A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis
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...
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MDPI AG
2020-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/1/142 |
| _version_ | 1819020046729478144 |
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| author | Qianli Zhou Hongming Mo Yong Deng |
| author_facet | Qianli Zhou Hongming Mo Yong Deng |
| author_sort | Qianli Zhou |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T03:44:59Z |
| format | Article |
| id | doaj.art-270df9af5e9648fdbe77b7935b28e93e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T03:44:59Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-270df9af5e9648fdbe77b7935b28e93e2022-12-21T19:17:06ZengMDPI AGMathematics2227-73902020-01-018114210.3390/math8010142math8010142A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical DiagnosisQianli Zhou0Hongming Mo1Yong Deng2Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, ChinaLibrary, Sichuan Minzu College, Kangding 626001, ChinaInstitute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, ChinaAs 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.https://www.mdpi.com/2227-7390/8/1/142pythagorean fuzzy setdempster–shafer evidence theorybasic probability assignmentmedical diagnosis |
| spellingShingle | Qianli Zhou Hongming Mo Yong Deng A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis Mathematics pythagorean fuzzy set dempster–shafer evidence theory basic probability assignment medical diagnosis |
| title | A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis |
| title_full | A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis |
| title_fullStr | A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis |
| title_full_unstemmed | A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis |
| title_short | A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis |
| title_sort | new divergence measure of pythagorean fuzzy sets based on belief function and its application in medical diagnosis |
| topic | pythagorean fuzzy set dempster–shafer evidence theory basic probability assignment medical diagnosis |
| url | https://www.mdpi.com/2227-7390/8/1/142 |
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