Similarity measure on interval valued intuitionistic fuzzy numbers based on non-hesitance score and its application to pattern recognition

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.