Intuitionistic Fuzzy Clustering Algorithm Based on Boole Matrix and Association Measure

In this paper we develop a measure for calculating the association coe±cient between Atanassov's intuitionistic fuzzy sets (A-IFSs), and show its desirable axiomatic properties. Then we present an algorithm for clustering A-IFSs. The algorithm ̄rst utilizes the association coe±cient of A-IFSs to construct an association matrix, and then calculates the -cutting matrix of the association matrix no matter whether it is an equivalent matrix or not. After that, the -cutting matrix is used to cluster A-IFSs (if the -cutting matrix is just only a similarity matrix, then we can easily transform it into an equivalent matrix). Three examples are used to show the e®ectiveness of the association coe±cient and the algorithm for clustering A-IFSs. Furthermore, we extend the algorithm to cluster interval-valued intuitionistic fuzzy sets (IVIFSs), and ̄nally, we use another numerical example to illustrate the latter algorithm.