are designed based on the strategies. One updates the selected features as each sample subset arrives, and outputs the final feature subset where no sample subset is left. The other updates the relative discernibility relations but only performs feature selection where there is no further subset arriving. Experimental comparisons suggest our incremental algorithms expedite fuzzy rough set based feature selection without compromising performance.

In rough set philosophy, each set of data can be seen as a fuzzy decision table. Since a decision table dynamically increases with time and space, these decision tables are integrated into a new one called fused decision table. In this paper, we focus on designing an incremental feature selection method on fused decision table by optimizing the space constraint of storing discernibility matrix. Here discernibility matrix is a known way of discernibility information measure in rough set theory. This paper applies the quasi/pseudo value of discernibility matrix rather than the true value of discernibility matrix to design an incremental mechanism. Unlike those discernibility matrix based non-incremental algorithms, the improved algorithm needs not save the whole discernibility matrix in main memory, which is desirable for the large data sets. More importantly, with the increment of decision tables, the discernibility matrix-based feature selection algorithm could constrain the computational cost by applying efficient information updating techniquesquasi/pseudo approximation operators. Finally, our experiments reveal that the proposed algorithm needs less computational cost, especially less occupied space, on the condition that the accuracy is limitedly lost.

We consider relationship between binary relations in approximation spaces and topologies defined by them. In any approximation space (X, R), a reflexive closure Rω determines an Alexandrov topology T (Rω ) and, for any Alexandrov topology T on X, there exists a reflexive relation RT such that T = TR. From the result, we also obtain that any Alexandrov topology satisfying (clop), A is open if and only if A is closed, can be characterized by reflexive and symmetric relation. Moreover, we provide a negative answer to the problem left open in [1].

This paper describes new methods for hand-written Arabic character recognition. We propose a novel algorithm for smoothing image and segmentation of the Arabic character using width writing estimated from skeleton character The moments and Fourier descriptor of profile projection and centroid distance are used as features of each character these feature are invariant in translation, rotation and scale we apply Principal component Analysis (PCA) as data processing algorithm to features vector in order to reduce dimension. The classifier proposed in this work is based on Support Vector Machines (SVM) wich considerd an recent optimal classifier up to now. The results show that these methods are very powerful for isolated handwritten arabic caracter.

In this paper we discuss three problems in Data Mining Sparse Decision Systems: the problem of short reduct calculation, discretization of numerical attributes and rule induction. We present algorithms that provide approximate solutions to these problems and analyze the complexity of these algorithms.

The topic of this paper is the use of fuzzy logic in the recognition and analysis of weather conditions. The fuzzy system used for weather recognition was created using Matlab, in the Fuzzy Logic Designer application, focusing on the integration of fuzzy logic and artificial intelligence (AI) techniques, demonstrating the possibilities offered by AI systems in managing uncertainty. The weather recognition model uses three input variables in the form of maximum temperature, minimum temperature and wind, as well as 35 rules that generate a weather forecast, namely precipitation, which can be very low, low, normal, high and very high.

The submitted article deals with the problematic of the quality of life and factors which can influence it. On the basis of previous research we know that this is a complex problem which is characterized by a huge number of components and connections among them. We focused on the main areas which influence the quality of life and tried to describe the connections among them. The goal of this paper was not the experimental examination based on real data; however, creation of a framework and a basis for the future quality of life research in a region which should cover – if possible – all the main indicators of the quality of life and link to our previously realized researches in this area.

This paper deals with air quality modelling by decision trees and by hybrid rough sets-decision trees in the Czech Republic. We focused on daily observations of air polluting substances concentrations in one of the cities in the Pardubice region. After data collection, data description, and data pre-processing, we worked on the creation of classification models and the analysis of the achieved results. As modelling algorithms we selected C5.0 algorithm, boosting, and CHAID method. Finally is proposed hybrid model, where Rough Sets algorithm for the purpose of attributes reduction is used.

