Comparisons between near open sets and rough approximations

The present paper is devoted to introduce the new concepts 'j-near approximations' and studying its applications. In fact, these operators can be considered as easy tools for removing the vagueness (uncertainty) of rough sets. The basic notions of j-near approximations introduced and sufficiently illustrated. Comparisons between the accuracy of these types of approximations are superimposed. We further investigated some new generalised definitions for rough membership functions. Accordingly, several types of fuzzy sets constructed. Finally, several examples given to indicate counter connections.