Preference Modeling and Classification Through Implication-Based Gödel Integrals

Gödel integral, along with Sugeno integral, are two of the well-known qualitative integrals. In this work, we discuss the utility of Gödel integrals both in providing an ordinal representation of a preference relation and as a classifier in the case of ordinal data. Typically, a preference relation defined over a scale is converted into equivalence classes and a monotone mapping of these classes into levels is done using a qualitative integral, which requires the existence of a common capacity. In this work, we give necessary and sufficient conditions for such a common capacity to exist for a Gödel integral, comparing its applicability with Sugeno integral. With the help of these conditions, we discuss the suitability of the Gödel integral as a classifier. Through a novel perspective of discussing the dependence of class-specific features in the data and their expression levels, we offer a commentary on the type of datasets that are amenable for classification through a threshold-type Gödel integral.