In this paper, we consider a rough set analysis of non-ordinal and ordinal classication data with missing attribute values. We show how this problem can be addressed by several variants of Indiscernibilitybased Rough Set Approach (IRSA) and Dominance-based Rough Set Approach (DRSA). We propose some desirable properties that a rough set approach being able to handle missing attribute values should possess. Then, we analyze which of these properties are satised by the considered variants of IRSA and DRSA.

This study introduces a novel framework leveraging Rough Set Theory (RST)based feature selection-MLReduct, MLSpecialReduct, and MLFuzzyRoughSet-to enhance machine learning performance on uncertain data. Applied to a private cardiovascular dataset, our MLSpecialReduct algorithm achieves a peak Random Forest accuracy of 0.99 (versus 0.85 without feature selection), while MLFuzzyRoughSet improves accuracy to 0.83, surpassing our MLVarianceThreshold (0.72-0.77), an adaptation of the traditional VarianceThreshold method. We integrate these RST techniques with preprocessing (discretization, normalization, encoding) and compare them against traditional approaches across classifiers like Random Forest and Naive Bayes. The results underscore RST's edge in accuracy, efficiency, and interpretability, with MLSpecialReduct leading in minimal attribute reduction. Against baseline classifiers without feature selection and MLVari-anceThreshold, our framework delivers significant improvements, establishing RST as a vital tool for explainable AI (XAI) in healthcare diagnostics and IoT systems. These findings open avenues for future hybrid RST-ML models, providing a robust, interpretable solution for complex data challenges.

Knowledge of an agent depends on the granulation procedure adopted by the agent. The knowledge granules may form a partition of the universe or a covering. In this paper dependency degrees of two knowledges have been considered in both the cases. A measure of consistency and inconsistency of knowledges are also discussed.

In this paper we investigate a technique for fusing approximate knowledge obtained from distributed, heterogeneous information sources. This issue is substantial, e.g., in modeling multiagent systems, where a group of loosely coupled heterogeneous agents cooperate in achieving a common goal. Information exchange, leading ultimately to knowledge fusion, is a natural and vital ingredient of this process. We use a generalization of rough sets and relations , which depends on allowing arbitrary similarity relations. The starting point of this research is , where a framework for knowledge fusion in multiagent systems is introduced. Agents' individual perceptual capabilities are represented by similarity relations, further aggregated to express joint capabilities of teams. This aggregation, expressing a shift from individual to social level of agents' activity, has been formalized by means of dynamic logic. The approach of Doherty et al. (2007) [6] uses the full propositional dynamic logic, which does not guarantee tractability of reasoning. Our idea is to adapt the techniques of Nguyen to provide an engine for tractable approximate database querying restricted to a Horn fragment of serial dynamic logic. We also show that the obtained formalism is quite powerful in applications.

We live in a world submerged with more information than ever before. We express information or data mathematically and it is growing faster than ever. If the data is imperfect, out of context or otherwise contaminated, it can lead to decisions that could undermine the competitiveness of an enterprise or damage the personal lives of individuals. Therefore, knowledge representation plays an important role in dealing with many aspects of problem solving. In order to obtain complete information systems, we use a mathematical tool, namely, Rough Set Theory (RST), which was introduced by Pawlak in 1982 as a way to deal with data analysis based on approximation methods in information systems. RST is a novel approach to cope with imperfect data analysis as well. In essence, the theory extends the classical crisp set to rough set by defining lower and upper approximations for any subset of a nonempty finite universe. The theory presupposes that with every object of the universe some informat...

