A Modalistic Formalization of Fuzzy Mathematical Programming Problems
Masahiro INUIGUCHI, Hidetomo ICHIHASHI, Yasufumi KUME
In this paper, the fuzzy mathematical programming problem is formalized based on the idea analogous with the chance constrained programming problem. The difference in meaning between the ambiguity of the coefficients and that of the decision maker's preference is emphasized. The fuzzy relations between possibility distributions proposed. by Inuiguchi et al. are introduced. The constraints with fuzzy coefficients are treated as the restrictions which should be satisfied properly rather than perfectly. Namely, the constraints are satisfied to at least a certain level given by the decision maker. The objective function with fuzzy coefficients is treated variously depending on the decision objectives, i. e. the optimization of the modalities, the optimization of the fractile and the minimization of the ambiguity. The determinstic equivalent constraints and the equivalent problems are shown when the constraints and the objective function are linear.