Title: Similarity measure of intuitionistic fuzzy numbers and its application to clustering

Authors: Satyajit Das; Debashree Guha

Addresses: Department of Mathematics, IIT Patna, India ' Department of Mathematics, IIT Patna, India

Abstract: The aim of this study is threefold. First of all, a novel method to calculate the degree of similarity between intuitionistic fuzzy numbers (IFNs) by using the concept of centroid point of IFNs is presented. Secondly, in order to compare the proposed method with the existing similarity measures some examples are demonstrated. The numerical results show that the new similarity measure can overcome the limitations of the existing methods and thus, the proposed similarity measure is more reasonable and effective from application point of view. Finally, a clustering algorithm, in which data are quantified by IFNs, is introduced by utilising the proposed similarity measure. In addition, a pattern recognition problem is demonstrated to illustrate the practicality and effectiveness of this similarity-based clustering technique.

Keywords: intuitionistic fuzzy number; centroid point; similarity measure; clustering; pattern recognition.

DOI: 10.1504/IJMOR.2017.084157

International Journal of Mathematics in Operational Research, 2017 Vol.10 No.4, pp.399 - 430

Received: 27 May 2015
Accepted: 25 Jul 2015
Published online: 16 May 2017 *

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