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A fuzzy value for the fuzzy TU-game based on the relative group marginal contribution of coalition with restricted size

Published: 15 August 2023 Publication History

Abstract

Considering the group marginal contribution of coalitions (with size no larger than k), we study the cooperative game (transferable utility game (TU-game)) with a fuzzy payoff (i.e., fuzzy TU-game). In order to reflect the impact of the coalition's size on the group contribution, the fuzzy relative group's marginal contribution (i.e., fuzzy RGMC) is introduced, and a new fuzzy value (i.e., the k-lateral per-capita value) is then proposed for the fuzzy TU-game based on the fuzzy RGMC. The k-lateral per-capita value is an extended form of the fuzzy Shapley value, where the coalition is restricted in size and the group contribution is considered. Similar to the fuzzy Shapley value, the k-lateral per-capita value satisfies the common axioms in the fuzzy TU-game, such as efficiency, symmetry and additivity, but not the null player property. In addition, the potential function of the fuzzy TU-game is extended, and the k-lateral per-capita value is characterized by a potential function. The proposed new value (i.e., k-lateral per-capita value) can be used as a solution for the fuzzy TU-game but it also considers the RGMC of a coalition with restricted size.

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            Published In

            cover image Fuzzy Sets and Systems
            Fuzzy Sets and Systems  Volume 465, Issue C
            Aug 2023
            434 pages

            Publisher

            Elsevier North-Holland, Inc.

            United States

            Publication History

            Published: 15 August 2023

            Author Tags

            1. Cooperative game
            2. Fuzzy
            3. Group contribution
            4. Relative marginal contribution

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