A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators
Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued enviro...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/783940 |
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| _version_ | 1832558143606882304 |
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| author | Tianyu Xue Zhan’ao Xue Huiru Cheng Jie Liu Tailong Zhu |
| author_facet | Tianyu Xue Zhan’ao Xue Huiru Cheng Jie Liu Tailong Zhu |
| author_sort | Tianyu Xue |
| collection | DOAJ |
| description | Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators. |
| format | Article |
| id | doaj-art-ed460fa81b3a4e92919f2d5c3f7fb627 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-ed460fa81b3a4e92919f2d5c3f7fb6272025-02-03T01:33:09ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/783940783940A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation OperatorsTianyu Xue0Zhan’ao Xue1Huiru Cheng2Jie Liu3Tailong Zhu4College of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, ChinaCollege of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, ChinaCollege of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaCollege of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, ChinaCollege of Computer and Information Engineering, Henan Normal University, Xinxiang 453007, ChinaRough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators.http://dx.doi.org/10.1155/2014/783940 |
| spellingShingle | Tianyu Xue Zhan’ao Xue Huiru Cheng Jie Liu Tailong Zhu A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators The Scientific World Journal |
| title | A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators |
| title_full | A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators |
| title_fullStr | A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators |
| title_full_unstemmed | A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators |
| title_short | A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators |
| title_sort | novel method of the generalized interval valued fuzzy rough approximation operators |
| url | http://dx.doi.org/10.1155/2014/783940 |
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