Interactive α-satisfactory method for multi-objective optimization with fuzzy parameters and linguistic preference

Abstract

 An interactive α-satisfactory method via relaxed order of desirable α-satisfactory degrees is proposed for multi-objective optimization with fuzzy parameters and linguistic preference in this paper. Fuzzy parameters existing in objectives and constraints of multi-objective optimization are defined as fuzzy numbers and α-level set is used to build the feasible domain of parameters. On the basis, the original problem with fuzzy parameters is transformed into multi-objective optimization with fuzzy goals. Linguistic preference of decision-maker is modelled by the relaxed order of desirable α-satisfactory degrees of all the objectives. In order to achieve a compromise between optimization and preference, the multi-objective optimization problem is divided into two single-objective sub-problems: the preliminary optimization and the linguistic preference optimization. A preferred solution can be found by parameter adjustment of inner-outer loop. The minimum stable relaxation algorithm of parameter is developed for calculating the relaxation bound of maximum desirable satisfaction difference. The M-α-Pareto optimality of solution is guaranteed by the test model. The effectiveness, flexibility and sensitivity of the proposed method are well demonstrated by numerical example and application example to heat conduction system.