Earlier, the authors introduced the logic IntGC, which is an extension of intuitionistic propositional logic by two rules of inference mimicking the performance of Galois connections (Logic J. of the IGPL, 18:837-858, 2010). In this paper, the extensions Int2GC and Int2GC+FS of IntGC are studied. Int2GC can be seen as a fusion of two IntGC logics, and Int2GC+FS is obtained from Int2GC by adding instances of duality-like connections $\Diamond(A \to\ B) \to (\Box A \to \Diamond B)$ and $(\Diamond A \to \Box B) \to \Box(A \to B)$, introduced by G. Fischer Servi (Rend. Sem. Mat. Univers. Politecn. Torino, 42:179-194, 1984), for interlinking the two Galois connections of Int2GC. Both Kripke-style and algebraic semantics are presented for Int2GC and Int2GC+FS, and the logics are proved to be complete with respect to both of these semantics. We show that rough lattice-valued fuzzy sets defined on complete Heyting algebras are proper algebraic models for Int2GC+FS. We also prove that Int2GC...

Rough set theory is a new approach to vagueness and uncertainty. The theory of rough sets has an overlap with many other theories. Specially interesting is the relationship to fuzzy set theory and the theory of evidence. Recently, it turned out that the theory has very interesting connections with Bayes' theorem. The look on Bayes' theorem offered by rough set theory reveals that any data set (decision table) satisfies total probability theorem and Bayes' theorem. These properties can be used directly to draw conclusions from objective data without referring to subjective prior knowledge and its revision if new evidence is available. Thus the rough set view on Bayes' theorem is rather objective in contrast to subjective "classical" interpretation of the theorem. Besides, it is revealed that Bayes' theorem can be interpreted as a flow conservation equation in a flow graph. However the flow graphs considered here are different from those introduced by Ford and Fulkerson. This property gives new perspective for applications of Bayes' theorem. Thus the paper brings two new interpretation of Bayes' theorem, without referring to its classical probabilistic interpretation: as properties of data tables and properties of flow graphs.

The present paper is devoted to discussion of extended covering rough sets from the relations point of view. In fact, we give new definitions to the lower and the upper approximations using a binary general relation. Moreover, our approach represent new generalizations of Pawlak approaches. New closure operators derived from relation are investigated too.

İşletmeler süreçlerini sistematik, hatasız yönetebilmek için bilgisayar yazılımlarına ihtiyaç duymaktadırlar. Bu yazılımlardan en önemlisi birçok departmanın bir arada çalışmasına olanak sağlayan Kurumsal Kaynak Planlama (ERP) yazılımlarıdır. ERP yazılımları işletmeler açısından kurulumu ve yönetilmesi zor projelerdir. ERP projelerinin işletmeye getirdiği yenilikler, beklentiler, kullanıcı sorunları, maliyet gibi birçok detay ERP projelerinin başarısını etkilemektedir. Aynı zamanda bu zorluklar riskleri de beraberinde getirmektedir. Bu noktada işletmeler projelerinin başarılı olması için danışmanlara ihtiyaç duymaktadır. ERP projelerinde danışman seçimi projenin başarısı için çok önemlidir. Özellikle günümüzde bir dönüşüm süreci yaşayan ERP yazılımları için bu süreç daha kritiktir. ERP yazılımları yeni teknolojilerin etkisiyle a-KKP (Akıllı ERP) ismi verilen yeni bir boyuta dönüşmektedir. Bu dönüşüm sürecinde danışman seçimi daha önemli ve stratejik bir hal almıştır. Artık sadece ERP veri yapısına ve süreçlerine hâkim olması yetmeyen farklı yetenekler ve tecrübeler aranan danışmanlara ihtiyaç duyulmaktadır. ERP yazılımlarının kendi içeriğinde ve işletmede yarattığı yeniliklerle beraber danışman seçiminde de farklı yaklaşımlara ihtiyaç duyulmaktadır. Bu çalışmada ERP danışman seçimi probleminde dikkate alınabilecek kriterler akıllı kurumsal kaynak planlama yazılımları açısından değerlendirilmiştir. Kriterlerin belirlenmesinde mevcut danışman seçimi literatürü ve uzman görüşünden yararlanılmıştır. Kriterlerin ağırlıklarını belirlemek için ÇKKV (Çok Kriterli Karar Verme) yöntemlerinden birisi olan LBWA (Düzey Temelli Ağırlık Değerlendirmesi) kullanılmıştır. Çalışmada LBWA yöntemi karar vericiler için diğer yöntemlere göre karar vermede daha avantajlı olması nedeniyle tercih edilmiştir. LBWA yöntemiyle elde edilen sonuçlara göre danışman seçiminde en önemli kriterler sırasıyla çalışan yetkinliği, referans ve destek maliyeti olarak belirlenmiştir. Literatürde danışman seçimine yönelik çalışmalar bulunmakta olsa da çalışma a-KKP projeleri perspektifinde danışman seçimine yönelik olması nedeniyle özgündür. Bu anlamda literatüre katkı sunacağı düşünülmektedir.

