Regularized Fuzzy Clustering by Confusion Degree based on Dempster-Shafer Theory

Most conventional Fuzzy c-Means methods have the strict constraint that Sigmamu(chi) = 1. From the view of Fuzziness, this constraint is not essential because it is the restriction derived from probability perspectives. On the other hand, possibilistic clustering does not have this restriction. But the shapes of identified membership functions by the possibilistic clustering are the identical ones. This means that the shapes of the membership functions do not depend on the data distributions. The identified cluster should represent the characteristics of the data appropriately. This paper presents a novel regularization method for Fuzzy c-Means using an index named confusion degree which are derived from Dempster-Shafer theory. With proposed method, each of the identified clusters has its own shapes of membership function. The membership functions do not have the additive constraints Sigmamu(chi) = 1. This means that the identified membership functions depend on the data distribution and the clusters will show the better understandings for us. To show the feasibility of the proposed method, some numerical experiments have been carried out.