Operations on Soft Sets Revisited
The concept of soft sets introduced by Molodtsov is a general mathematical tool for dealing with uncertainty. Just as the conventional set-theoretic operations of intersection, union, complement, and difference, some corresponding operations on soft sets have been proposed. Unfortunately, such opera...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/105752 |
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| _version_ | 1832556505337954304 |
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| author | Ping Zhu Qiaoyan Wen |
| author_facet | Ping Zhu Qiaoyan Wen |
| author_sort | Ping Zhu |
| collection | DOAJ |
| description | The concept of soft sets introduced by Molodtsov is a general mathematical tool for dealing with uncertainty. Just as the conventional set-theoretic operations of intersection, union, complement, and difference, some corresponding operations on soft sets have been proposed. Unfortunately, such operations cannot keep all classical set-theoretic laws true for soft sets. In this paper, we redefine the intersection, complement, and difference of soft sets and investigate the algebraic properties of these operations along with a known union operation. We find that the new operation system on soft sets inherits all basic properties of operations on classical sets, which justifies our definitions. |
| format | Article |
| id | doaj-art-d823f500e92b4d3d8c2ac4df6f94ca52 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-d823f500e92b4d3d8c2ac4df6f94ca522025-02-03T05:45:23ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/105752105752Operations on Soft Sets RevisitedPing Zhu0Qiaoyan Wen1School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaState Key Laboratory of Networking and Switching, Beijing University of Posts and Telecommunications, Beijing 100876, ChinaThe concept of soft sets introduced by Molodtsov is a general mathematical tool for dealing with uncertainty. Just as the conventional set-theoretic operations of intersection, union, complement, and difference, some corresponding operations on soft sets have been proposed. Unfortunately, such operations cannot keep all classical set-theoretic laws true for soft sets. In this paper, we redefine the intersection, complement, and difference of soft sets and investigate the algebraic properties of these operations along with a known union operation. We find that the new operation system on soft sets inherits all basic properties of operations on classical sets, which justifies our definitions.http://dx.doi.org/10.1155/2013/105752 |
| spellingShingle | Ping Zhu Qiaoyan Wen Operations on Soft Sets Revisited Journal of Applied Mathematics |
| title | Operations on Soft Sets Revisited |
| title_full | Operations on Soft Sets Revisited |
| title_fullStr | Operations on Soft Sets Revisited |
| title_full_unstemmed | Operations on Soft Sets Revisited |
| title_short | Operations on Soft Sets Revisited |
| title_sort | operations on soft sets revisited |
| url | http://dx.doi.org/10.1155/2013/105752 |
| work_keys_str_mv | AT pingzhu operationsonsoftsetsrevisited AT qiaoyanwen operationsonsoftsetsrevisited |