Qualitative Decision Theory with Sugeno Integrals

TL;DR

This paper develops an axiomatic framework for qualitative decision-making under uncertainty using Sugeno integrals, providing a median-based utility concept as a qualitative alternative to expected utility.

Contribution

It introduces a novel axiomatic foundation for Sugeno integral-based utility in qualitative decision theory, connecting it to Savage's preference axioms.

Findings

Sugeno integral acts as a median utility in qualitative decision models.

The framework unifies pessimistic and optimistic utilities via additional axioms.

Provides a formal justification for qualitative utilities based on necessity and possibility measures.

Abstract

This paper presents an axiomatic framework for qualitative decision under uncertainty in a finite setting. The corresponding utility is expressed by a sup-min expression, called Sugeno (or fuzzy) integral. Technically speaking, Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility. The axiomatic justification of Sugeno integral-based utility is expressed in terms of preference between acts as in Savage decision theory. Pessimistic and optimistic qualitative utilities, based on necessity and possibility measures, previously introduced by two of the authors, can be retrieved in this setting by adding appropriate axioms.