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

Author

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  • Qianli Zhou

    (Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, China)

  • Hongming Mo

    (Library, Sichuan Minzu College, Kangding 626001, China)

  • Yong Deng

    (Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu 610054, China)

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.

Suggested Citation

  • Qianli Zhou & Hongming Mo & Yong Deng, 2020. "A New Divergence Measure of Pythagorean Fuzzy Sets Based on Belief Function and Its Application in Medical Diagnosis," Mathematics, MDPI, vol. 8(1), pages 1-20, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:142-:d:310910
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    References listed on IDEAS

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    1. Wu, Xingli & Liao, Huchang, 2019. "A consensus-based probabilistic linguistic gained and lost dominance score method," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1017-1027.
    2. Fu, Chao & Chang, Wenjun & Xue, Min & Yang, Shanlin, 2019. "Multiple criteria group decision making with belief distributions and distributed preference relations," European Journal of Operational Research, Elsevier, vol. 273(2), pages 623-633.
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    Cited by:

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    3. A. S. Wungreiphi & Fokrul Alom Mazarbhuiya & Mohamed Shenify, 2023. "On Extended L r -Norm-Based Derivatives to Intuitionistic Fuzzy Sets," Mathematics, MDPI, vol. 12(1), pages 1-19, December.
    4. Paul Augustine Ejegwa & Manasseh Terna Anum & Nasreen Kausar & Chukwudi Obinna Nwokoro & Nezir Aydin & Hao Yu, 2024. "New Fermatean Fuzzy Distance Metric and Its Utilization in the Assessment of Security Crises Using the MCDM Technique," Mathematics, MDPI, vol. 12(20), pages 1-27, October.
    5. Zaoli Yang & Xin Li & Harish Garg & Meng Qi, 2020. "Decision Support Algorithm for Selecting an Antivirus Mask over COVID-19 Pandemic under Spherical Normal Fuzzy Environment," IJERPH, MDPI, vol. 17(10), pages 1-27, May.
    6. Saidjon Shiralievich Tavarov & Pavel Matrenin & Murodbek Safaraliev & Mihail Senyuk & Svetlana Beryozkina & Inga Zicmane, 2023. "Forecasting of Electricity Consumption by Household Consumers Using Fuzzy Logic Based on the Development Plan of the Power System of the Republic of Tajikistan," Sustainability, MDPI, vol. 15(4), pages 1-14, February.
    7. Yograj Singh & Dinesh C. S. Bisht, 2025. "Enhanced dissimilarity measurement for pythagorean fuzzy sets in real-world scenarios," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 16(1), pages 402-424, January.

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