Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6858984 | International Journal of Approximate Reasoning | 2013 | 22 Pages |
Abstract
In this paper, a general framework for the study of dual fuzzy rough approximation operators determined by a fuzzy implication operator I in infinite universes of discourse is investigated. Lower and upper approximations of fuzzy sets with respect to a fuzzy approximation space in infinite universes of discourse are first introduced. Properties of I-fuzzy rough approximation operators are then examined. An operator-oriented characterization of fuzzy rough sets is further proposed, that is, I-fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper I-fuzzy set-theoretic operators guarantee the existence of different types of fuzzy relations which produce the same operators. Finally, a comparative study of I-fuzzy rough sets with fuzzy topological spaces is presented. It is proved that there exists a one-to-one correspondence between the set of all reflexive and T-transitive fuzzy approximation spaces and the set of all fuzzy Alexandrov spaces such that the lower and upper I-fuzzy rough approximation operators in a fuzzy approximation space are, respectively, the fuzzy interior and closure operators in a fuzzy topological space.
Related Topics
Physical Sciences and Engineering
Computer Science
Artificial Intelligence
Authors
Wei-Zhi Wu, Yee Leung, Ming-Wen Shao,