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AIMS Mathematics

2023, Volume 8, Issue 12: 30405-30418. doi: 10.3934/math.20231552
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Research article

On an axiomatization of the grey Banzhaf value

  • Faculty of Education, Department of Mathematics and Science Education, Canakkale Onsekiz Mart University, Canakkake 17100, Turky
  • Received: 28 July 2023 Revised: 23 October 2023 Accepted: 24 October 2023 Published: 08 November 2023

  • MSC : 90B70, 91A12

  • The Banzhaf value with grey data is a solution concept in cooperative grey games that has been extensively studied in the context of operations research. The author aims to define the traits of the Banzhaf value in cooperative grey games, where the values of coalitions are depicted as grey numbers within intervals. The grey Banzhaf value is defined by several axioms, including the grey dummy player, grey van den Brink fairness, and grey superadditivity. By presenting these axioms, this investigation contributes novel insights to the axiomatic characterization of the grey Banzhaf value, offering a distinct perspective. Finally, the study concludes by presenting applications in cooperative grey game models, thereby enriching the understanding of this concept.

    Citation: Mustafa Ekici. On an axiomatization of the grey Banzhaf value[J]. AIMS Mathematics, 2023, 8(12): 30405-30418. doi: 10.3934/math.20231552

    Related Papers:

  • The Banzhaf value with grey data is a solution concept in cooperative grey games that has been extensively studied in the context of operations research. The author aims to define the traits of the Banzhaf value in cooperative grey games, where the values of coalitions are depicted as grey numbers within intervals. The grey Banzhaf value is defined by several axioms, including the grey dummy player, grey van den Brink fairness, and grey superadditivity. By presenting these axioms, this investigation contributes novel insights to the axiomatic characterization of the grey Banzhaf value, offering a distinct perspective. Finally, the study concludes by presenting applications in cooperative grey game models, thereby enriching the understanding of this concept.


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