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Solving fuzzy equations using evolutionary algorithms and neural nets |
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| Authors: | J. J. Buckley T. Feuring Y. Hayashi |
| Affiliation: | University of Alabama at Birmingham, Department of Mathematics, Birmingham, Alabama, 35294, USA e-mail: buckley@math.uab.edu, US University of Siegen, Computer Science Department, H?lderlinstr. 3, 57068 Siegen, Germany e-mail: feuring@informatik.uni-siegen.de, DE Meiji University, Department of Computer Science, Tama-ku, Kawasaki 214-8571, Japan e-mail: hayashiy@cs.meiji.ac.jp, JP |
| 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 AˉXˉ + Bˉ= Cˉ; for Xˉ 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 AˉXˉ + Bˉ= Cˉ for Xˉ and (2) then survey the results for systems of fuzzy linear equations and the fuzzy quadratic. |
| Keywords: | Fuzzy equations, Fuzzy differential equations, Fuzzy eigenvalue, Neural networks |
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