Similarity measure on interval valued intuitionistic fuzzy numbers based on non-hesitance score and its application to p
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Similarity measure on interval valued intuitionistic fuzzy numbers based on non-hesitance score and its application to pattern recognition S Jeevaraj1 Received: 30 December 2019 / Revised: 11 May 2020 / Accepted: 5 July 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract Interval-valued intuitionistic fuzzy numbers (IVIFNs) are better in modelling real-life problems more naturally, and it can apply to many fields such as Pattern Recognition, Decision Making, Cluster Analysis, Medical Diagnosis, Image Processing, etc. Especially similarity measures defined on the class of IVIFNs does play a significant role in the field of Pattern Recognition and Decision Making. Many authors from all over the world were trying to define a standard method (Similarity measure) that can be suitable for most of the problems. Unfortunately, each of the similarity measures has certain drawbacks as well as some advantages among different similarity measures available in the literature. Most of the similarity measures defined in the particular class (subset) of IVIFNs. These issues open up a pathway for further/ future research. In this study, we aim at introducing a new similarity measure defined in another class of an IVIFNs that can cover more IVIFNs in it. In this paper, first, we define a new similarity measure on the class of interval-valued intuitionistic fuzzy numbers (IVIFNs) based on the non-hesitance score function defined on the class of IVIFNs. Second, we discuss the drawback of various existing similarity measures and compare them with the proposed similarity measures using different cases. Third, the efficacy of the proposed similarity measure to familiar existing methods is studied using illustrative examples. Finally, the applicability of the proposed method in solving pattern recognition problem is depicted. Keywords Interval-valued intuitionistic fuzzy number · Distance measure · Similarity measure · Non-hesitance score · Pattern recognition Mathematics Subject Classification 03B52 · 03E72 · 26E50
Communicated by Leonardo Tomazeli Duarte.
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S Jeevaraj [email protected] Atal Bihari Vajpayee Indian Institute of Information Technology and Management, Gwalior 474015, India 0123456789().: V,-vol
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S Jeevaraj
1 Introduction Intuitionistic fuzzy numbers (IFNs) generalized from fuzzy numbers (FNs) are very much important in modelling problems with imprecise and incomplete information. In particular, interval-valued intuitionistic fuzzy numbers (IVIFNs) are widely used in the field of decision analysis and pattern recognition. Similarity measures in the class of IVIFNs play an essential role in pattern recognition problems. The concept of similarity measure is widely used in different image processing techniques, behaviour analysis, and pattern recognition/ Multicriteria Decision Making (MCDM) problems. Chen (1997) has introduced a new similarity measure on vague sets and applied it in the behaviour analysis problem. Xu (2007) has proposed another similarity o
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