MOPIC Properties in the Representation of Preferences by a 2-Additive Choquet Integral

Abstract

In the context of Multiple Criteria Decision aiding MCDA, we present necessary conditions to obtain a representation of a cardinal information by a Choquet integral w.r.t a 2-additive capacity. A cardinal information is a preferential information provided by a Decision Maker DM containing a strict preference, a quaternary and indifference relations. Our work is focused on the representation of a cardinal information by a particular Choquet integral defined by a 2-additive capacity. Used as an aggregation function, it arises as a generalization of the arithmetic mean, taking into account the interaction between two criteria. Then, it is a good compromise between simple models like arithmetic mean and complex models like general Choquet integral. We consider also the set of fictitious alternatives called binary alternatives or binary actions from which the Choquet integral w.r.t a 2-additive capacity can be entirely specified. The proposed MOPIC MOnotonicity of Preferential Information for Cardinal conditions can be viewed as an alternative to balanced cyclones which are complex necessary and sufficient conditions, used in the characterization of a 2-additive Choquet integral through a cardinal information.