Topic
Fuzzy associative matrix
About: Fuzzy associative matrix is a research topic. Over the lifetime, 8027 publications have been published within this topic receiving 194790 citations.
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TL;DR: The concept of Alpha-matrix games is introduced and it is proved that players' fuzzy values are always identical, and hereby, any matrix game with payoffs expressed by TrFNs has a fuzzy value, which is also a TrFN.
Abstract: Of the different types of games, the matrix games with fuzzy payoffs have been extensively discussed. Two major kinds of solution methods have been devised. One is the defuzzification approach based on ranking functions. Another is the two-level linear programming method which can obtain membership functions of players' fuzzy values (or gain floor and loss ceiling). These methods cannot always ensure that players' fuzzy/defuzzified values have a common value. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs expressed by trapezoidal fuzzy numbers (TrFNs). In this methodology, we introduce the concept of Alpha-matrix games and prove that players' fuzzy values are always identical, and hereby, any matrix game with payoffs expressed by TrFNs has a fuzzy value, which is also a TrFN. The upper and lower bounds of any Alpha-cut of the fuzzy value and the players' optimal strategies are easily obtained through solving the derived four linear programming problems with the upper and lower bounds of Alpha-cuts of the fuzzy payoffs. In particular, the fuzzy value can be explicitly estimated through solving the auxiliary linear programming with data taken from the 1-cut and 0-cut of the fuzzy payoffs. The proposed method in this paper is illustrated with a real example and compared with other methods to show validity and applicability.
54 citations
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TL;DR: A four-layer fuzzy-neural network structure and some algorithms for extracting fuzzy rules from numeric data by applying the functional equivalence between radial basis function (RBF) networks and a simplified class of fuzzy inference systems are proposed.
Abstract: A four-layer fuzzy-neural network structure and some algorithms for extracting fuzzy rules from numeric data by applying the functional equivalence between radial basis function (RBF) networks and a simplified class of fuzzy inference systems are proposed. The RBF neural network not only expresses the architecture of fuzzy systems clearly but also maintains the explanative characteristic of linguistic meaning. The fuzzy partition algorithm of input space, inference algorithm, and parameter tuning algorithm are also discussed. Simulation examples are given to illustrate the validity of the proposed algorithms
54 citations
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TL;DR: Three algorithms are established for the computation of the min-transitive closure of a symmetric matrix with elements in [0,1].
54 citations
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TL;DR: A novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy linear and nonlinear regression models with fuzzy output and crisp inputs, is presented.
54 citations
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TL;DR: A method by which a reduced linguistic (fuzzy) set of a labeled multi-dimensional data set can be identi"ed automatically after the projection of the original data set onto a fuzzy space, the optimal subset of fuzzy features is determined using conventional search techniques.
54 citations