Fuzzy-Based Probabilistic Multi-objective Optimization for Material Selection

In this chapter, the probability-based method for multi-objective optimization (PMOO) is adopted to develop a rational fuzzy-related multi-objective optimization for material selection, the fundamental idea and algorithm of fuzzy as well as probability theory are taken as the footstone to conduct the formulation. The utility of the material performance index is determined by the intersection of the membership function of fuzzy numbers of candidate material performance and the membership function of fuzzy numbers of desired material performance. Thereafter, the utility of each material performance index is employed to conduct the evaluation of partial preferable probability and formulate the multi-objective optimization by means of probability theory. Furthermore, a typical example is given to illustrate the rational process of fuzzy multi-objective optimization for material selection.