Generating an α-Pareto Optimal Solution to Multiobjective Nonlinear Programming Problems with Fuzzy Parameters: A Decomposition Method

摘要

This paper proposes a decomposition method for generating an α-Pareto optimal solution for multiobjective nonlinear programming (MONLP) problems with fuzzy solution for multiobjective nonlinear programming (MONLP) problems with fuzzy parameters in the objective functions (FMONLP). These fuzzy parameters are characterized be fuzzy numbers. For such problems, the concept of α-Pareto optimality is introduced by extending the ordinary Pareto optimality on the basis of the α-Level sets of the fuzzy numbers. The decomposition method is based on the principle of optimality in dynamic programming (DP), and on the concept of fuzzy "decision" model (FDM). Assuming the separability and monotonicity of the problem, a generalized functional equation of dynamic programming (DP) is derived. Also, an interactive fuzzy decision-making algorithm for generating α-Pareto optimal solution through the decomposition method is developed. A numerical example is given to illustrate the results developed in this paper.