Difference operators on fuzzy sets.

Based on the properties of the difference operator on crisp sets, a fuzzy difference operator in fuzzy logic is defined as a continuous binary operator on the closed unit interval with some boundary conditions. In this paper, the structures and properties of fuzzy difference operators are studied. The main results are: (1) Using the axiomatic approach, some generalizations of classical tautologies for fuzzy difference operators are obtained. (2) Based on the model theoretic approach, the fuzzy difference operator constructed by a nilpotent t-norm and a strong negation is characterized. (3) the paper discusses the relationship between the fuzzy difference operator and symmetric difference operator which was raised in [3]. • The difference operator in the Boolean logic is extended to the fuzzy setting. • Using the axiomatic and model theoretic approaches, the generalizations of classical tautologies are obtained. • The relationship between the fuzzy difference operator and symmetric difference operator is obtained. [ABSTRACT FROM AUTHOR]