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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 work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised generalised type-2 fuzzy sets as created by the inference stage of a Mamdani Fuzzy Inferencing System and finds Vertical Slice Centroid Type-Reduction to be the fastest technique.
60 citations
TL;DR: The chromatic fuzzy sum and strength of fuzzy graph are defined and it is shown that there exists an upper (a lower) bound for the chromatics fuzzy sum of a fuzzy graph.
Abstract: The fuzzy coloring of a fuzzy graph was defined by the authors in Eslahchi and Onagh (2004). In this paper we define the chromatic fuzzy sum and strength of fuzzy graph. Some properties of these concepts are studied. It is shown that there exists an upper (a lower) bound for the chromatic fuzzy sum of a fuzzy graph.
60 citations
TL;DR: It is shown that the state reduction problem for fuzzy automata is related to the problem of finding a solution to a particular system of fuzzy relation equations in the set of all fuzzy equivalences on its set of states, and an effective procedure is given for computing the greatest right (resp. left) invariant fuzzy equivalence.
60 citations
TL;DR: It is shown how neural nets can produce both real, and complex, fuzzy number solutions, and how the fuzzy quadratic equation can be solved using neural nets.
60 citations
TL;DR: The proposed method can solve a variety of PDEs encountered in engineering and is shown to be able to solve the convergence of error equations in mesh points from the energy perspective.
Abstract: A new technique using an adaptive fuzzy algorithm to obtain the solutions to a class of partial differential equations (PDEs) is presented. The design objective is to find a fuzzy solution to satisfy precisely the PDEs with boundary conditions. According to the adaptive scheme of fuzzy logic systems, a fuzzy solution with adjustable parameters for the PDE is first described. Then, a set of adaptive laws for tuning the free parameters in the consequent part is derived from minimizing an appropriate error function. In addition, an elegant approximated error bound between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors has also been derived. Furthermore, the convergence of error equations in mesh points is also discussed from the energy perspective. In this paper, we show that the proposed method can solve a variety of PDEs encountered in engineering. Comparisons are also made with solutions obtained by the finite-element method.
60 citations