Int. J. of Granular Computing, Rough Sets and Intelligent Systems   »   2014 Vol.3, No.4

 

 

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.

 

DOI: 10.1504/IJGCRSIS.2014.068022

 

Int. J. of Granular Computing, Rough Sets and Intelligent Systems, 2014 Vol.3, No.4, pp.257 - 271

 

Submission date: 21 Oct 2013
Date of acceptance: 12 Mar 2014
Available online: 10 Mar 2015

 

 

Editors Full text accessAccess for SubscribersPurchase this articleComment on this article