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Notes on the lattice of fuzzy rough sets with crisp reference sets.
- Source :
-
International Journal of Approximate Reasoning . Nov2020, Vol. 126, p124-132. 9p. - Publication Year :
- 2020
-
Abstract
- Since the theory of rough sets was introduced by Zdzislaw Pawlak, several approaches have been proposed to combine rough set theory with fuzzy set theory. In this paper, we examine one of these approaches, namely fuzzy rough sets with crisp reference sets, from a lattice-theoretic point of view. We connect the lower and upper approximations of a fuzzy relation R to the approximations of the core and support of R. We also show that the lattice of fuzzy rough sets corresponding to a fuzzy equivalence relation R and the crisp subsets of its universe is isomorphic to the lattice of rough sets for the (crisp) equivalence relation E , where E is the core of R. We establish a connection between the exact (fuzzy) sets of R and the exact (crisp) sets of the support of R. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ROUGH sets
*FUZZY sets
*SET theory
*MATHEMATICAL equivalence
Subjects
Details
- Language :
- English
- ISSN :
- 0888613X
- Volume :
- 126
- Database :
- Academic Search Index
- Journal :
- International Journal of Approximate Reasoning
- Publication Type :
- Periodical
- Accession number :
- 146194557
- Full Text :
- https://doi.org/10.1016/j.ijar.2020.08.007