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New Fuzzy Aggregation Operators Based on the Finite Choquet Integral — Application in the MADM Problem

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  • Gia Sirbiladze

    (Department of Computer Sciences, IV. Javakhishvili Tbilisi State University 13, University Street, Tbilisi 0186, Georgia)

Abstract

In this paper, new generalizations of the probabilistic averaging operator — Associated Fuzzy Probabilistic Averaging (As-PA and As-FPA) and Immediate Probabilistic Fuzzy Ordered Weighted Averaging (As-IP-OWA and As-IP-FOWA) operators are presented in the environment of fuzzy uncertainty. An uncertainty is presented by associated probabilities of a fuzzy measure. Expert’s evaluations as arguments of the aggregation operators are described by a variable, values of which are compatibility levels on the states of nature defined in positive real or triangular fuzzy numbers (TFNs). Two propositions on the As-FPA operator are proved: (1) The As-FPA operator for the fuzzy measure — capacity of order two coincides with the finite Choquet Averaging (CA) Operator; (2) the As-FPA operator coincides with the FPA operator when a probability measure is used in the role of a fuzzy measure. Analogous propositions for the As-IP-FOWA operator are proved. Some propositions on the connection of the As-FPA and As-IP-FOWA operators are also proved. Information measures — Orness and Divergence for the constructed operators are defined. Some propositions on the connections of these parameters with the corresponding parameters of the finite CA Operator are proved. Two illustrative examples on the applicability of the As-FPA and As-IP-FOWA operators are presented: (1) Several variants of the As-FPA and As-IP-FOWA operators are used for comparison of decision-making results for the problems regarding the fiscal policy of a country; (2) The As-FPA operator is used in the Multi-attribute decision-making (MADM) problem of choosing the best version of the students’ project.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijitdm:v:15:y:2016:i:03:n:s0219622016500127
    DOI: 10.1142/S0219622016500127
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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.
    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 & 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.
    4. 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.
    5. Gia Sirbiladze & Tariel Khvedelidze, 2023. "Associated Statistical Parameters’ Aggregations in Interactive MADM," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    6. 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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