Qualitative Decision Theory with Sugeno Integrals
This work provides a theoretical foundation for qualitative decision theory, addressing uncertainty in finite settings, but it appears incremental as it builds on existing concepts like necessity and possibility measures.
The paper tackles the problem of qualitative decision-making under uncertainty by proposing an axiomatic framework based on Sugeno integrals, which serve as a qualitative counterpart to expected utility, and shows that existing pessimistic and optimistic utilities can be derived by adding specific axioms.
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.