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Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making

Author

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  • Gia Sirbiladze

    (Department of Computer Sciences, Iv. Javakhishvili Tbilisi State University, 13, University St., Tbilisi 0186, Georgia, USA)

  • Otar Badagadze

    (Department of Computer Sciences, Iv. Javakhishvili Tbilisi State University, 13, University St., Tbilisi 0186, Georgia, USA)

Abstract

Associated Intuitionistic Fuzzy Probabilistic Averaging (As-IFPA) and Associated Intuitionistic Fuzzy Probabilistic Geometric (As-IFPG) operators based on the Choquet integral and an associated probability class of a fuzzy measure are constructed. Propositions on the correctness of the extensions are proved: (1) The As-IFPA (As-IFPG) operator for the fuzzy measure — capacity of order two coincides with the Intuitionistic Fuzzy Choquet Averaging (Intuitionistic Fuzzy Choquet Geometric) operator; (2) The As-IFPA (As-IFPG) operator coincides with the Intuitionistic Fuzzy Probabilistic Averaging (Intuitionistic Fuzzy Probabilistic Geometric) operator when a probability measure is used in the role of a fuzzy measure. Connections between the constructed operators and the compositions of dual triangular norms (Tp,Sp) and (Tmin,Smax) are constructed. The conjugate connections between the constructed operators are shown. Two illustrative examples on the applicability of the As-IFPA and As-IFPG operators are presented. Several variants of the new operators (1) for the decision-making problem regarding the fiscal policy of a country; (2) for the decision-making problem regarding the best global supplier selection according to the core competencies of suppliers for a manufacturing company are used. Interactions and dependencies among all the combinations of the criteria in the decision-making process are considered.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijitdm:v:16:y:2017:i:01:n:s0219622016500449
    DOI: 10.1142/S0219622016500449
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    References listed on IDEAS

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    7. Gia Sirbiladze & Koba Gelashvili & Irina Khutsishvili & Anna Sikharulidze, 2015. "Temporalized Structure of Bodies of Evidence in the Multi-Criteria Decision-Making Model," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 565-596.
    8. Sirbiladze, Gia & Khutsishvili, Irina & Ghvaberidze, Bezhan, 2014. "Multistage decision-making fuzzy methodology for optimal investments based on experts’ evaluations," European Journal of Operational Research, Elsevier, vol. 232(1), pages 169-177.
    9. 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.
    10. Guangxu Li & Gang Kou & Changsheng Lin & Liang Xu & Yi Liao, 2015. "Multi-attribute decision making with generalized fuzzy numbers," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(11), pages 1793-1803, November.
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    Cited by:

    1. 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.
    2. Gia Sirbiladze & Tariel Khvedelidze, 2023. "Associated Statistical Parameters’ Aggregations in Interactive MADM," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    3. 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.

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