基于正弦函数的直觉模糊集相似度测量及其应用

摘要

相似度测量是度量两个直觉模糊集相似程度的重要方法,现已有很多测量公式被相继提出,但现有的部分公式在一些实际应用中会出现无法归类或计算过程相对复杂现象.针对这种问题,通过对Tian提出的余切相似度测量方法的研究,同时考虑隶属度、非隶属度和犹豫度三个方面信息,提出了两个正弦相似度测量公式,证明了公式的正确性,并用几组数值例子将其与其它测量公式进行比较分析,验证了新公式的合理性.最后通过实例说明了该方法的有效性.%Similarity measure is an important method to measure the similarity between two intuitionsitic fuzzy sets.Many formulas about similarity measure have been proposed,but some are unable to classify or involve complicated calculation in practical applications.To solve this problem,based on the cotangent similarity measurement method proposed by Tian and the information carried by the membership degree,nonmembership degree and hesitancy degree,we propose two sine similarity measure formulas which prove to be correct.Then we conduct comparative analysis among various similarity measures by several numerical examples to illustrate the effectiveness of the proposed sine similarity measures.Finally,the effectiveness of the method is illustrated by an example.