Fuzzy relations based on two-dimensional vague partition from the perspective of axiomation

摘要

The axiomatic definition of fuzzy set, which is based on the axioms of membership degrees, has been introduced by Xiaodong Pan and Yang Xu. On this basis, this paper focuses on establishing the axiomatical foundation of membership degree for fuzzy relations (binary fuzzy relation). The concept of two-dimensional vague partition is introduced, on this basis, the concept of fuzzy relation in Zadeh's sense is redefined based on two-dimensional vague partition from the perspective of axiomatization. The results obtained in this paper can be easily extended to multiple fuzzy relations.