Choquet capacity identification for multiple criteria sorting problems: A novel proposal based on Stochastic Acceptability Multicriteria Analysis

Abstract

The Choquet integral is an aggregation operator widely used to deal with interacting criteria in multiple criteria decision analysis (MCDA). A practical problem regarding the use of the Choquet integral is the identification of its parameters, which are known as Choquet capacity. While capacity identification has received considerable attention in the context of ranking problems, it is difficult to find solutions tailored to sorting problems, which is the focus of this paper. We propose a novel method based on the Stochastic Acceptability Multicriteria Analysis (SMAA), by introducing the concept of feasible categorization scenarios. Moreover, two novel SMAA-based descriptive measures are proposed in order to provide valuable information for decision aiding, including the interpretation of the Choquet capacity and the possibility of exploiting the space of capacities by considering the decision makers’ initial preferences. Another feature of our proposal is the ability of dealing with unbalanced three-dimensional decision arrays. Numerical experiments with synthetic data were conducted to assess the proposed method. Furthermore, the applicability of our proposal is also attested to a case study related to the evaluation of research institutions.