Multi-objective optimizing with random variable coefficients based on interactive fuzzy satisfying method

Focus on multi-objective linear optimizing 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. Assuming that the decision maker has a fuzzy goal for each of the objective functions, having determined the fuzzy goals of the decision maker, we present an interactive fuzzy satisfying method to derive a satisfying solution for the decision maker by updating the reference membership levels. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method.