FUZZY CLUSTERING BASED ON INTUITIONISTIC FUZZY RELATIONS

Abstract

It is well known that an intuitionistic fuzzy relation is a generalization of a fuzzy relation. In fact there are situations where intuitionistic fuzzy relations are more appropriate. This paper discusses the fuzzy clustering based on intuitionistic fuzzy relations. On the basis of max -t & min -s compositions, we discuss an n-step procedure which is an extension of Yang and Shih's [17] n-step procedure. A similarity-relation matrix is obtained by beginning with a proximity-relation matrix using the proposed n-step procedure. Then we propose a clustering algorithm for the similarity-relation matrix. Numerical comparisons of three critical max -t & min -s compositions: max -t1 & min -s1, max -t2 & min -s2 and max -t3 & min -s3, are made. The results show that max -t1 & min -s1 compositions has better performance. Sometimes, data may be missed with an incomplete proximity-relation matrix. Imputation is a general and flexible method for handling missing-data problem. In this paper we also discuss a simple form of imputation is to estimate missing values by max -t & min -s compositions.