Preference information modeling by empty interaction index based on monotone measure

In this paper, we consider the monotone measure identification issue from the perspective of the Shapley importance and interaction index, and propose Shapely importance and interaction index oriented monotone measure identification methods. We investigate some properties of the probabilistic interaction indices of the empty set, analyze the meaning of the Shapely interaction index of the empty set in the context of multicriteria decision analysis, and propose the maximum and minimum empty set interaction principles based monotone easure identification methods.