Three-Step Optimization Method Based on Posteriori Satisfying Degree for Fuzzy Multiple Objective Optimization

Abstract

A three-step satisfying method based on posteriori satisfying degree is proposed for fuzzy multiple objective optimization problem. Firstly, the uniformly distributed Pareto optimal set is acquired by the multiple objective genetic algorithm. Then, the eliminating optimization method is presented to reduce this set to the M-Pareto optimal set. Finally, the fuzzy mean clustering with the validity criteria is used to classify the obtained set to construct the representative M-Pareto optimal subset such that DM can choose the preferred result easily. The numerical example shows the power of the proposed method.