ABSTRACT In this paper, we introduce the notion of a cooperative game with multiple attributes where players can provide partial participations in multiple attributes and form coalitions. The power or influence of the players due to their multiple attributes is evaluated based on their memberships in the coalitions. Our game therefore, extends the notion of cooperative games with fuzzy coalitions. The Shapley function for this class of games is proposed as a rational and fair solution concept. Every fuzzy game stems out of a specific crisp game under the assumption that the players provide partial memberships in forming multiple coalitions simultaneously. We adopt similar techniques to obtain the cooperative games with multiple attributes from their crisp counterparts and subsequently determine their Shapley functions.

中文翻译：

---

多属性合作游戏

摘要 在本文中，我们介绍了具有多个属性的合作博弈的概念，其中玩家可以部分参与多个属性并形成联盟。由于玩家的多重属性，他们的权力或影响力是根据他们在联盟中的成员身份来评估的。因此，我们的游戏通过模糊联盟扩展了合作游戏的概念。此类博弈的 Shapley 函数被提出作为一个理性和公平的解决方案概念。每个模糊游戏都源于一个特定的清晰游戏，假设参与者在同时形成多个联盟时提供部分成员资格。我们采用类似的技术从他们的清晰对手那里获得具有多个属性的合作博弈，并随后确定他们的沙普利函数。