Businesses require computer software to manage their processes systematically and flawlessly. The most important of these software is Enterprise Resource Planning (ERP) software that allows many departments to work together. However, ERP software is difficult to install and manage for businesses. Various factors such as the innovations, expectations, user problems, and costs that ERP projects bring to businesses affect the success of ERP projects. At the same time, these difficulties also carry risks. Businesses need consultants to ensure the success of their projects at this point. The selection of consultants for ERP projects is crucial for project success. This is especially critical for ERP software, which is currently transforming. With the influence of new technologies, ERP software is transforming into a new dimension called intelligent ERP (i-ERP). In this transformation process, the selection of consultants has become more critical and strategic. Currently, consultants are required to possess different skills and experiences besides being familiar with ERP data structures and processes. With ERP software's innovations within itself and in the business, other approaches are needed in consultant selection. In this study, the criteria that could be considered in the selection problem of ERP consultants were evaluated from the perspective of intelligent enterprise resource planning software. The criteria were determined based on the existing consultant selection literature and expert opinions. The LBWA (Level Based Weight Assessment) method, one of the multi-criteria decisionmaking (MCDM) methods, was used to determine the criteria weights. LBWA method was preferred in this study because it is more advantageous for decision-makers in decision-making compared to other methods. According to the results obtained with the LBWA method, the most critical criteria in selecting consultants were respectively determined as employee competence, references and support cost. Although there are studies in the literature on consultant selection, this study is considered unique because it focuses on consultant selection from the perspective of i-ERP projects. In this sense, it is expected to contribute to the literature.

Pooling layers help reduce redundancy and the number of parameters before building a multilayered neural network that performs the remaining processing operations. Usually, pooling operators in deep learning models use an explicit topological organization, which is not always possible to obtain on multi-label data. In a previous paper, we proposed a pooling architecture based on association to deal with this issue. The association was defined by means of Pearson's correlation. However, features must exhibit a certain degree of correlation with each other, which might not hold in all situations. In this paper, we propose a new method that replaces the correlation measure with another one that computes the entropy in the information granules that are generated from two features or labels. Numerical simulations have shown that our proposal is superior in those datasets with low correlation. This means that it induces a significant reduction in the number of parameters of neural networks, without affecting their accuracy.

Fuzzy Cognitive Maps (FCMs) are recurrent neural networks made up of well-defined neurons and causal relations. Fuzzy Grey Cognitive Maps (FGCMs) are an extension of FCMs, intended to surpass the intrinsic uncertainties modeling real-world problems by means of Grey theory. Despite the rising number of studies about FGCM-based models, little has been investigated with regard to the convergence of such networks. In this paper, we build a mathematical basis to uncover the behavior FGCM-based models equipped with transfer F -functions. To do so, we propose sufficient conditions for the existence and unicity of fixed-point attractors. Also, the results reported in the literature on the convergence of FGCMs, are compared with ours. Furthermore, we elucidate the reach and depth of our findings, especially and not exclusive to the prediction of FCMs' behavior.

