A NEW AXIOMATIC FOUNDATION OF PARTIAL COMPARABILITY

The paper presents some results obtained in searching for a new axioma tic foundation for partial comparability (PC) in the frame of non-conv entional preference modeling. The basic idea is to define an extended preference structure able to represent lack of information, uncertaint y, ambiguity, multidimensional and conflicting preferences, using form al 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 re lations 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 f oundation of PC. The main result obtained is a preference structure th at is a maximal well founded f.r.s.p. This preference structure facili tates a more flexible, reliable and robust preference modeling. Moreov er 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 e xamples are provided at the end of the paper in order to give an accou nt of the operational potentialities of the new theory, mainly in the area of multicriteria decision aid and social choice theory. Further r esearch directions conclude the paper.