Interval-Valued Fuzzy c-Means Algorithm and Interval-Valued Density-Based Fuzzy c-Means Algorithm

Ayush K. Varshney, Priyanka Mehra, Pranab K. Muhuri, Q. M. Danish Lohani

Abstract: Most of the time membership value in the fuzzy set cannot be exactly defined. Interval-valued fuzzy set (IVFS) is a special type of type-2 fuzzy sets which represents the membership value of the fuzzy set as an interval. IVFS assumes that membership interval can better represent the uncertainty in the data. Accordingly, IVFS can be used to obtain good clustering results since it can represent the uncertainty more appropriately. Thus, this paper proposes the interval-valued fuzzy c-means algorithm (IVFCM) which uses IVFSs to represent the data. The concept of the proposed IVFCM is then extended to introduce the interval-valued density based fuzzy c-means (IVDFCM) algorithm based on the distance measure of IVFSs. Both IVFCM and IVDFCM are simulated over various UCI benchmark datasets to show their suitability and supremacy over their existing counterparts.