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Solving fuzzy equations using evolutionary algorithms and neural nets

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Abstract

 In this paper we use evolutionary algorithms and neural nets to solve fuzzy equations. In Part I we: (1) first introduce our three solution methods for solving the fuzzy linear equation A¯X¯ + B¯= C¯; for X¯ and (2) then survey the results for the fuzzy quadratic equations, fuzzy differential equations, fuzzy difference equations, fuzzy partial differential equations, systems of fuzzy linear equations, and fuzzy integral equations; and (3) apply an evolutionary algorithm to construct one of the solution types for the fuzzy eigenvalue problem. In Part II we: (1) first discuss how to design and train a neural net to solve A¯X¯ + B¯= C¯ for X¯ and (2) then survey the results for systems of fuzzy linear equations and the fuzzy quadratic.

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Authors and Affiliations

  1. University of Alabama at Birmingham, Department of Mathematics, Birmingham, Alabama, 35294, USA e-mail: buckley@math.uab.edu, , , , , , US

    J. J. Buckley

  2. University of Siegen, Computer Science Department, Hölderlinstr. 3, 57068 Siegen, Germany e-mail: feuring@informatik.uni-siegen.de, , , , , , DE

    T. Feuring

  3. Meiji University, Department of Computer Science, Tama-ku, Kawasaki 214-8571, Japan e-mail: hayashiy@cs.meiji.ac.jp, , , , , , JP

    Y. Hayashi

Authors
  1. J. J. Buckley
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  2. T. Feuring
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  3. Y. Hayashi
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Buckley, J., Feuring, T. & Hayashi, Y. Solving fuzzy equations using evolutionary algorithms and neural nets. Soft Computing 6, 116–123 (2002). https://doi.org/10.1007/s005000100147

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  • DOI: https://doi.org/10.1007/s005000100147