Five Kinds of Contradictory Relations and Opposite Relations in Inconsistent Knowledge

Inconsistent knowledge processing is an important problem in the study of knowledge, especially in fuzzy knowledge. In this paper, we consider that research of inconsistent knowledge should differentiate between contradictory concept and opposite concept. Based on this cognition, we discovered a sort of character on opposite concepts, which a pair of opposite concepts is fuzzy concepts if and only if there is medium concept between them, and five kinds of contradictory relations and opposite relations in the distinct knowledge and fuzzy knowledge were defined. Furthermore, we studied these relations using the medium predicate logic MF and the infinite-valued model Phi of MF, and obtained the conditions of processing these relations.