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An axiomatic approach to the measurement of the amount of interaction among criteria or players

机译：公理的方法来衡量标准或参与者之间的互动量

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摘要

In the framework of multicriteria decision making based on fuzzy measures or cooperative game theory, an axiomatization of the concept of amount of interaction index is given. It is based on four axioms: a natuua property called "absence of interaction", a boundary condition for which the index reduces to the Shapley or Banzhaf interaction index, apseudo-additivity axiom, and arecursivity property. The resulting index, which can be interpreted as a measure of the average degree of independence among criteria or players, takes a particularly simple and natural form for supermodular or submodular measures. The approach to the notion of interaction adopted in this paper can be seen as complementary to that recently adopted by Grabisch and Roubens.
机译：在基于模糊测度或合作博弈的多准则决策框架下，给出了交互指标量概念的公理化。它基于四个公理：称为“不存在相互作用”的自然属性，将索引减少为Shapley或Banzhaf相互作用索引的边界条件，伪加性公理和递归属性。所得的指数可以解释为标准或参与者之间平均独立程度的度量，对于超模数或亚模数度量采取特别简单自然的形式。本文中采用的交互概念方法可以看作是Grabisch和Roubens最近采用的方法的补充。

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