IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i1p142-d310910.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/1/142/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/1/142/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lei, Mingli, 2022. "Information dimension based on Deng entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    2. Zeeshan Ali & Tahir Mahmood & Miin-Shen Yang, 2020. "TOPSIS Method Based on Complex Spherical Fuzzy Sets with Bonferroni Mean Operators," Mathematics, MDPI, vol. 8(10), pages 1-19, October.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Min Xue & Chao Fu & Shanlin Yang, 2022. "A comparative analysis of probabilistic linguistic preference relations and distributed preference relations for decision making," Fuzzy Optimization and Decision Making, Springer, vol. 21(1), pages 71-97, March.
    2. Zhao, Meng & Xu, Chang & Zhao, Wenxian & Lin, Mingwei, 2023. "New energy vehicle online selection method considering attribute compensation relationship and aspiration strength," Journal of Retailing and Consumer Services, Elsevier, vol. 75(C).
    3. Chao Fu & Wenjun Chang, 2024. "A Markov Chain-Based Group Consensus Method with Unknown Parameters," Group Decision and Negotiation, Springer, vol. 33(5), pages 1019-1048, October.
    4. Gong, Zaiwu & Guo, Weiwei & Słowiński, Roman, 2021. "Transaction and interaction behavior-based consensus model and its application to optimal carbon emission reduction," Omega, Elsevier, vol. 104(C).
    5. Tang, Ming & Liao, Huchang, 2021. "From conventional group decision making to large-scale group decision making: What are the challenges and how to meet them in big data era? A state-of-the-art survey," Omega, Elsevier, vol. 100(C).
    6. Yu Zhang & Wen Jiang & Xinyang Deng, 2019. "Fault diagnosis method based on time domain weighted data aggregation and information fusion," International Journal of Distributed Sensor Networks, , vol. 15(9), pages 15501477198, September.
    7. Eduardo Fernández & Claudia Gómez-Santillán & Nelson Rangel-Valdez & Laura Cruz-Reyes, 2022. "Group Multi-Objective Optimization Under Imprecision and Uncertainty Using a Novel Interval Outranking Approach," Group Decision and Negotiation, Springer, vol. 31(5), pages 945-994, October.
    8. Zhi Wen & Huchang Liao & Ruxue Ren & Chunguang Bai & Edmundas Kazimieras Zavadskas & Jurgita Antucheviciene & Abdullah Al-Barakati, 2019. "Cold Chain Logistics Management of Medicine with an Integrated Multi-Criteria Decision-Making Method," IJERPH, MDPI, vol. 16(23), pages 1-21, December.
    9. Huimin Xiao & Shouwen Wu & Chunsheng Cui, 2022. "The Research on Consistency Checking and Improvement of Probabilistic Linguistic Preference Relation Based on Similarity Measure and Minimum Adjustment Model," Mathematics, MDPI, vol. 10(9), pages 1-18, April.
    10. Chao Song & Jian-Qiang Wang & Jun-Bo Li, 2020. "New Framework for Quality Function Deployment Using Linguistic Z-Numbers," Mathematics, MDPI, vol. 8(2), pages 1-20, February.
    11. Liguo Fei & Jun Xia & Yuqiang Feng & Luning Liu, 2019. "A novel method to determine basic probability assignment in Dempster–Shafer theory and its application in multi-sensor information fusion," International Journal of Distributed Sensor Networks, , vol. 15(7), pages 15501477198, July.
    12. Sumin Yu & Zhijiao Du & Xuanhua Xu, 2021. "Hierarchical Punishment-Driven Consensus Model for Probabilistic Linguistic Large-Group Decision Making with Application to Global Supplier Selection," Group Decision and Negotiation, Springer, vol. 30(6), pages 1343-1372, December.
    13. Ran Fang & Huchang Liao, 2021. "Emergency material reserve location selection by a time-series-based evidential reasoning approach under bounded rationality," Quality & Quantity: International Journal of Methodology, Springer, vol. 55(4), pages 1397-1417, August.
    14. Xiaohong Chen & Hui Wang & Xihua Li, 2024. "Doctor recommendation under probabilistic linguistic environment considering patient’s risk preference," Annals of Operations Research, Springer, vol. 341(1), pages 555-581, October.
    15. Roman Kaminskiy & Nataliya Shakhovska & Jana Kajanová & Yurii Kryvenchuk, 2021. "Method of Distinguishing Styles by Fractal and Statistical Indicators of the Text as a Sequence of the Number of Letters in Its Words," Mathematics, MDPI, vol. 9(19), pages 1-16, September.
    16. Namin, Farhad Samimi & Ghadi, Aliakbar & Saki, Farshad, 2022. "A literature review of Multi Criteria Decision-Making (MCDM) towards mining method selection (MMS)," Resources Policy, Elsevier, vol. 77(C).
    17. Li, Yanhong & Kou, Gang & Li, Guangxu & Peng, Yi, 2022. "Consensus reaching process in large-scale group decision making based on bounded confidence and social network," European Journal of Operational Research, Elsevier, vol. 303(2), pages 790-802.
    18. Xiaohan Yan & Yi Liu & Tiezhong Liu & Yan Chen, 2025. "Research on the Mechanism of Social Emotion Formation in Public Emergencies Based on the DeGroot Model," Mathematics, MDPI, vol. 13(6), pages 1-28, March.
    19. Mehrbakhsh Nilashi & Abbas Mardani & Huchang Liao & Hossein Ahmadi & Azizah Abdul Manaf & Wafa Almukadi, 2019. "A Hybrid Method with TOPSIS and Machine Learning Techniques for Sustainable Development of Green Hotels Considering Online Reviews," Sustainability, MDPI, vol. 11(21), pages 1-21, October.
    20. Juan Antonio Morente-Molinera & Francisco Javier Cabrerizo & Sergio Alonso & Ignacio Javier Pérez & Enrique Herrera-Viedma, 2020. "Assisting Users in Decisions Using Fuzzy Ontologies: Application in the Wine Market," Mathematics, MDPI, vol. 8(10), pages 1-18, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:142-:d:310910. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.