Similarity Measures Based on T-Spherical Fuzzy Information with Applications to Pattern Recognition and Decision Making

Muhammad Nabeel Abid,Miin-Shen Yang,Hanen Karamti,Dragan Pamucar,Kifayat Ullah

doi:10.3390/sym14020410

Abstract

T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited room for processing such kinds of information. On a scale of zero to one, similarity measures (SMs) are a tool for evaluating the degrees of resemblance between various items or phenomena. The goal of this paper is to investigate the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment. The newly improved SM has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss. The proposed SM’s validity is demonstrated mathematically and by examples. To examine the application of the suggested SM two real-life issues are discussed, including the concerns of medical diagnosis and pattern recognition. A comparison of the suggested SMs with current SMs is also made to assess the proposed work’s reliability. Since symmetric triangular fuzzy numbers are quite useful in database acquisition, we will consider the proposed SM for symmetric T-spherical triangular fuzzy numbers in the near future.

Highlights

Zadeh [1] conceived the concept of fuzzy sets (FSs) in 1965
To check the effectiveness of the proposed similarity measures (SMs) we provide an example of a pattern recognition system with its application for decision-making
There are various parks and picnic areas in Islamabad where a large number of people visit on a daily basis

Summary

Introduction

Zadeh [1] conceived the concept of fuzzy sets (FSs) in 1965. In FSs, a function of memberships on a scale of {0, 1} was used to show the degree of membership (DM) of an element in a set with the degree of non-membership (DNM) calculated by subtracting DM from 1, i.e., DN M = 1 − DM. Atanassov [2] refined the concept from FSs to intuitionistic fuzzy sets (IFSs) which define DM and DNM separately, but have their full scope in the range of {0, 1}, i.e., DM + DN M ∈ [0, 1]. Atanassov’s model of IFSs has significant limitations, as the sum of DM and DNM might sometimes surpass the range of {0, 1}. Yager [4] introduced the concept of q-Rung Orthopair FSs (q-ROFSs). In q-ROFSs, the sum of qth power of DM and qth power of DNM is equal to or less than 1, i.e., DMq + DN Mq ∈ [0, 1]

Objectives

Results

Conclusion