基于均分贡献值的直觉模糊合作博弈Shapley值

Intuitionistic fuzzy shapley value for cooperative game based on the equal contribution value

  • 摘要: 在解决现实场景中的合作博弈问题时,局中人的合作收益分配策略既追求效益原则,又重视公平原则. 构建带有Choquet积分的直觉模糊平方贡献超量,以局中人不满意度最小为目标求出均分贡献值,并用其取代传统Shapley值中的边际贡献,从而得到一类改进的直觉模糊合作博弈Shapley值. 经证明,该直觉模糊合作博弈Shapley值满足单调性条件,可采用简易算法获得分配策略,从而避免模糊数运算带来的不确定性放大等问题. 此外,该值还满足经典Shapley值具有的有效性、对称性、可加性和匿名性等性质. 通过案例分析,将其与现有的三种模糊合作博弈解对比可知,该值计算误差小,满足有效性且兼顾分配的公平性,说明该值在不丢失经典Shapley值的性质的前提下,更有利于解决实际的经济管理问题.

     

    Abstract: When solving cooperative game problems in real-world scenarios, the cooperative profit allocation strategies of players pursue both efficiency and fairness. This study constructs an intuitionistic fuzzy squared contribution excess with Choquet integral, aims to minimize players' dissatisfaction to derive the equal distribution of contribution values, and replaces the marginal contributions in the traditional Shapley value with these values, thereby obtaining an improved Shapley value for intuitionistic fuzzy cooperative games. It is proved that this Shapley value satisfies the monotonicity condition and can be used to obtain allocation strategies through a simple algorithm, avoiding issues such as uncertainty amplification caused by fuzzy number operations. Additionally, this value maintains the properties of the classical Shapley value, including efficiency, symmetry, additivity, and anonymity. Through a case study, comparing it with three existing fuzzy cooperative game solutions shows that this value has small calculation errors, satisfies efficiency, and balances the fairness of allocation. This indicates that while preserving the properties of the classical Shapley value, it is more conducive to solving practical economic management problems.

     

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