基于Einstein算子的直觉模糊值相似度及其在聚类中的应用

Intuitionistic Fuzzy Value Similarity Based on Einstein Operator and Its Application in Clustering

基于直觉模糊等价矩阵聚类的关键在于合理构建样本之间的直觉模糊值相似度,这种相似度是有2个分量的二元形式,其中一个分量代表着2个对象之间的相似程度,另一个代表非相似程度.提出一种基于Einstein算子的直觉模糊值相似度构造方法并将其应用到聚类分析.首先,给出Einstein算子诱导的直觉模糊剩余蕴含,并通过聚合直觉模糊剩余蕴含得到直觉模糊值相似度;然后,利用这种直觉模糊值相似度构建直觉模糊相似矩阵,并通过直觉模糊相似矩阵的合成运算得到直觉模糊等价矩阵,进而给出直觉模糊聚类算法;最后,通过算例对该方法进行说明和分析.

The key of clustering based on an intuitionistic fuzzy equivalence matrix is to reasonably construct an intuitionistic fuzzy similarity between samples,which is a binary relation with two components,among which the first component represents the degree of similarity between two objects,and the other represents the degree of dissimilarity.This paper presents a construction method for the intuitionistic fuzzy value similarity construction method based on Einstein operator and applies it to cluster analysis.First,an intuitionistic fuzzy residual implication induced by Einstein operator is given,and an intuitionistic fuzzy value similarity is obtained by aggregating intuitionistic fuzzy residual implication.Then the intuitionistic fuzzy value similarity is used to construct an intuitionistic fuzzy similarity matrix,and the intuitionistic fuzzy equivalent matrix is obtained by the compositional operation of intuitionistic fuzzy similarity matrix,where then an intuitionistic fuzzy clustering algorithm is given.Finally,an example is given to illustrate and analyze the method.