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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
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    References listed on IDEAS

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    1. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    2. 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.
    3. 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.
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