Rough set theory has many interesting applications in circumstances characterized by vagueness. In this paper, the applications of rough set theory in community detection analysis are discussed based on the Rough Net definition. We will focus the application of Rough Net on community detection validity in both monoplex and multiplex networks. Also, the topological evolution estimation between adjacent layers in dynamic networks is discussed and a new community interaction visualization approach combining both complex network representation and Rough Net definition is adopted to interpret the community structure. We provide some examples that illustrate how the Rough Net definition can be used to analyze the properties of the community structure in real-world networks, including dynamic networks.

This paper presents the merging of two sets of experiments in the continuing endeavor to mine epileptiform activity from Electroencephalograms (EEG). The goal is to develop robust classification rules for identifying epileptiform activity in the human brain. We present advancements using the author's proprietary developed spectral analysis software to link power spectra of rat EEGs experiencing epilepsy seizures with the authors DFA algorithm and their MATLAB spectral analysis. Our system links 1) power spectra of ...

1School of Information Dalian Maritime University No. 1, Linghai Road, Dalian 116026, PR China teesiv@dlmu.edu.cn ∗ Corresponding author: lhb@dlmu.edu.cn 2School of Computer Dalian University of Technology No. 2, Linggong Road, Ganjingzi District, Dalian 116023, PR ...

An important part of the interpretation of a decision process lies on the ascertainment of the in uence of the input features, that is, of how much the implemented model relies on a given input feature to perform the desired task. Recently data analysis techniques based on fuzzy logic have gained attention because of their interpretability. Many real-world applications, however, have very high dimensionality and require very complex decision borders. In this case the numbe rof fuzzy rules can proliferate and the easy interpretability of the fuzzy model can progressively disappear. A method is presented that quanti es the discriminative po wer of the input features in a fuzzy model. The proposed quanti cation helps the interpretation of fuzzy models constructed on high dimensional and very fragmented training sets. First, a measure of the information contained in the fuzzy model is de ned on the basis of its fuzzy rules. The classi cation is then performed along one of the input features, that is, the fuzzy rules are split according to that feature's linguistic values. For each linguistic value, a fuzzy sub-model is generated from the original fuzzy model. The average information contained in these fuzzy sub-models is measured and its relative comparison with the information measure of the original fuzzy model quanti es the information gain that derives from the classi cation performed on the selected input feature. This information gain characterizes the discriminative po wer of that input feature. Therefore, the proposed information gain can beused to obtain better insights into the selected fuzzy classi cation strategy, even in very high dimensional cases, and possibly to reduce the input dimension. Several arti cial and real-world data analysis are reported as examples, in order to illustrate the characteristics and potentialities of the proposed algorithm. As real-world examples, the most informative electrocardiographic measures are detected for an arrhythmia classi cation problem and the role of duration, amplitude and pitch variations of syllabic nuclei in American English spoken sentences is investigated for prosodic stress classi cation.

This paper studies expansions of bounded distributive lattices equipped with a Galois connection. We introduce GC-frames and canonical frames for these algebras. The complex algebras of GC-frames are defined in terms of rough set approximation operators. We prove that each bounded distributive lattice with a Galois connection can be embedded into the complex algebra of its canonical frame. We show that for every spatial Heyting algebra L equipped with a Galois connection, there exists a GC-frame such that L is isomorphic to the complex algebra of this frame, and an analogous result holds for weakly atomic Heyting-Brouwer algebras with a Galois connection. In each case of representation, given Galois connections are represented by rough set upper and lower approximations.

The hybridization of rough sets and fuzzy sets has focused on creating an end product that extends both contributing computing paradigms in a conservative way. As a result, the hybrid theory inherits their respective strengths, but also exhibits some weaknesses. In particular, although they allow for gradual membership, fuzzy rough sets are still abrupt in a sense that adding or omitting a single element may drastically alter the outcome of the approximations. In this paper, we revisit the hybridization process by introducing vague quantifiers like "some" or "most" into the definition of upper and lower approximation. The resulting vaguely quantified rough set (VQRS) model is closely related to Ziarko's variable precision rough set (VPRS) model.

