基于改进记分函数和累积前景理论的直觉模糊TOPSIS法

Intuitionistic Fuzzy TOPSIS Method Based on Improved Score Function and Cumulative Prospect Theory

针对属性值由直觉模糊数表示且属性权重未知的多属性决策问题,首先,提出一种改进的记分函数,通过证明其相关定理和与现有记分函数进行算例比较,验证其正确性与优越性,解决了现有记分函数需要二次比较和在某些情况下与客观事实不符的缺陷。其次,引入累积前景理论,提出基于改进记分函数和累积前景理论的直觉模糊TOPSIS法,以正负理想方案为参考点,采用综合前景值代替距离测度,有效地避免了忽略属性间相关性的问题,通过计算各方案的相对贴近度对方案进行排序择优。最后,通过实例比较分析和仿真数据对比验证所提记分函数和决策方法的可行性和有效性。

Aiming at the multi-attribute decision-making problem where the attribute value is represented by the intuitionistic fuzzy number and the attribute weight is unknown.Firstly,an improved score function is proposed,its correctness and superiority are verified by proving its related theorems and comparing numerical examples with existing score functions.It solves the defects that the existing score function requires secondary comparison and is inconsistent with objective facts in some cases.Secondly,the cumulative prospect theory is introduced,and a TOPSIS method for intuitionistic fuzzy multi-attribute decision-making based on improved score function and cumulative prospect theory is proposed.This method uses the positive and negative ideal alternatives as a reference point.The comprehensive prospect value is used to replace the distance measure,which effectively avoids ignoring the correlation between attributes.The order of alternatives is listed by calculating the relative closeness degree of each alternative.Finally,the feasibility and effectiveness of the proposed score function and decision-making method are verified by comparing examples and simulation data with existing decision-making method.