On relationships between revised rough fuzzy approximation operators and fuzzy topological spaces. (1st January 2014)

• Record Type: Journal Article
• Authors: Abd El-Monsef, M.E.; El-Gayar, M.A.; Aqeel, R.M.
• Is Part Of: International journal of granular computing, rough sets and intelligent systems. Volume 3:Number 4(2014)
• Page Start: 257
• Page End: 271
• Publication Date: 2014-01-01
• Subjects: rough fuzzy sets -- revised rough fuzzy sets -- approximation operators -- inverse serial relations -- fuzzy topological spaces; Intelligent agents (Computer science) -- Periodicals; 006.3
• DOI: 10.1504/IJGCRSIS.2014.068022
• Languages: English
• ISSNs: 1757-2703

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.