Multiobjective Probabilistic Constrained Programming Problems Using Fuzzy Goal

Abstract

We have fuzzy mathematical programming and stochastic programming which are used in making a plan under uncertainty. Stochastic programming has a merit of dealing with dependency among coefficients that is not dealt with by fuzzy mathematical programming. One of the popu-lar methods of stochastic programming is probabilistic constrained programming problems(PCPP). Generally speaking, if probabilistic distribution is continuous, PCPP are nonlinear programming problems. But if probabilistic distribution is discrete, PCPP are mixed 0-1 integer programming problems. In this paper, considering a merit of technique to solve, we express discrete distribution as scenarios. PCPP optimize objective functions after setting probability level. But it may be difficult for decision maker to set probability level uniquely and to catch a relation between objective functions and probability level. In this paper we propose a method of dealing with flexibly a relation between objective functions and probability level using fuzzy goal and interactive method.