On Using the Shapley Value to Approximate the Choquet Integral in Cases of Uncertain Arguments

Abstract

In multicriteria decision making, the Choquet integral provides a commonly used method for the aggregation of the individual criteria satisfaction. Information about the criteria importance is expressed via a fuzzy measure on the set of criteria. One requirement in using the Choquet integral is to provide an ordering over the individual criteria satisfactions. When there exists some uncertainty regarding the criteria satisfactions, there typically exists some difficulty in providing this ordering. In an attempt to circumvent this difficulty, we suggest an approximation to the Choquet integral criteria aggregation that does not require an ordering. In this approximation, the criteria satisfactions are aggregated using as weights the Shapley index of the criteria. We provide an assessment of the merit of the approximation using the cardinality indices of the importance measure.