A global optimization method for solving fuzzy relation equations

Authors:
Ş. Ilker Birbil;Orhan Feyzioğlu
Affiliations:
Erasmus Research Institute of Management, Erasmus University, Rotterdam, The Netherlands;Galatasaray University, Department of Industrial Engineering, Ortaköy, Istanbul, Turkey
Venue:
IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
Year:
2003

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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.