Axiomatic approaches of fuzzy concept operators

In formal concept analysis, various fuzzy generalizations of formal concepts have been made. The fuzzy concept operators defined under the condition that the truth values (degrees) coming from a complete residuated lattice satisfy many interesting properties. Conversely, fuzzy concept operators can be characterized in terms of their properties. In this paper, the axiomatic approaches in the theory of fuzzy formal concept analysis based on a complete residuated lattice are presented. In the axiomatic approach, the fuzzy conceptual knowledge system is defined, and axiom sets satisfied by the fuzzy conceptual knowledge system are stated. It is proved that axioms of the fuzzy conceptual knowledge system guarantee the existence of certain types of binary fuzzy relations producing the same fuzzy formal concepts. The independence of axiom sets characterizing the fuzzy conceptual knowledge system is examined.