Based on the definition of double fuzzy relations, two types of new rough set models are constructed, which are multi-granulation double fuzzy rough sets called optimistic and pessimistic multi-granulation double fuzzy rough sets, and some of their properties were studied. In addition, we study the relationship between optimistic and pessimistic multi-granulation double fuzzy rough sets and double fuzzy rough sets.

In this paper, we study the class of a BH lattices as a common frame to Brouwerian and Heyting lattices and investigate some related properties. Also, we characterize the divisibility condition in the definition of BH lattice and we obtain that the set H of all idempotent elements in a BH lattice L forms a Heyting algebra. We introduce the notion of an IBH lattice and under some specific conditions, we characterize an MV algebra, a bounded Wajsberg hoop, a Boolean Algebra, and a commutative bounded BCK algebra in terms on IBH lattices.

The high social costs associated with bankruptcy have spurred searches for better theoretical understanding and prediction capability. In this paper, we investigate a hybrid approach to bankruptcy prediction, using a genetic pro- gramming algorithm to construct a bankruptcy prediction model with variables from a rough sets model derived in prior research. Both studies used data from 291 US public companies for the period 1991 to 1997. The second stage genetic programming model developed in this research consists of a decision model that is 80% accurate on a validation sample as compared to the original rough sets model which was 67% accurate. Additionally, the genetic programming model reveals relationships between variables that are not apparent in either the rough sets model or prior research. These findings indicate that genetic programming coupled with rough sets theory can be an efficient and effective hybrid modeling approach both for developing a robust bankruptcy prediction ...

The discovery of new knowledge by mining medical databases is crucial in order to make an effective use of stored data, enhancing patient management tasks. One of the main objectives of data mining methods is to provide a clear and understandable description of patterns held in data. We introduce a new approach to ®nd association rules among quantitative values in relational databases. The semantics of such rules are improved by introducing imprecise terms in both the antecedent and the consequent, as these terms are the most commonly used in human conversation and reasoning. The terms are modeled by means of fuzzy sets de®ned in the appropriate domains. However, the mining task is performed on the precise data. These ``fuzzy association rules'' are more informative than rules relating precise values. We also introduce a new measure of accuracy, based on Shortliffe and Buchanan's certainty factors [Shortliffe E, Buchanan B. Math Biosci 1975;23:351±79]. Also, the semantics of the usual measure of usefulness of an association rule, called support are discussed and some new criteria are introduced. Our new measures have been shown to be more understandable and appropriate than ordinary ones. Several experiments on large medical databases show that our new approach can provide useful knowledge with better semantics in this ®eld.

This paper consists of an extensive survey of various generalized approaches to the lower and upper approximations of a set, the two approximations being first defined by Pawlak while introducing rough set theory. Particularly, relational, covering based and operator based approaches are considered. Categorization of various approaches in terms of implication lattices is shown. Significance of this categorization in rough logics is briefly mentioned.

In this paper the notion of a kind of clusters of subsets of a set based on rough membership function is introduced. The algebraic structure emerged thereby is studied. A comparison with classical rough sets with respect to the algebraic properties has been made. A many-valued propositional logic for such entities is proposed. Representation theorems in the style of Obtułowicz have been established.

Real-world datasets are often vague and redundant, creating problem to take decision accurately. Very recently, Rough-set theory has been used successfully for dimensionality reduction but is applicable only on discrete dataset. Discreti-sation of data leads to information loss and may add inconsistency in the datasets. The paper aims at applying fuzzy-rough concept to overcome the above limitations. However, handling of non discretized values increases computational complexity of the system. Therefore, to build an efficient classifier Genetic Algorithm (GA) has been applied to obtain optimal subset of attributes, sufficient to classify the objects. The proposed algorithm reduces dimensionality to a great extent without degrading the accuracy of classification and avoid of being trapped at local minima. Results are compared with the existing algorithms , demonstrate compatible outcome.