Preference structures and co-comparability graphs

Order structures such as linear orders, weak orders, semiorders and interval orders are often considered as models of a decision maker’s preferences. This paper introduces and studies new order structures characterized by their symmetric part belonging to certain classes of co-comparability graphs. It outlines possible interpretations and suggest special representations of these structures and points out their potential use for approximating relations obtained through a multicriteria aggregation procedure. It provides various characterizations of the new structures (as well as of older ones) in terms of minimal forbidden configurations and by algebraic conditions.