Multiple Objective Linear Programming with Fuzzy Coefficients

In this paper, we treat multiple objective programming problems with fuzzy coefficients. We introduce the approaches based on possibility and necessity measures. Our aim in this paper is to describe the treatments of the problem rather than the solution method for the problem. We describe the modality constrained programming approach, the modality goal programming approach and modal efficiency approach. In the first approach, we discuss treatments of fuzziness in the programming problems. The extensions of a fuzzy relation to the relation between fuzzy numbers are developed in order to treat generalized constraints. In the second approach, we show that two kinds of differences between a fuzzy objective function value and a fuzzy target are conceivable under the fuzziness. We describe the distinction of their applications in programming problems. In the third approach, we describe how the efficiency can be extended to multiple objective programming problems with fuzzy coefficients. Necessary and sufficient conditions for a feasible solution to satisfy the extended efficiency are discussed. Finally some concluding remarks are given.

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