A Review of Construction and Representation Results for Fuzzy Weak Orders

Weak orders, i.e. reflexive, transitive, and complete binary relations, are among the most fundamental concepts in preference modeling. It is wellknown that weak orders are nothing else but linear orders of equivalence classes, where the corresponding equivalence relation is the symmetric kernel of the weak order. If the underlying set of alternatives X is finite, a weak order can be represented by a single score function [2].