An interactive fuzzy satisficing method for multiobjective linear programming problems with random variable coefficients through a probability maximization model

Abstract

Two major approaches to deal with randomness or ambiguity involved in mathematical programming problems have been developed. They are stochastic programming approaches and fuzzy programming approaches. In this paper, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using the probability maximization model to maximize the probability that each objective function becomes a certain value under chance constrained conditions, the stochastic programming problems are transformed into deterministic ones. As a fusion of stochastic approaches and fuzzy ones, after determining the fuzzy goals of the decision maker, an interactive fuzzy satisficing method to derive a satisficing solution for the decision maker by updating the reference membership levels is presented. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.