Minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations

Authors:
Xiao-Bing Qu;Xue-Ping Wang
Affiliations:
Department of Mathematics, Leshan Teachers College, Leshan, Sichuan 614004, People's Republic of China;Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan 610066, People's Republic of China
Venue:
Information Sciences: an International Journal
Year:
2008

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Abstract

This paper considers the following optimization problem: minimization of linear objective functions under the constraints expressed by a system of fuzzy relation equations using max-product composition. We first show some properties of minimal solutions of a system of fuzzy relation equations with max-product composition and present some rules for reducing the original problem. Then we derive an algorithm which enables us to find all the optimal solutions for solving the optimization problem and provide some numerical examples to illustrate.