A global optimization method for solving fuzzy relation equations

Birbil S., Feyzioglu O.

FUZZY SETS AND SYSTEMS - IFSA 2003, PROCEEDINGS, vol.2715, pp.718-724, 2003 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2715
  • Publication Date: 2003
  • Journal Name: FUZZY SETS AND SYSTEMS - IFSA 2003, PROCEEDINGS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, EMBASE, MathSciNet, Philosopher's Index, zbMATH
  • Page Numbers: pp.718-724
  • Galatasaray University Affiliated: Yes

Abstract

A system of fuzzy relation equations can be reformulated as a global optimization problem. The optimum solution of this new model corresponds to a solution of the system of fuzzy relation equations whenever the solution set of the system is nonempty. Moreover, even if the solution set of the fuzzy relation equations is empty, a solution to the global optimization problem provides a point such that the difference between the right and the left hand side of the fuzzy relation equations is minimized. The new global optimization problem has a nonconvex and nondifferentiable objective function. Therefore, a recent stochastic search approach is applied to solve this new model. The performance of the approach is tested on a set of problems with different dimensions.