A new divergence measure of interval-valued pythagorean fuzzy sets and its application

N Arthi ,Mohana K

doi:10.26524/cm103

Abstract

As the extension of the Fuzzy sets (FSs) theory, the Interval-valued Pythagorean Fuzzy Sets (IVPFS) was introduced which play an important role in handling the uncertainty. The Pythagorean fuzzy sets (PFSs) proposed by Yager in 2013 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. How to measure the distance of Interval-valued Pythagorean fuzzy sets is still an open issue. Jensen–Shannon divergence is a useful distance measure in the probability distribution space. In order to efficiently deal with uncertainty in practical applications, this paper proposes a new divergence measure of Interval-valued Pythagorean fuzzy sets,which is based on the belief function in Dempster–Shafer evidence theory, and is called IVPFSDM distance. It describes the Interval-Valued Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of IVPFSs, which is the step in establishing a link between the IVPFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods.

Highlights

Distance measure plays a vital role in pattern recognition, information fusion, decision-making, and other fields
A general distance measurement of Pythagorean fuzzy sets (PFSs) was proposed by Chen [2], which is an extension of Euclidean distance and Hamming distance, and generates a reasonable result in multiple-criteria decision analysis
Song [16] presented a divergence measure of belief function based on Kullback–Leibler (KL) [10] divergence and Deng entropy[4], which has better results when dealing with the distance between basic probability assignments (BPAs) with greater uncertainty

Summary

Introduction

Distance measure plays a vital role in pattern recognition, information fusion, decision-making, and other fields. Xiao[9] presented a distance measurement of PFSs based on divergence, called PFSJS distance. The distance measurement in Interval-valued Pythagorean Fuzzy Set(IVPFS) is still an open issue, which attracts many researchers to explore the distance measurement of Interval -valued Pythagorean Fuzzy Sets(IVPFSs) and its related applications. This motives us to propose a new method to describe the Basic Probability Assignment(BPA) in the form of Interval-valued Pythagorean Fuzzy Set(IVPFS), and uses an improved divergence measurement of Basic Probability Assignments(BPAs) based on Jensen–Shannon divergence to measure the distance of Interval-valued Pythagorean Fuzzy Set(IVPFS)

Preliminaries

A New Divergence Measure Of IVPFSS

IVPFS Is Expressed in the Form of BPA

A New Divergence Measure of IVPFSs

5.Conclusions