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Difference operators on fuzzy sets
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DOI：10.1016/j.ijar.2024.109254.png)
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Abstract
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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].
Keywords:
Fuzzy difference operator
T-norm
T-conorm
Negation
Symmetric difference operator
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