Elicitation of Sugeno Integrals: A Version Space Learning Perspective

Abstract

Sugeno integrals can be viewed as multiple criteria aggregation functions which take into account a form of synergy between criteria. As such, Sugeno integrals constitute an important family of tools for modeling qualitative preferences defined on ordinal scales. The elicitation of Sugeno integrals starts from a set of data that associates a global evaluation assessment to situations described by multiple criteria values. A consistent set of data corresponds to a non-empty family of Sugeno integrals with which the data are compatible. This elicitation process presents some similarity with the revision process underlying the version space approach in concept learning, when new data are introduced. More precisely, the elicitation corresponds to a graded extension of version space learning, recently proposed in the framework of bipolar possibility theory. This paper establishes the relation between these two formal settings.