Fuzzy Optimization of Multivariable Fuzzy Functions

EMRAH Ş., Askerzade İ.

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, cilt.70, sa.1, ss.1-9, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 70 Sayı: 1
  • Basım Tarihi: 2010
  • Dergi Adı: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1-9
  • Anahtar Kelimeler: Multivariable Fuzzy Functions, Maximizing and minimizing set, Pareto optimum, Lagrange multipliers, membership function, nonlinear optimization
  • Ankara Üniversitesi Adresli: Evet

Özet

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.