Interactive Fuzzy Multi-Objective Stochastic Linear Programming

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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 chapter, we focus on multiobjective linear programming problems with random variable coefficients in objective functions and/or constraints. Using several stochastic models such as an expectation optimization model, a variance minimization model, a probability maximization model, and a fractile criterion optimization model in chance constrained programming, 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, several interactive fuzzy satisfying methods to derive a satisfying solution for the decision maker by updating the reference membership levels are presented.