Poset valued intuitionistic preference relations

Abstract

It is known that in every finite poset each element can be presented as a join of completely join-irreducible elements. This representation is used here to justify a new notion of poset-valued reciprocal (preference) relations and also the intuitionistic version of this definition. Join-irreducible elements would represent pieces of information representing grade of preference in this framework. It is demonstrated that no restriction on type of a poset is needed for developing the intuitionistic approach, except that the poset should be bounded with the top element T and the bottom element B (T representing the total preference). Some properties are proved and connections with previous definitions are shown. It is demonstrated that the new definition is in a sense more general (and in some aspects more convenient) than previous ones.