A new axiomatic foundation of partial comparability

The paper presents some results obtained in searching for a new axiomatic foundation for partial comparability (PC) in the frame of non-conventional preference modeling. The basic idea is to define an extended preference structure able to represent lack of information, uncertainty, ambiguity, multidimensional and conflicting preferences, using formal logic as the basic formalism.A four-valued paraconsistent logic is therefore described in the paper as a more suitable language for the purposes of the research. The concepts of partition, general binary relations properties, fundamental relational system of preferences (f.r.s.p.), maximal f.r.s.p. and well founded f.r.s.p. are then introduced and some theorems are demonstrated in order to provide the axiomatic foundation of PC. The main result obtained is a preference structure that is a maximal well founded f.r.s.p. This preference structure facilitates a more flexible, reliable and robust preference modeling. Moreover it can be viewed as a generalization of the conventional approach, so that all the results obtained until now can be used under it.Two examples are provided at the end of the paper in order to give an account of the operational potentialities of the new theory, mainly in the area of multicriteria decision aid and social choice theory. Further research directions conclude the paper.This research has been done while the first author was in the Université Libre de Bruxelles under the Research in Brussels actions.