A New Method for Ordinal Classification Based on Comparisons with Representative Objects Through a Logical Predicate Regarding Preference Closeness

This chapter introduces a broad theoretical framework concerning the assignment rules applied in ordinal classification (sorting) methods. The proposed methods involve utilizing pairwise comparisons of actions against limiting profiles or subsets of representative elements from classes, also known as characteristic profiles. The crucial ideas behind this proposal are: (1) to model the decision maker’s preferences through a fuzzy logic predicate that expresses the “preference closeness” of objects to a certain aspiration point; (2) to use this predicate to define a reflexive binary preference relation; and (3) to apply a general approach that was recently published using the preference relation defined in (2). This new method is useful when (1) the decision makers can express their preferences in natural language statements that can be translated to a logic model; (2) the decision makers can set a few (even a single) objects as representative of their related class, or alternatively, they can set limiting objects between adjacent classes. The proposed framework links two important decision paradigms, namely, artificial intelligence and the relational paradigm.