Canonical Hierarchical Decomposition of Choquet Integral Over Finite Set with Respect to Null Additive Fuzzy Measure

Abstract

In this paper, we provide the necessary and sufficient condition for a Choquet integral model to be decomposable into a canonical hierarchical Choquet integral model constructed by hierarchical combinations of some ordinary Choquet integral models. This condition is characterized by the pre-Znclusion-Exclusion Covering (pre-IEC). Moreover, we show that the pre-IEC is the subdivision of an IEC and that the additive hierarchical structure is the most fundamental one on considering a hierarchical decomposition of the Choquet integral model.