Fuzzy clustering based on intuitionistic fuzzy relations

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 similairity-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-t(1) & min-s(1), max-t(2) & min-s(2) and max-t(3) & min-s(3), are made. The results show that max-t(1) & min-s(1) 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.