This paper constructs ℒ-covering fuzzy variable precision rough set and mainly studies some properties of type I and type II ℒ-covering fuzzy lower and upper approximation operators of ℒ-fuzzy sets on X. Topology properties of type I and type II ℒ-covering fuzzy lower and upper approximation operators are also discussed through a fuzzy interior operator and fuzzy closure operator. Moreover, we investigate the dual properties and compare between ℒ-covering fuzzy variable precision rough approximation operators.
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