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Fuzzy Domination Graphs in Decision Support Tasks

Author

Listed:
  • Vladimir Sudakov

    (Department of Data Analysis and Machine Learning, Financial University under the Government of the Russian Federation, 125167 Moscow, Russia
    Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 125047 Moscow, Russia)

  • Alexander Zhukov

    (FGBSI The Federal Center of Analysis, 109316 Moscow, Russia)

Abstract

In decision support tasks, one often has to deal with uncertainty due to fuzzy judgments of the decision maker or the expert. This paper proposes methods that allow you to rank the alternatives based on fuzzy evaluations. This is achieved by using fuzzy weighted summation, fuzzy implication, a computation graph showing the criteria, and a fuzzy dominance graph showing the alternatives. If the criteria have equal importance, then fuzzy graphs corresponding to the dominance of each of the criteria are used. An algorithm that is used for both the transition from fuzzy dominance graphs and the ranking of alternatives is proposed. This algorithm is based on the idea of constructing Kemeny medians or other concordant rankings at a given confidence level in the existence of corresponding arcs. Computational experiments have shown the performance of these approaches. It is reasonable to apply them in problems that require complex expert evaluations with a large number of alternatives and criteria.

Suggested Citation

  • Vladimir Sudakov & Alexander Zhukov, 2023. "Fuzzy Domination Graphs in Decision Support Tasks," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2837-:d:1178206
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    References listed on IDEAS

    as
    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Rasul Kochkarov, 2022. "Multicriteria Optimization Problem on Prefractal Graph," Mathematics, MDPI, vol. 10(6), pages 1-17, March.
    3. Vladimir Sudakov, 2021. "Improving Air Transportation by Using the Fuzzy Origin–Destination Matrix," Mathematics, MDPI, vol. 9(11), pages 1-13, May.
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