Generalized fuzzy rough approximation operators determined by fuzzy implicators
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...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Elsevier
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/58060 |
| _version_ | 1848760167367180288 |
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| author | Wu, W. Leung, Yee-Hong Shao, M. |
| author_facet | Wu, W. Leung, Yee-Hong Shao, M. |
| author_sort | Wu, W. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. © 2013 Elsevier Inc. All rights reserved. |
| first_indexed | 2025-11-14T10:11:28Z |
| format | Journal Article |
| id | curtin-20.500.11937-58060 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:11:28Z |
| publishDate | 2013 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-580602018-12-14T00:58:31Z Generalized fuzzy rough approximation operators determined by fuzzy implicators Wu, W. Leung, Yee-Hong Shao, M. 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. © 2013 Elsevier Inc. All rights reserved. 2013 Journal Article http://hdl.handle.net/20.500.11937/58060 10.1016/j.ijar.2013.05.004 Elsevier restricted |
| spellingShingle | Wu, W. Leung, Yee-Hong Shao, M. Generalized fuzzy rough approximation operators determined by fuzzy implicators |
| title | Generalized fuzzy rough approximation operators determined by fuzzy implicators |
| title_full | Generalized fuzzy rough approximation operators determined by fuzzy implicators |
| title_fullStr | Generalized fuzzy rough approximation operators determined by fuzzy implicators |
| title_full_unstemmed | Generalized fuzzy rough approximation operators determined by fuzzy implicators |
| title_short | Generalized fuzzy rough approximation operators determined by fuzzy implicators |
| title_sort | generalized fuzzy rough approximation operators determined by fuzzy implicators |
| url | http://hdl.handle.net/20.500.11937/58060 |