Stochastic Multiobjective Acceptability Analysis for the Choquet integral preference model and the scale construction problem

TL;DR

This paper integrates SMAA with the Choquet integral to provide robust decision support in MCDA, accounting for imprecision and preference data variability in criteria interactions and scale construction.

Contribution

It introduces a novel method combining SMAA with the Choquet integral to explore the entire space of compatible preference parameters for robust decision recommendations.

Findings

Enables exploration of preference parameter space for robust analysis

Handles criteria evaluated on different scales effectively

Provides probabilistic rankings considering preference imprecision

Abstract

The Choquet integral is a preference model used in Multiple Criteria Decision Aiding (MCDA) to deal with interactions between criteria. The Stochastic Multiobjective Acceptability Analysis (SMAA) is an MCDA methodology used to take into account imprecision or lack of data in the problem at hand. For example, SMAA permits to compute the frequency that an alternative takes the k-th rank in the whole space of the admissible preference parameters, e.g. in case evaluations on the considered criteria are aggregated through the weighted sum model, in the space of weights compatible with the preference information supplied by the Decision Maker (DM). In this paper, we propose to integrate the SMAA methodology with the Choquet integral preference model in order to get robust recommendations taking into account the whole space of preference parameters compatible with the DM's preference information. In case the alternatives are evaluated by all the criteria on a common scale, the preference parameters are given by the capacity expressing the non-additive weights, representing the importance of criteria and their interaction. If the criteria are instead evaluated on different scales, besides the capacity, preference parameters include the common scale on which the evaluations of criteria have to be recoded to be compared. Our approach permits to explore the whole space of preference parameters being capacities and common scales compatible with the DM's preference information.