Enhanced Two-Step Satisfactory Method for Multi-Objective Optimization with Fuzzy Parameters

An enhanced two-step satisfactory method for multi-objective optimization problem with fuzzy parameters is proposed in this paper. By means of the alpha-level sets of the fuzzy numbers, all the objectives with fuzzy parameters are modeled as the fuzzy goals. The order of satisfactory degrees about different denoting that the higher priority achieves the higher satisfactory degree is applied to preemptive priority requirement. The strict order constraints are relaxed by decreasing the maximum overall satisfactory degree. The original optimization problem is divided into two models to be solved iteratively. The satisfactory solution can be acquired by changing parameter or regulating alpha. The numerical example demonstrates the power of the proposed method.