Title: Comparisons between near open sets and rough approximations

Authors: M.K. El-Bably

Addresses: Department of Mathematics, Faculty of Science and Arts, Taibah University, Al-Madinah Al-Munawwarah, Saudi Arabia; Department of Mathematics, Faculty of Science, Tanta University, Egypt

Abstract: 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.

Keywords: j-neighbourhood spaces; rough sets; rough membership functions; fuzzy sets; topology; near open sets; rough approximations.

DOI: 10.1504/IJGCRSIS.2015.074749

International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2015 Vol.4 No.1, pp.64 - 83

Available online: 16 Feb 2016 *

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