Approximation Set of the Interval Set in Pawlak's Space
The interval set is a special set, which describes uncertainty of an uncertain concept or set Z with its two crisp boundaries named upper-bound set and lower-bound set. In this paper, the concept of similarity degree between two interval sets is defined at first, and then the similarity degrees betw...
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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/10.1155/2014/317387 |
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| author | Qinghua Zhang Jin Wang Guoyin Wang Feng Hu |
| author_facet | Qinghua Zhang Jin Wang Guoyin Wang Feng Hu |
| author_sort | Qinghua Zhang |
| collection | DOAJ |
| description | The interval set is a special set, which describes uncertainty of an uncertain concept or set Z with its two crisp boundaries named upper-bound set and lower-bound set. In this paper, the concept of similarity degree between two interval sets is defined at first, and then the similarity degrees between an interval set and its two approximations (i.e., upper approximation set R¯(Z) and lower approximation set R_(Z)) are presented, respectively. The disadvantages of using upper-approximation set R¯(Z) or lower-approximation set R_(Z) as approximation sets of the uncertain set (uncertain concept) Z are analyzed, and a new method for looking for a better approximation set of the interval set Z is proposed. The conclusion that the approximation set R0.5(Z) is an optimal approximation set of interval set Z is drawn and proved successfully. The change rules of R0.5(Z) with different binary relations are analyzed in detail. Finally, a kind of crisp approximation set of the interval set Z is constructed. We hope this research work will promote the development of both the interval set model and granular computing theory. |
| format | Article |
| id | doaj-art-db23f93b401a47a6b0b08fea3ee26e27 |
| institution | OA Journals |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-db23f93b401a47a6b0b08fea3ee26e272025-08-20T02:21:25ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/317387317387Approximation Set of the Interval Set in Pawlak's SpaceQinghua Zhang0Jin Wang1Guoyin Wang2Feng Hu3The Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaThe Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaThe Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaThe Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing 400065, ChinaThe interval set is a special set, which describes uncertainty of an uncertain concept or set Z with its two crisp boundaries named upper-bound set and lower-bound set. In this paper, the concept of similarity degree between two interval sets is defined at first, and then the similarity degrees between an interval set and its two approximations (i.e., upper approximation set R¯(Z) and lower approximation set R_(Z)) are presented, respectively. The disadvantages of using upper-approximation set R¯(Z) or lower-approximation set R_(Z) as approximation sets of the uncertain set (uncertain concept) Z are analyzed, and a new method for looking for a better approximation set of the interval set Z is proposed. The conclusion that the approximation set R0.5(Z) is an optimal approximation set of interval set Z is drawn and proved successfully. The change rules of R0.5(Z) with different binary relations are analyzed in detail. Finally, a kind of crisp approximation set of the interval set Z is constructed. We hope this research work will promote the development of both the interval set model and granular computing theory.http://dx.doi.org/10.1155/2014/317387 |
| spellingShingle | Qinghua Zhang Jin Wang Guoyin Wang Feng Hu Approximation Set of the Interval Set in Pawlak's Space The Scientific World Journal |
| title | Approximation Set of the Interval Set in Pawlak's Space |
| title_full | Approximation Set of the Interval Set in Pawlak's Space |
| title_fullStr | Approximation Set of the Interval Set in Pawlak's Space |
| title_full_unstemmed | Approximation Set of the Interval Set in Pawlak's Space |
| title_short | Approximation Set of the Interval Set in Pawlak's Space |
| title_sort | approximation set of the interval set in pawlak s space |
| url | http://dx.doi.org/10.1155/2014/317387 |
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