Intuitionistic Fuzzy Modulus Similarity Measure

Abbreviations

• FSs - Fuzzy sets

• IFSs - Intuitionistic fuzzy sets

• VSs - vague sets

• IVFSs – Interval-valued fuzzy sets

• IFMSs - Intuitionistic fuzzy multisets

• IFVs - Intuitionistic fuzzy values

• RTFTNs - Right-angled transformed fuzzy triangular numbers

• PFSs- Pythagorean Fuzzy Sets

Introduction

Information theory is a scientific study for finding the uncleared information. The FSs theory is a significant component of IFSs theory, it makes the study as tractable. IFSs were created Atanassov (1986) with the combination of membership, non-membership and hesitancy index. In general, the available vague, insufficient or inexact information is improved in uncertain ways by the decision maker which can be termed as the measure. With the help of these measures, the authors can find the accurate and reasonable information. This concept is expanded by some various higher order fuzzy sets, including the intuitionistic fuzzy set, hence, the IFSs theory achieved the affluence to arrange the uncertainty. The probabilistic entropy measure is related to the equation of thermodynamical entropy, which is generally quantifiable as randomness, disorder, and uncertainty. In recent years, numerous studies have developed similarity measure & distance measures between intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IVFSs). Through the literature, Gau and Buehrer (1993) described the concept of vague sets (VSs), it the further generalized extension of fuzzy sets (FSs). The fuzzy set theory is an approach which is used to getting the accurate and desirable information. Later on, Bustince & Burillo (1996) shows that the developed vague set is identical to the IFS; it treated as the further extension of fuzzy sets. IFSs theory has been proved suitable in its assessment for some diverse applications to their related studies. The study of similarity measures is a fascinating and vital approach for finding hidden information. In this contrast, similarity measure provides the comparison between the information carried by IFSs. Consequently, similarity measure is an approach to which detect the degree of similarity between IFSs. It is a tool to be applied to various applications such as pattern recognition, decision making, medical diagnosis, image processing, machine learning, and cluster analysis. Through the concept of similarity measures, many authors introduced the various similarity measures in IFSs. In different studies, it was found that some contradictory cases, which could not provide accurate information. Consequently, as a result of some respective studies, numerous authors overcame the drawback and proposed some novel measures. Therefore, more similarity measures can be derived from distance measures and vice versa. Furthermore, the numerous authors (Arora & Tomar, 2020; Dass et al., 2019; Tomar, 2019; Tomar & Ohlan, 2014) have developed the entropy and discrimination measures related to FSs and IFSs. Initially, IFSs distance measures were conceptualised by Szmidt & Kacprzyk (2000). After that, Wang and Xin (2005) are point out, Szmidt & Kacprzyk (2000) distance measure is not well in some cases. So, they have suggested some new distance measures and their implementation in the pattern recognition problem. IFSs distance measures are tools used to describe the study of differences between IFSs. These are primarily useful for problems involving decision-making, pattern recognition, and medical diagnosis problem.