Title :
Topological Spaces for Fuzzy Rough Sets Determined by Fuzzy Implication Operators
Author :
Wu, Wei-Zhi ; Lin, Peirong
Author_Institution :
Sch. of Math., Phys. & Inf. Sci., Zhejiang Ocean Univ., Zhoushan, China
Abstract :
In this paper, a dual pair of lower and upper fuzzy rough approximation operators determined by a fuzzy implication operator are defined and their properties are presented. Topological structures of fuzzy rough sets are then investigated. It is shown that the lower and upper fuzzy rough approximation operators are, respectively, an interior operator and a closure operator in a fuzzy topological space if and only if the fuzzy binary relation is reflexive and transitive.
Keywords :
fuzzy set theory; rough set theory; closure operator; fuzzy binary relation; fuzzy implication operators; fuzzy rough approximation operators; fuzzy rough sets; interior operator; topological spaces; Boundary conditions; Fuzzy set theory; Fuzzy sets; Fuzzy systems; Information science; Mathematics; Oceans; Physics; Rough sets; Set theory; fuzzy implication operators; fuzzy rough sets; rough sets; topological spaces;
Conference_Titel :
Fuzzy Systems and Knowledge Discovery, 2009. FSKD '09. Sixth International Conference on
Conference_Location :
Tianjin
Print_ISBN :
978-0-7695-3735-1
DOI :
10.1109/FSKD.2009.375
