Necessity measure optimization in linear programming problems with fuzzy polytopes

Authors:
Masahiro Inuiguchi
Affiliations:
Division of Mathematical Science for Social Systems, Department of Systems Innovation, Graduate School of Engineering Science, Osaka University 1-3, Machikaneyama, Toyonaka, Osaka 560-8531, Japan
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

In this paper, we treat fuzzy linear programming problems with uncertain parameters whose ranges are specified as fuzzy polytopes. The problem is formulated as a necessity measure optimization model. It is shown that the problem can be reduced to a semi-infinite programming problem and solved by a combination of a bisection method and a relaxation procedure. An algorithm in which the bisection method and the relaxation procedure converge simultaneously is proposed. A simple numerical example is given to illustrate the solution procedure.