New bounded variation based similarity measures between Atanassov intuitionistic fuzzy sets for clustering and pattern recognition

• Published in: Applied soft computing 2019-12, Vol.85, p.105529, Article 105529
• Main Authors: Ashraf, Zubair, Khan, Mohd Shoaib, Lohani, Q.M. Danish
• Format: Article
• Language: English
• Subjects: Bounded variation; Clustering analysis; Intuitionistic fuzzy set (IFS); Pattern recognition; Similarity measure
• ISSN: 1568-4946; 1872-9681
• DOI: 10.1016/j.asoc.2019.105529

The distance and similarity measures are two interrelated depictions of the patterns which signify the categorization between the Atanassov intuitionistic fuzzy sets (AIFSs) by evaluating the degree of belongingness. In this work, we propose a new similarity measure, termed as hybrid similarity measure, by the combination of intuitionistic fuzzy bounded variation (IFBV) and intuitionistic fuzzy metric based measures. The concept of IFBV which is a technique to approximate arc length of an intuitionistic fuzzy-valued function (IFVF) is also introduced here. The IFVF over an AIFS is geometrically evolved through the generalization of the p-summable IFBV, that is, connecting all the elements of AIFS lie on the structure of IFBV corresponding to power p. The proposed measure overcomes the shortcomings of intuitionistic fuzzy metric based similarity measures by incorporating more flexibility into it. The hybrid similarity measure has been successfully implemented and applied on the several real-world applications in the field of pattern recognition as well as clustering. Further, a detailed comparison of results has been shown against the other existing similarity measures to demonstrate the superiority and validity of the proposed hybrid similarity measure. •New similarity measure, named as a hybrid similarity measure between the AIFSs has been proposed.•It introduces a concept of intuitionistic fuzzy bounded variation (IFBV) of an intuitionistic fuzzy-valued function (IFVF).•The IFVF is geometrically evolved through the generalization of IFBV and intuitionistic fuzzy lp metric.•It experimentally is shown that the proposed hybrid similarity measure obtained better results for pattern recognition and hierarchical clustering problems.•Through comparative analysis against the well-known similarity measures have been conducted to show the effectiveness of the proposed measure.