Qualitative Decision Theory with Sugeno Integrals

This paper presents an axiomatic framework for qualitative decision under uncertainty in a finite setting. The corresponding util­ ity is expressed by a sup-min expression, called Sugeno (or fuzzy) integral. Techni­ cally 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 qualita­ tive utilities, based on necessity and possibil­ ity measures, previously introduced by two of the authors, can be retrieved in this setting by adding appropriate axioms.