双层目标规划问题与基于TOPSIS的直觉模糊交叉式方法

Bi-Level Multi-Objective Programming and Intuitionistic Interactive Fuzzy Optimization Method Based on TOPSIS

针对双层多目标规划问题提出了一种求解该问题的基于TOPSIS的直觉模糊交互式方法。首先,为了尽可能减少决策者的主观因素影响,利用直觉模糊集理论中隶属函数和非隶属函数来刻画各层决策者的主观愿望;考虑到精确函数比得分函数能更好地刻画决策者的满意程度,利用精确函数构造直觉模糊优化模型。其次,为了度量上层决策者和下层决策者的整体满意解,基于TOPSIS原理构造平衡函数来刻画所有决策者的整体满意度。最后,利用数值实验说明了本文提出的基于TOPSIS的直觉模糊交互式方法可行。

This paper proposed an intuitionistic interactive fuzzy optimization method based on theTOPSIS theory for solving a bi-level multi-objective programming. Firstly,in order to reduce decisionmakers′ subjective humanity,the membership function and non-membership function of intuitionisticfuzzy theory can be used to describe decision makers′ subjective intension;Since the accurate function isbetter than the score function used to describe the satisfaction degree,in this algorithm,the accuratefunction is used to construct intuitionistic fuzzy optimization model. Then,in order to measure the overallsatisfaction solution of lower and upper-level decision makers,a balance function is introduced based onthe TOPSIS theory by considering the overall satisfactory balance between the two levels. Finally,numerical examples illustrate the feasibility and efficiency of the proposed algorithm.