Roughness in basic algebras

We introduce rough approximations into basic algebras. After investigating elementary properties of the upper (lower) approximations in basic algebras and discussing the convexity of these two approximations in linearly ordered basic algebras, we generalize related results for MV-algebras, lattice ordered effect algebras, and orthomodular lattices to basic algebras. We also study the relationship between upper (lower) rough ideals of basic algebras and upper (lower) approximations of their homomorphic images.