Fuzzy Multi-Criteria Optimization: Possibilistic and Fuzzy/Stochastic Approaches

In this chapter, we review fuzzy multi-criteria optimization focusing on possibilistic treatments of objective functions with fuzzy coefficients and on interactive fuzzy stochastic multiple objective programming approaches. In the first part, treatments of objective functions with fuzzy coefficients dividing into single objective function case and multiple objective function case. In single objective function case, multi-criteria treatments, possibly and necessarily optimal solutions, and minimax regret solutions are described showing the relations to multi-criteria optimization. In multiple objective function case, possibly and necessarily efficient solutions are investigated. Their properties and possible and necessary efficiency tests are shown. As one of interactive fuzzy stochastic programming approaches, multiple objective programming problems with fuzzy random parameters are discussed. Possibilistic expectation and variance models are proposed through incorporation of possibilistic and stochastic programming approaches. Interactive algorithms for deriving a satisficing solution of a decision maker are shown.