IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i4p518-d1335223.html
   My bibliography  Save this article

Associated Probabilities in Insufficient Expert Data Analysis

Author

Listed:
  • Gia Sirbiladze

    (Department of Computer Sciences, Iv. Javakhishvili Tbilisi State University, 0179 Tbilisi, Georgia)

  • Janusz Kacprzyk

    (Intelligent Systems Laboratory, Systems Research Institute, Polish Academy of Sciences, 01-447 Warsaw, Poland)

  • Tinatin Davitashvili

    (Department of Computer Sciences, Iv. Javakhishvili Tbilisi State University, 0179 Tbilisi, Georgia)

  • Bidzina Midodashvili

    (Department of Computer Sciences, Iv. Javakhishvili Tbilisi State University, 0179 Tbilisi, Georgia)

Abstract

Problems of modeling uncertainty and imprecision for the analysis of insufficient expert data (IED) are considered in the environment of interactive multi-group decision-making (MGDM). Based on the Choquet finite integral, a moments’ method for the IED is developed for the evaluation of the associated probabilities class (APC) of Choquet’s second-order capacity based on the informational entropy maximum principle. Based on the IED new approach of the lower and upper Choquet’s second-order capacities, identification is developed. The second pole of insufficient expert data, the data imprecision indicator, is presented in the form of a fuzzy subset and image on the alternatives set. In the environment of the Dempster–Shafer belief structure, connections between an associated possibilities class (APosC), with the APC, and an associated focal probabilities class (AFPC) are constructed. In the approach of A. Kaufman’s theory of expertons, based on the APosC and the AFPC unique fuzzy subset, the IED image on the alternatives set is constructed. Based on Sugeno’s finite integral most typical value (MTV), as a prediction on possible alternatives set, the IED is constructed. In the example, a sensitive and comparative analysis is provided for the evaluation of the new approach’s stability and reliability.

Suggested Citation

  • Gia Sirbiladze & Janusz Kacprzyk & Tinatin Davitashvili & Bidzina Midodashvili, 2024. "Associated Probabilities in Insufficient Expert Data Analysis," Mathematics, MDPI, vol. 12(4), pages 1-24, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:518-:d:1335223
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/4/518/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/4/518/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Merigó, José M. & Casanovas, Montserrat & Yang, Jian-Bo, 2014. "Group decision making with expertons and uncertain generalized probabilistic weighted aggregation operators," European Journal of Operational Research, Elsevier, vol. 235(1), pages 215-224.
    2. Gia Sirbiladze, 2016. "New Fuzzy Aggregation Operators Based on the Finite Choquet Integral — Application in the MADM Problem," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 517-551, May.
    Full references (including those not matched with items on IDEAS)

    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. Gia Sirbiladze & Otar Badagadze, 2017. "Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 245-279, January.
    2. Gia Sirbiladze & Anna Sikharulidze, 2018. "Extensions of Probability Intuitionistic Fuzzy Aggregation Operators in Fuzzy MCDM/MADM," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 621-655, March.
    3. Gia Sirbiladze & Irina Khutsishvili & Otar Badagadze & Mikheil Kapanadze, 2016. "More Precise Decision-Making Methodology in the Temporalized Body of Evidence. Application in the Information Technology Management," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(06), pages 1469-1502, November.
    4. Pingtao Yi & Qiankun Dong & Weiwei Li, 2021. "A family of IOWA operators with reliability measurement under interval-valued group decision-making environment," Group Decision and Negotiation, Springer, vol. 30(3), pages 483-505, June.
    5. Gia Sirbiladze & Tariel Khvedelidze, 2023. "Associated Statistical Parameters’ Aggregations in Interactive MADM," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    6. Marlenne G. Velazquez-Cazares & Anna M. Gil-Lafuente & Ernesto Leon-Castro & Fabio Blanco-Mesa, 2021. "Innovation capabilities measurement using fuzzy methodologies: a Colombian SMEs case," Computational and Mathematical Organization Theory, Springer, vol. 27(4), pages 384-413, December.
    7. Gao, Jianwei & Li, Ming & Liu, Huihui, 2015. "Generalized ordered weighted utility proportional averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 114-132.
    8. Merigó, José M. & Palacios-Marqués, Daniel & Zeng, Shouzhen, 2016. "Subjective and objective information in linguistic multi-criteria group decision making," European Journal of Operational Research, Elsevier, vol. 248(2), pages 522-531.
    9. Min Jiang & Rui Shen & Zhiqing Meng, 2019. "A Concession Equilibrium Solution Method without Weighted Aggregation Operators for Multiattribute Group Decision-Making Problems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-10, January.
    10. Martha B. Flores-Romero & Miriam E. Pérez-Romero & José Álvarez-García & María de la Cruz del Río-Rama, 2021. "Fuzzy Techniques Applied to the Analysis of the Causes and Effects of Tourism Competitiveness," Mathematics, MDPI, vol. 9(7), pages 1-17, April.
    11. Gia Sirbiladze, 2016. "New Fuzzy Aggregation Operators Based on the Finite Choquet Integral — Application in the MADM Problem," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 517-551, May.
    12. Liu, Bingsheng & Shen, Yinghua & Zhang, Wei & Chen, Xiaohong & Wang, Xueqing, 2015. "An interval-valued intuitionistic fuzzy principal component analysis model-based method for complex multi-attribute large-group decision-making," European Journal of Operational Research, Elsevier, vol. 245(1), pages 209-225.
    13. Li, Kevin W. & Wang, Zhou-Jing & Tong, Xiayu, 2016. "Acceptability analysis and priority weight elicitation for interval multiplicative comparison matrices," European Journal of Operational Research, Elsevier, vol. 250(2), pages 628-638.
    14. Gao, Jianwei & Li, Ming & Liu, Huihui, 2015. "Generalized ordered weighted utility averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making," European Journal of Operational Research, Elsevier, vol. 243(1), pages 258-270.
    15. Wenjun Chang & Chao Fu & Nanping Feng & Shanlin Yang, 2021. "Multi-criteria Group Decision Making with Various Ordinal Assessments," Group Decision and Negotiation, Springer, vol. 30(6), pages 1285-1314, December.
    16. Ignacio Montes & Enrique Miranda & Susana Montes, 2017. "Imprecise stochastic orders and fuzzy rankings," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 297-327, September.
    17. Tehreem Ayaz & Mohammad M. Al-Shomrani & Saleem Abdullah & Amjad Hussain, 2020. "Evaluation of Enterprise Production Based on Spherical Cubic Hamacher Aggregation Operators," Mathematics, MDPI, vol. 8(10), pages 1-40, October.
    18. Gia Sirbiladze, 2021. "Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment," Mathematics, MDPI, vol. 9(18), pages 1-36, September.
    19. Fu, Chao & Yang, Jian-Bo & Yang, Shan-Lin, 2015. "A group evidential reasoning approach based on expert reliability," European Journal of Operational Research, Elsevier, vol. 246(3), pages 886-893.
    20. Gia Sirbiladze & Teimuraz Manjafarashvili, 2022. "Connections between Campos-Bolanos and Murofushi–Sugeno Representations of a Fuzzy Measure," Mathematics, MDPI, vol. 10(3), pages 1-21, February.

    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:12:y:2024:i:4:p:518-:d:1335223. 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.