基于公理化模糊集合的TOPSIS多属性决策方法

TOPSIS Multi-attribute Decision-making Method Based on Axiomatic Fuzzy Sets

针对属性值为语言值并且属性权重为实数的多属性决策问题,本文提出了一种以公理化模糊集合为基础的TOPSIS多属性决策方法。首先确定多属性决策过程中语言评价集与相对应的模糊划分以及由此模糊划分所生成的公理化模糊集合,将多属性决策过程中的语言值数学量化为公理化模糊集合处理;定义了公理化模糊集合上的序关系,并利用该序关系定义了正负理想方案;利用公理化模糊集合的Euclidean距离,分别计算备选方案与正、负理想方案之间的相对贴近度,并由此得到备选方案的综合排序指数。最后,本文通过一个实例来说明该模型的有效性和实用性。

Aiming at the multi-attribute decision-making problem where the attribute value is a linguistic value and the attribute weight is a real number,this paper proposes a TOPSIS multi-attribute decision-making method based on an axiomatic fuzzy set.Firstly,determine the language evaluation set and the corresponding Fuzzy division and the axiomatic fuzzy set generated by the fuzzy division to mathematically quantify the linguistic value in the process of multi-attribute decision-making into axiomatic fuzzy set processing.Then define the order relationship on the axiomatic fuzzy set,and based on the order relationship define the positive and negative ideal schemes.The Euclidean distance of the axiomatic fuzzy set is used to calculate the relative closeness between the alternative schemes and the positive and negative ideal schemes,and the comprehensive ranking index of the alternative schemes is obtained.Finally,an example is used to illustrate the effectiveness and practicability of the model.