Possibilistic Linear Programming with Fuzzy If-Then Rule Coefficients

In this paper, we propose a scenario decomposition approach for the treatment of interactive fuzzy numbers. Scenario decomposed fuzzy numbers (SDFNs) reflect a fact that we may have different estimations of possible ranges of uncertain variables depending on scenarios, which are expressed by fuzzy if-then rules. The properties of SDFNs are investigated. Possibilistic linear programming problems with SDFNs are formulated by two different approaches, fractile and modality optimization approaches. It is shown that the problems are reduced to linear programming problems in fractile optimization models with the necessity measures and that the problems can be solved by a linear programming technique and a bisection method in modality optimization models with necessity measures. A simple numerical example is given.