Fuzzy数理計画法

抄録

In recent years, it has become very important to build mathematical models for uncertain situations of systems in the fields of systems control or systems engineering. Among the uncertain situations of systems there are randomness and fuzziness. Probability theory is usually used for the former, but a new concept becomes necessary for the latter. Fuzzy sets were introduced by L.A. Zadeh to provide a concept for this purpose.
Decision-making in a fuzzy environment, which is an important problem in fuzzy systems, was researched by R.E. Bellman and L.A. Zadeh on the basis of the fuzzy sets. In that research an optimal decision is an alternative which attains to the maximum of a membership function of a fuzzy decision.
In this paper, we formulate a fuzzy mathematical programming by introducing the idea of level sets on the basis of the optimal decision. The programming decides also a constraint set, because the constraint set is fuzzy. In this meaning a fuzzy mathematical programming differs from ordinary mathematical programming. This fuzzy mathematical programming may be reduced to ordinary mathematical programming under the two sufficient conditions of the α-continuity and the uniqueness of the optimal level. These two conditions are shown in this paper. An algorithm proposed by the authors may be used to solve the problem in which only the condition of α-continuity exists.