Approaches to Linear Programming Problems with Interactive Fuzzy Numbers

Fuzzy programming has been developed mainly under the assumption of non-interaction among fuzzy coefficients. However, this assumption is not always suitable in the treatment of real world problems. Several approaches have been proposed to treat the interaction among fuzzy coefficients. In this paper, we review treatments of interaction among fuzzy coefficients in fuzzy linear programming problems. Using a necessity fractile model of a simple linear program with fuzzy coefficients, we will see the differences between non-interactive and interactive problems. We review the five approaches to interactive fuzzy numbers, i.e., weak independent fuzzy numbers, a fuzzy vector with a quadratic membership function, scenario decomposed fuzzy numbers, an oblique fuzzy vector, and a fuzzy polytope.

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