A New Characterization of Compact Sets in Fuzzy Number Spaces
We give a new characterization of compact subsets of the fuzzy number space equipped with the level convergence topology. Based on this, it is shown that compactness is equivalent to sequential compactness on the fuzzy number space endowed with the level convergence topology. Our results imply that...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/820141 |
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| _version_ | 1849402556531343360 |
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| author | Huan Huang Congxin Wu |
| author_facet | Huan Huang Congxin Wu |
| author_sort | Huan Huang |
| collection | DOAJ |
| description | We give a new characterization of compact subsets of the fuzzy number
space equipped with the level convergence topology. Based on this, it is shown that compactness is equivalent to sequential compactness on the fuzzy number space endowed with the level convergence topology. Our results imply that some previous compactness criteria are wrong. A counterexample also is given to validate this judgment. |
| format | Article |
| id | doaj-art-96aa3e83c8214e49a9b076e726b7d61d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-96aa3e83c8214e49a9b076e726b7d61d2025-08-20T03:37:30ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/820141820141A New Characterization of Compact Sets in Fuzzy Number SpacesHuan Huang0Congxin Wu1Department of Mathematics, Jimei University, Xiamen 361021, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaWe give a new characterization of compact subsets of the fuzzy number space equipped with the level convergence topology. Based on this, it is shown that compactness is equivalent to sequential compactness on the fuzzy number space endowed with the level convergence topology. Our results imply that some previous compactness criteria are wrong. A counterexample also is given to validate this judgment.http://dx.doi.org/10.1155/2013/820141 |
| spellingShingle | Huan Huang Congxin Wu A New Characterization of Compact Sets in Fuzzy Number Spaces Abstract and Applied Analysis |
| title | A New Characterization of Compact Sets in Fuzzy Number Spaces |
| title_full | A New Characterization of Compact Sets in Fuzzy Number Spaces |
| title_fullStr | A New Characterization of Compact Sets in Fuzzy Number Spaces |
| title_full_unstemmed | A New Characterization of Compact Sets in Fuzzy Number Spaces |
| title_short | A New Characterization of Compact Sets in Fuzzy Number Spaces |
| title_sort | new characterization of compact sets in fuzzy number spaces |
| url | http://dx.doi.org/10.1155/2013/820141 |
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