Brief Description of Probabilistic Multi-objective Optimization of a System

This chapter gives a brief description of probabilistic multi-objective optimization of a system, which includes the scientific connotation and essence of multi-objective optimization from viewpoint of systems theory. The main thought is to reflect the “simultaneity of multi-objective optimization” by using probabilistic approach from viewpoint of systems theory. The concept of “preferable probability” and its evaluation are overviewed in respects of set theory and probability theory. Besides, robust design is an optimal approach that aims to reduce effect of uncertain factors on product quality, which is a specific case of probabilistic multi-objective optimization and outlined. The fuzzification treatment is utilized to the case of desired value as target in robust design as an auxiliary approach. Additionally, the reliability design and assessment involving optimization with multiple objectives is taken as another specific case of probabilistic multi-objective optimization as well.