INTUITIONISTIC FUZZY CLUSTERING ALGORITHM BASED ON BOOLE MATRIX AND ASSOCIATION MEASURE

Abstract

In this paper we develop a measure for calculating the association coefficient 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 first utilizes the association coefficient of A-IFSs to construct an association matrix, and then calculates the λ-cutting matrix of the association matrix no matter whether it is an equivalent matrix or not. After that, the λ-cutting matrix is used to cluster A-IFSs (if the λ-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 effectiveness of the association coefficient and the algorithm for clustering A-IFSs. Furthermore, we extend the algorithm to cluster interval-valued intuitionistic fuzzy sets (IVIFSs), and finally, we use another numerical example to illustrate the latter algorithm.