A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis

Abstract

As the extension of the fuzzy sets (FSs) theory, the intuitionistic fuzzy sets (IFSs) play an important role in handling the uncertainty under the uncertain environments. The Pythagoreanfuzzy 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 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 Pythagorean fuzzy sets, which is based on the belief function in Dempster–Shafer evidence theory, and is called PFSDM distance. It describes the Pythagorean fuzzy sets in the form of basic probability assignments (BPAs) and calculates the divergence of BPAs to get the divergence of PFSs, which is the step in establishing a link between the PFSs and BPAs. Since the proposed method combines the characters of belief function and divergence, it has a more powerful resolution than other existing methods. Additionally, an improved algorithm using PFSDM distance is proposed in medical diagnosis, which can avoid producing counter-intuitive results especially when a data conflict exists. The proposed method and the magnified algorithm are both demonstrated to be rational and practical in applications.

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Entailment for intuitionistic fuzzy sets based on generalized belief structures

“…In real life, there are a lot of uncertainties in the real world. To address the uncertainties, many mathematical theories are proposed, such as probability theory, 1 fuzzy sets (FS), 2 Dempster‐Shafer evidence theory, 3,4 intuitionistic fuzzy sets (IFS), 5,6 information quality, 7–11 Z‐number, 12 fuzzy reasoning, 13–15 D‐number, 16–18 entropy function, 19–22 and belief structure 23,24 . Among these theories and models, the IFS 25 considering the degree of hesitancy, membership, and non‐membership of objects, can deal with the uncertainties more flexibly and accurately, which has been used in many fields widely, 26 such as the uncertainty decision making, 27,28 pattern recognition 29 and so on.…”