In this paper, we consider roughness in m-semilattices, which combine the ∨-semilattice structure and the operation · of a semigroup. Firstly, we propose some kinds of equivalence relations on m-semilattices and investigate the properties of Pawlak rough sets w.r.t. them. Secondly, by replacing equivalence classes in Pawlak rough approximations with neighborhoods, we introduce and study minimal neighborhood approximation operators on m-semilattices, and obtain some order properties of the set of all fixed points of minimal neighborhood approximation operators. Finally, we present the definition of fuzzy rough sets based on fuzzy coverings of m-semilattices, discuss some fundamental properties of fuzzy rough sets and investigate relations between fuzzy rough sets and fuzzy coverings.
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