A novel clustering algorithm based on a new similarity measure over Intuitionistic fuzzy sets

Abstract

In Intuitionistic fuzzy sets(IFSs), experts assign both membership value and non-membership value to each fuzzy element x with a certain degree of hesitation. The hesitancy in the opinion of the experts appear due to incomplete information available regarding x. Therefore, precise estimation of its both membership value and non-membership value becomes highly difficult. Hence, there is a high chance that both membership value and the non-membership value assigned to x by the expert may not be absolutely correct. So, whenever we try to measure similarity between the IFSs using the various distance measures involving all the components of IFSs like membership value, non-membership value together with hesitation, then we often notice that all of them fails to describe the underlying situation completely. Therefore, the similarity measures derived from these distance measures also fails to produce good results. So, we introduce a new similarity measure by properly defining a similarity degree through the result established in this paper. The similarity measure has a central role in developing a modified λ-cutting algorithm for clustering. Here we also establish the efficacy of our modified λ-cutting algorithm while implementing it on a real world data set.