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The potential and consistency of the Owen value for fuzzy cooperative games with a coalition structure

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Abstract

This paper extends the potential function and consistency to the Owen value for fuzzy cooperative games with a coalition structure. First, we prove that the unique payoff index satisfying the potential function is the Owen value. Then, we characterize the Owen value for fuzzy cooperative games with a coalition structure by fuzzy balanced contributions and fuzzy consistency, respectively. Finally, an example in supply chain is given to illustrate the relationship between the Owen value and potential function for fuzzy cooperative games with a coalition structure and solve the problem of payoff distribution in supply chain under fuzzy environment.

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Notes

  1. Tsurumi et al. (2001) defined fuzzy games with Choquet integral form, the value of fuzzy coalition for fuzzy games with Choquet integral form is given as \(v_{C} (U) = \sum\limits_{l = 1}^{q(U)} {v_{0} ([U]_{{h_{l} }} )(h_{l} - h_{l - 1} )}\), for any \(U \in L(N)\), where \(Q(U) = \{ \left. {U(i)} \right|U(i) > 0,i \in N\}\) and \([U]_{{h_{l} }} = \{ \left. {i \in {\text{Supp}} U} \right|U(i) \ge h_{l} \}\). \(q(U)\) is the cardinality of \(Q(U)\). The elements in \(Q(U)\) are written in the increasing order as \(0 = h_{0} \le h_{1} \le \ldots \le h_{q(U)}\). Later, Meng et al. (2012) gave the definition of the Owen value for fuzzy cooperative games with a coalition structure and Choquet integral form.

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Acknowledgements

This work was supported by the Major Project for National Natural Science Foundation of China (No. 72091515), the Fundamental Research Funds for the Central Universities of Central South University (No. 2022ZZTS0344), the Natural Science Foundation of Changsha in China (No. kq2202112), and the Startup Foundation for Introducing Talent of NUIST (No. 2022r059).

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  1. School of Business, Central South University, Changsha, 410083, China

    Zijun Li & Fanyong Meng

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  1. Zijun Li
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  2. Fanyong Meng
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Correspondence to Fanyong Meng.

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Li, Z., Meng, F. The potential and consistency of the Owen value for fuzzy cooperative games with a coalition structure. Fuzzy Optim Decis Making 22, 387–414 (2023). https://doi.org/10.1007/s10700-022-09397-w

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