ON TRANSITIVITY OF STRICT PREFERENCE RELATIONS

A general notion of a strict preference relation associated with a preference relation valued in a semilattice with difference is introduced. If a preference relation is valued in a linear scale then the associated strict preference relation is always transitive. In contrast, for some nonlinear scales transitivity of a preference relation does not imply transitivity of the associated strict preference relation. The identity (x AND y) - z = (x - z) AND (y - z) is characteristic for the class of lower semilattices with difference for which associated strict preference relations preserve transitivity of preference relations.