Purpose

This paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. This means that one observes a lower and an upper bound of the considered coalitions. This is very important, for example, from a computational and algorithmic viewpoint. The authors notice that the approach is general, since the characteristic function fuzzy interval values may result from solving general optimization problems.

Design/methodology/approach

This paper deals with cooperative games whose characteristic functions are fuzzy intervals, i.e. the worth of a coalition is not a real number but a fuzzy interval. A situation in which a finite set of players can obtain certain fuzzy payoffs by cooperation can be described by a cooperative fuzzy interval game.

Findings

In this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty.

Originality/value

In this paper, the authors extend a class of solutions for cooperative games that all have some egalitarian flavour in the sense that they assign to every player some initial payoff and distribute the remainder of the worth v(N) of the grand coalition N equally among all players under fuzzy uncertainty. Examples of such solutions are the centre-of-gravity of the imputation-set value, shortly denoted by CIS value, egalitarian non-separable contribution value, shortly denoted by ENSC value and the equal division solution. Further, the authors discuss a class of equal surplus sharing solutions consisting of all convex combinations of the CIS value, the ENSC value and the equal division solution. The authors provide several characterizations of this class of solutions on variable and fixed player set. Specifications of several properties characterize specific solutions in this class.

中文翻译：

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关于模糊区间等盈分摊解

目的

本文研究了特征函数为模糊区间的合作博弈，即联盟的价值不是实数而是模糊区间。这意味着人们观察到所考虑的联盟的下限和上限。例如，从计算和算法的角度来看，这非常重要。作者注意到该方法是通用的，因为特征函数模糊区间值可能来自解决一般优化问题。

设计/方法/方法

本文研究了特征函数为模糊区间的合作博弈，即联盟的价值不是实数而是模糊区间。一个有限的参与者集合可以通过合作获得一定的模糊收益的情况可以用合作模糊区间博弈来描述。

发现

在这篇论文中，作者为合作博弈扩展了一类解决方案，这些解决方案都具有某种平等主义的味道，因为他们为每个参与者分配了一些初始收益，并将大联盟N的剩余价值v ( N )平均分配给所有玩家都处于模糊不确定性。

原创性/价值

在这篇论文中，作者为合作博弈扩展了一类解决方案，这些解决方案都具有某种平等主义的味道，因为他们为每个玩家分配了一些初始收益并分配了大联盟N的价值v ( N )的剩余部分在模糊不确定性下的所有参与者之间平等。此类解决方案的示例是插补集值的重心，简称为 CIS 值，平等主义的不可分离贡献值，简称为 ENSC 值和等分解决方案。此外，作者还讨论了一类由 CIS 值、ENSC 值和等分解的所有凸组合组成的等盈共享解。作者在可变和固定玩家集上提供了此类解决方案的几个特征。几个属性的规范表征了此类中的特定解决方案。