Multi-objective optimization with a max-t-norm fuzzy relational equation constraint

Authors:
Sy-Ming Guu;Yan-Kuen Wu;E. S. Lee
Affiliations:
College of Management, Yuan Ze University, Taoyuan, 320, Taiwan, ROC;Department of Management and Information Technology, Vanung University, Taoyuan, 320, Taiwan, ROC;Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, KS 66506, United States
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

In this paper, we consider minimizing multiple linear objective functions under a max-t-norm fuzzy relational equation constraint. Since the feasible domain of a max-Archimedean t-norm relational equation constraint is generally nonconvex, traditional mathematical programming techniques may have difficulty in yielding efficient solutions for such problems. In this paper, we apply the two-phase approach, utilizing the min operator and the average operator to aggregate those objectives, to yield an efficient solution. A numerical example is provided to illustrate the procedure.