{P, Q, I, J} — Preference Structures

This paper is concerned with preference models including four relations: strict preference (P), weak preference (Q), indifference (I) and incomparability (J). The purpose is to establish conditions allowing to represent these four relations by numerical functions and thresholds, in order to generalize previous results concerning complete or partial semiorders and interval orders, pseudo-orders and {P, Q, I} — preference structures.