In Int. J. Comput. Inf. Sci. 11, 341-356 (1982; Zbl 0501.68053
) the rough top equality between subsets of a finite set was introduced by the second author. In Ann. Soc. Math. Pol., Ser. IV, Fundam. Inf. 6, 289-296 (1983; Zbl 0522.68094
) the rough top equality was proved by the authors to be a congruence on a certain semilattice. In this article, we characterize rough top equalities among all congruences of the mentioned semilattice. A similar result is obtained for rough bottom equalities.