Complete, consistent and compatible preference relations

Preferences are usually formalized by means of relations. If one takes into account not only strict preference and indifference but also incomparability, preference relations are not complete by necessity. Two preference relations may also contradict each other. The aim of this paper is to develop an appropriate framework to systematize these connections between preference relations. This is done by defining and analysing when a preference relation is more complete, consistent and compatible in respect to another one. As a possible application the conceptual framework can be used to compare the preference relations induced by dominance and PROMETHEE and to examine not necessarily complete preference relations which come from utility theory.