Correlation Measures of Dual Hesitant Fuzzy Sets
The dual hesitant fuzzy sets (DHFSs) were proposed by Zhu et al. (2012), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Correlation measures analysis is an important research topic. In this paper, we define the correlation measures f...
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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/10.1155/2013/593739 |
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| _version_ | 1832556822457745408 |
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| author | Lei Wang Mingfang Ni Lei Zhu |
| author_facet | Lei Wang Mingfang Ni Lei Zhu |
| author_sort | Lei Wang |
| collection | DOAJ |
| description | The dual hesitant fuzzy sets (DHFSs) were proposed by Zhu et al. (2012), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Correlation measures analysis is an important research topic. In this paper, we define the correlation measures for dual hesitant fuzzy information and then discuss their properties in detail. One numerical example is provided to illustrate these correlation measures. Then we present a direct transfer algorithm with respect to the problem of complex operation of matrix synthesis when reconstructing an equivalent correlation matrix for clustering DHFSs. Furthermore, we prove that the direct transfer algorithm is equivalent to transfer closure algorithm, but its asymptotic time complexity and space complexity are superior to the latter. Another real world example, that is, diamond evaluation and classification, is employed to show the effectiveness of the association coefficient and the algorithm for clustering DHFSs. |
| format | Article |
| id | doaj-art-77c9697112414d6c87550a3321f94f6b |
| 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-77c9697112414d6c87550a3321f94f6b2025-02-03T05:44:23ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/593739593739Correlation Measures of Dual Hesitant Fuzzy SetsLei Wang0Mingfang Ni1Lei Zhu2 Institute of Communication Engineering, PLA University of Science and Technology, Nanjing, Jiangsu 210007, China Institute of Communication Engineering, PLA University of Science and Technology, Nanjing, Jiangsu 210007, China Institute of Communication Engineering, PLA University of Science and Technology, Nanjing, Jiangsu 210007, ChinaThe dual hesitant fuzzy sets (DHFSs) were proposed by Zhu et al. (2012), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Correlation measures analysis is an important research topic. In this paper, we define the correlation measures for dual hesitant fuzzy information and then discuss their properties in detail. One numerical example is provided to illustrate these correlation measures. Then we present a direct transfer algorithm with respect to the problem of complex operation of matrix synthesis when reconstructing an equivalent correlation matrix for clustering DHFSs. Furthermore, we prove that the direct transfer algorithm is equivalent to transfer closure algorithm, but its asymptotic time complexity and space complexity are superior to the latter. Another real world example, that is, diamond evaluation and classification, is employed to show the effectiveness of the association coefficient and the algorithm for clustering DHFSs.http://dx.doi.org/10.1155/2013/593739 |
| spellingShingle | Lei Wang Mingfang Ni Lei Zhu Correlation Measures of Dual Hesitant Fuzzy Sets Journal of Applied Mathematics |
| title | Correlation Measures of Dual Hesitant Fuzzy Sets |
| title_full | Correlation Measures of Dual Hesitant Fuzzy Sets |
| title_fullStr | Correlation Measures of Dual Hesitant Fuzzy Sets |
| title_full_unstemmed | Correlation Measures of Dual Hesitant Fuzzy Sets |
| title_short | Correlation Measures of Dual Hesitant Fuzzy Sets |
| title_sort | correlation measures of dual hesitant fuzzy sets |
| url | http://dx.doi.org/10.1155/2013/593739 |
| work_keys_str_mv | AT leiwang correlationmeasuresofdualhesitantfuzzysets AT mingfangni correlationmeasuresofdualhesitantfuzzysets AT leizhu correlationmeasuresofdualhesitantfuzzysets |