Abstract:

Using rough set theory, we proposed the congruences induced by fuzzy (prime) ideals of an m-semilattice and studied the properties of the upper (lower) rough fuzzy approximation operators with respect to these congruences. Then we introduced the notions of rough fuzzy (prime) ideals of m-semilattice, and established the relationships between rough fuzzy (prime) ideals and fuzzy (prime) ideals and the relationships between rough fuzzy (prime) ideals and (prime) ideals of m-semilattices.

Key words: m-semilattice, upper (lower) rough fuzzy approximation operator, (fuzzy) ideal, rough fuzzy (prime) ideal