Many mathematical conceptions, such as group, closure (interior) operator, and approximation operator in rough set, can be characterized by one axiom, respectively. Focusing on four kinds of widely used lattice-valued closure (interior) operators, which are natural extensions of closure (interior) operators, we use one axiom to characterize each of them. Then by using these characterizations, we prove that two pairs of L-fuzzy covering-based upper (lower) approximation operators are some lattice-valued closure (interior) operators.
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