Consistency in preference modelling

Abstract

Coherence in preference modelling has been introduced in standard decision making frameworks, taking many different formulations in each context, as a need in order to assure consistent decision making procedures. In the classical crisp context, preferences use to be assumed to be transitive in order to assure consistent behavior. In the fuzzy framework, a standard assumption is the condition of max-min transitivity; alternatively, consistency has been understood by Cutello-Montero as a rationality measure, therefore allowing degrees of performance. In this paper we stress that, neither in the crisp nor in the fuzzy case, consistency should not be necessarily associated with underlying linear orders.