On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria

TL;DR

This paper explores how integrals like Choquet, Sipos, and multilinear models extend pseudo-Boolean functions to model interactions among criteria in multicriteria decision making, emphasizing the use of difference information and neutral levels.

Contribution

It introduces the Sipos integral as a suitable, though non-unique, extension for aggregating interacting criteria, highlighting its properties and interaction modeling capabilities.

Findings

Sipos integral effectively models criterion interactions.

Inclusion of difference and neutral level information enhances aggregation.

Sipos integral offers a new perspective on criterion aggregation.

Abstract

The paper presents an analysis on the use of integrals defined for non-additive measures (or capacities) as the Choquet and the \Sipos{} integral, and the multilinear model, all seen as extensions of pseudo-Boolean functions, and used as a means to model interaction between criteria in a multicriteria decision making problem. The emphasis is put on the use, besides classical comparative information, of information about difference of attractiveness between acts, and on the existence, for each point of view, of a ``neutral level'', allowing to introduce the absolute notion of attractive or repulsive act. It is shown that in this case, the Sipos integral is a suitable solution, although not unique. Properties of the Sipos integral as a new way of aggregating criteria are shown, with emphasis on the interaction among criteria.