Title: On relationships between revised rough fuzzy approximation operators and fuzzy topological spaces
Authors: M.E. Abd El-Monsef; M.A. El-Gayar; R.M. Aqeel
Addresses: Department of Mathematics, Faculty of Science, Tanta University, Egypt ' General Authority for Meteorology, Egypt ' Department of Mathematics, Faculty of Science, Tanta University, Egypt
Abstract: In this paper, revised rough fuzzy lower and revised rough fuzzy upper approximations of fuzzy sets are defined. Properties of revised rough fuzzy approximation operators are examined. We first show that an inverse serial revised rough fuzzy approximation space can induce a fuzzy Alexandrov space. Relationships between revised rough fuzzy approximation operators and fuzzy topological spaces are then discussed. We then prove that the revised lower and upper rough fuzzy approximation operators are, respectively, the fuzzy interior operator and fuzzy closure operator if and only if the binary relation in the crisp approximation space is inverse serial. Finally, we prove that a strong inverse serial revised rough fuzzy approximation space can produce a fuzzy clopen topological space.
Keywords: rough sets; fuzzy sets; revised rough fuzzy sets; approximation operators; inverse serial relations; fuzzy topological spaces.
International Journal of Granular Computing, Rough Sets and Intelligent Systems, 2014 Vol.3 No.4, pp.257 - 271
Received: 21 Oct 2013
Accepted: 12 Mar 2014
Published online: 10 Mar 2015 *