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Fuzzy Optimization of Multivariable Fuzzy Functions

Şahin Emrah Amrahov1, Iman N.Askerzade1

Ankara University. Computer Engineering Department, Turkey

Computer Modeling in Engineering & Sciences 2010, 70(1), 1-10. https://doi.org/10.3970/cmes.2010.070.001

Abstract

In this paper we define multivariable fuzzy functions (MFF) and corresponding multivariable crisp functions (MCF). Then we give a definition for the maximum value of MFF, which in some cases coincides with the maximum value in Pareto sense. We introduce generalized maximizing and minimizing sets in order to determine the maximum values of MFF. By equating membership functions of a given fuzzy domain set and the corresponding maximizing set, we obtain a curve of equal possibilities. Then we use the method of Lagrange multipliers to solve the resulting nonlinear optimization problem when the membership functions are differentiable. We finally present examples of finding extreme points of MFF.

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Cite This Article

Amrahov, . E., N.Askerzade, I. (2010). Fuzzy Optimization of Multivariable Fuzzy Functions. CMES-Computer Modeling in Engineering & Sciences, 70(1), 1–10. https://doi.org/10.3970/cmes.2010.070.001



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