区间值直觉模糊相似度及其应用

Similarity Measure for Interval-Valued Intuitionistic Fuzzy Set and Its Applications

摘要: 相似度是模糊集理论中的一个测度，常用来度量两个模糊集的接近程度。在区间值直觉模糊环境下的多属性决策问题中，一个相似度的优劣影响着决策结果的准确性。在以往的研究中，已经有大量的区间值直觉模糊相似度被提出，在分析这些相似度过程中，发现其中大多存在着反直觉的情况。本文从熵测度的角度出发，基于熵测度和相似度的相关关系，由熵测度导出一个对应的相似度，并证明其满足相似度的公理化定义，接着通过实例说明提出的相似度的有效性和优越性。最后将其与传统VIKOR方法相结合，应用于多属性决策问题之中。

Abstract: Similarity measure is ameasure in fuzzy set theory, which is often used to measure the closeness between two fuzzy sets. In the decision making problem in the environment of interval-value intuitionistic fuzzy set, the superiority and disadvantage of a similarity have an important impact on the accuracy of the decision result. In previous studies, a large number of interval-values intuitionistic fuzzy similarity measures have been proposed, and in the process of analyzing these similarity measures, it is found that most of them have counterintuitive cases. From the perspective of entropy, based on the correlation between entropy measure and similarity measure, this paper derives a corresponding similarity measure from a two-parameter entropy, proves that it satisfies the axiomatic definition of similarity measure, and illustrates its validity and superiority through comparative analysis. Finally, it is combined with the traditional VIKOR method and applied to multi-attribute decision-making problems.