New Consistency Properties for Preference Relations

Abstract

Consistency of preference relations is associated with the study of the transitivity property. This chapter presents a set of properties or restrictions to be satisfied by preference relations to make consistent choices when dealing with preference relations. In the multiplicative model, a multiplicative preference relation is consistent when it verifies the multiplicative consistency property. In the additive model, a fuzzy preference relation is considered consistent when it verifies the additive consistency property. However, there exists a conflict between the multiplicative and additive consistency properties and the scales used to assign preference values to judgments. There exist many arguments to support that a change in the scales used in the multiplicative and fuzzy models seems unpractical and unrealistic. Therefore, the only possible solution to overcome the existing conflict seems to be a change of the definition of the consistency properties. This chapter introduces the concepts of T-additive consistency property in the case of fuzzy preference relations and T-multiplicative consistency property for multiplicative preference relations, which consist of a relaxation of the additive, and multiplicative consistency properties.