A fuzzy approach to hierarchical multiobjective programming problems and its application to an industrial pollution control problem

In this paper, we focus on hierarchical multiobjective programming problems where multiple decision makers in a hierarchical organization have their own multiple objective functions, and propose an interactive algorithm based on the dual decomposition method to obtain the satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers but also their own preferences for their objective functions. In the proposed algorithm, assuming that each of the decision makers has fuzzy goals for his/her objective functions, corresponding membership functions are elicited from the decision makers in their subjective manner. In order to deal with hierarchical multiobjective programming problems, a new kind of Pareto optimality concept in membership spaces is defined and the concept of decision powers of multiple decision makers in a hierarchical decision structure is introduced. The proposed algorithm is applied to the industrial pollution control problem in Osaka City in Japan in order to show the efficiency of the proposed method.