The characterizations of upper approximation operators based on coverings.

In this paper, We propose a condition of symmetry for the covering C in a covering-based approximation space (U , C) . By using this condition, we obtain general, topological and intuitive characterizations of the covering C for two types of covering-based upper approximation operators being closure operators. We investigate axiomatic systems for apr ¯ S and discuss the relationships among upper approximation operators. We also give a description of (U , C) in terms of information exchange systems when these operators are closure ones. We also solve an open problem raised by Ge et al. [ABSTRACT FROM AUTHOR]