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Associated Statistical Parameters’ Aggregations in Interactive MADM

Author

Listed:
  • Gia Sirbiladze

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

  • Tariel Khvedelidze

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

Abstract

From recent studies, the concept of “monotone expectation” (ME) of Interactive Multi-Attribute Decision Making (MADM) is well known, which was developed for the case of different fuzzy sets. This article develops the concept of “monotone expectation” for such statistical parameters as variance, k -order moment and covariance. We investigate the problem of the definition of some statistical parameters, when the uncertainty is represented by a monotone measure—a fuzzy measure—instead of an additive measure. The study presents the concept of the definition of monotone statistical parameters based on the Choquet finite integral for the definition of monotone expectation, monotone variance, monotone k -order moment and monotone covariance. Associated statistical parameters are also presented—expectation, variance, k -order moment and covariance—which are defined in relation to associated probabilities of a fuzzy measure. It is shown that the monotone statistical parameters defined in the study are defined by one particular relevant associated statistical parameter out of the total number n ! of such parameters. It is also shown that the aggregations with monotone statistical parameters used in interactive MADM models take into account interactions of the focal elements of only one consonant structure from the n ! consonant structures of attributes. In order to take into account the interactions of the focal elements of all n ! consonant structures of attributes, the monotone statistical parameters were expanded into the F -associated statistical parameters. Expansion correctness implies that if dual second-order Choquet capacities are taken as the fuzzy measures of aggregation of the F -associated statistical parameters, then the F -associated statistical parameters coincide with the corresponding monotone statistical parameters. A scheme for embedding new aggregation operators, monotone statistical parameters and F -associated statistical parameters into the interactive MADM model has been developed. Specific numerical examples are presented to illustrate the obtained results.

Suggested Citation

  • Gia Sirbiladze & Tariel Khvedelidze, 2023. "Associated Statistical Parameters’ Aggregations in Interactive MADM," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:1061-:d:1074733
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    References listed on IDEAS

    as
    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. Fernando Reche & María Morales & Antonio Salmerón, 2020. "Construction of Fuzzy Measures over Product Spaces," Mathematics, MDPI, vol. 8(9), pages 1-18, September.
    3. Jun Li, 2020. "On Null-Continuity of Monotone Measures," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    4. 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.
    5. Coppi, Renato & D’Urso, Pierpaolo & Giordani, Paolo, 2012. "Fuzzy and possibilistic clustering for fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 915-927.
    6. Rong Zhang & Baabak Ashuri & Yong Deng, 2017. "A novel method for forecasting time series based on fuzzy logic and visibility graph," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 759-783, December.
    7. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2010. "Fuzzy p-value in testing fuzzy hypotheses with crisp data," Statistical Papers, Springer, vol. 51(1), pages 209-226, January.
    8. Fernando Reche & María Morales & Antonio Salmerón, 2020. "Statistical Parameters Based on Fuzzy Measures," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    9. 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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