A fuzzy dual decomposition method for large-scale multiobjective nonlinear programming problems
Fuzzy Sets and Systems - Special issue on operations research
Hierarchical optimization: a satisfactory solution
Fuzzy Sets and Systems
Fuzzy approach for multi-level programming problems
Computers and Operations Research
Fuzzy Sets and Systems - Special issue on fuzzy optimization
Fuzzy and Multi-Level Decision Making: And Interactive Computational Approach
Fuzzy and Multi-Level Decision Making: And Interactive Computational Approach
A neural network approach to multiobjective and multilevel programming problems
Computers & Mathematics with Applications
Fuzzy approach to multilevel knapsack problems
Computers & Mathematics with Applications
An interactive approach for integrated multilevel systems in a fuzzy environment
Mathematical and Computer Modelling: An International Journal
Information Sciences: an International Journal
Hi-index | 0.20 |
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.