区间直觉模糊集的相似性测度及其应用

Similarity Measure of Interval Valued Intuitionistic Fuzzy Sets and Its Application

在度量两个集合时，用相似性测度来表示两集合的相似性程度．在度量区间直觉模糊集的相似性程度时，现有的很多方法都没有把犹豫度考虑在内．针对这个问题，根据区间直觉模糊集理论，在Szmidt的区间直觉模糊集的海明距离、规范化海明距离、欧几里得距离、规范化欧几里得距离的基础上．定义了基于Szmidt的区间直觉模糊集的加权海明距离和基于Szmidt的区间直觉模糊集的加权欧几里得距离，分别包含了隶属度，非隶属度和犹豫度，并给出了定理和证明．然后定义了两种区间直觉模糊集的相似性测度．最后将这两种相似性测度应用到模式识别领域．

Similarity measures are used to represent the similarity degree of two sets when measuring two sets. Many existing methods do not take into account the degree of hesitation in measuring the degree of similarity of of interval valued intuitionistic fuzzy sets.To solve this problem, based on interval intuitionistic fuzzy set theory, On the basis of the Szmidt＇s the interval valued intuitionistic fuzzy sets Hamming distance, standardized Hamming distance, Euclidean distance,standardized Euclidean distance. This paper defines based on Szmidt＇s the interval valued intuitionistic fuzzy set weighted Hamming distance and based on Szmidt＇s the interval intuitionistic fuzzy set weighted Euclidean distance. The membership degree, the non membership degree and the hesitation degree are included, and the theorems and proofs are given. Then two kinds of similarity measure of interval valued intuitionistic fuzzy sets are defined. Finally, the two similarity measures are applied to the field of pattern recognition.