Enhanced Two-Step Method via Relaxed Order of α-Satisfactory Degrees for Fuzzy Multiobjective Optimization

An enhanced two-step method via relaxed order of satisfactory degrees for fuzzy multiobjective optimization is proposed in this paper. By introducing the concept of fuzzy numbers and α-level set theory, fuzzy parameters are taken as variables, and all the objectives are transformed into fuzzy goals involving three fuzzy relations. The order of α-satisfactory degrees which means the objectives with higher priority achieving higher satisfactory degree is applied to model preemptive priority requirement. This strict order constraint is relaxed by priority variable to find the preferred solution satisfying optimization and priority. The original optimization problem is divided into two steps to be solved iteratively. The M-α-Pareto optimality of the solution is ensured, and the satisfactory solution can be acquired by regulating the slack parameter Δδ or changing α. The numerical examples demonstrate the power of the proposed method