Axiomatizations and factorizations of Sugeno utility functions

TL;DR

This paper introduces a general framework for analyzing Sugeno utility functions in multicriteria decision making, providing axiomatizations and methods for their factorization into simpler components.

Contribution

It proposes the concept of pseudo-Sugeno integrals to generalize Sugeno integrals and offers solutions for factorizing Sugeno utility functions into compositions of integrals and local utility functions.

Findings

Provided axiomatizations for pseudo-Sugeno functions

Developed methods to factorize Sugeno utility functions

Extended understanding of multicriteria aggregation models

Abstract

In this paper we consider a multicriteria aggregation model where local utility functions of different sorts are aggregated using Sugeno integrals, and which we refer to as Sugeno utility functions. We propose a general approach to study such functions via the notion of pseudo-Sugeno integral (or, equivalently, pseudo-polynomial function), which naturally generalizes that of Sugeno integral, and provide several axiomatizations for this class of functions. Moreover, we address and solve the problem of factorizing a Sugeno utility function as a composition of a Sugeno integral with local utility functions, if such a factorization exists.