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.
Highlights
With the development of fuzzy mathematics, medical diagnosis has addressed more and more attention from the research society of applied computer mathematics
Calculates the divergence of basic probability assignments (BPAs) to get the divergence of Pythagoreanfuzzy sets (PFSs), which is the step in establishing a link between the PFSs and BPAs
This paper proposes a new method to describe the PFSs in the form of BPAs, and uses an improverd divergence measurement of BPAs based on Jensen–Shannon divergence to measure the distance of PFSs
Summary
With the development of fuzzy mathematics, medical diagnosis has addressed more and more attention from the research society of applied computer mathematics. Wei [56] proposed a PFS measurement method based on cosine function and applied it to medical diagnosis to achieve an ideal result. It is well known that the hesitancy expresses the uncertainty of membership and non-membership, so finding a proper method to distribute hesitancy to membership and non-membership can more reasonably handle the distance of PFSs. The basic probability assignment (BPA) in evidence theory presented by Dempster–Shafer [58,59] unifies uncertainty in a new set, and can handle various uncertainty reasonably. The related concepts and properties of Pythagorean fuzzy set (PFS), basic probability assignment (BPA), the Jensen–Shannon divergence, and some widely applied methods of measuring distance are introduced. The merits and uses of the PFSDM distance are summarized and the future direction of algorithm improvement is expected
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