A new axiomatic foundation of the partial comparability theory

The paper presents some results obtained in searching a new axiomatic foundation for the partial comparability theory (PCT) 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. Then the concepts of partition, general binary relations properties, foundamental relational system of preferences (f.r.s.p.), maximal f.r.s.p. and well founded f.r.s.p. are introduced and some theorems are demonstrated in order to provide the axiomatic foundation of the PCT. The main result obtained is a preference structure that is a maximal well founded f.r.s.p.. This preference structure enables 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 under it can be used. 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.