Dual Hesitant Fuzzy Sets
In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type 𝑛 fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/879629 |
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| _version_ | 1832566698982506496 |
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| author | Bin Zhu Zeshui Xu Meimei Xia |
| author_facet | Bin Zhu Zeshui Xu Meimei Xia |
| author_sort | Bin Zhu |
| collection | DOAJ |
| description | In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type 𝑛 fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, use a notion of nested interval to reflect their common ground, then propose an extension principle of DHFSs. Additionally, we give an example to illustrate the application of DHFSs in group forecasting. |
| format | Article |
| id | doaj-art-a7cfda2012414c648099c0634799e1de |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-a7cfda2012414c648099c0634799e1de2025-02-03T01:03:33ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/879629879629Dual Hesitant Fuzzy SetsBin Zhu0Zeshui Xu1Meimei Xia2School of Economics and Management, Southeast University Nanjing, Jiangsu 211189, ChinaSchool of Economics and Management, Southeast University Nanjing, Jiangsu 211189, ChinaSchool of Economics and Management, Southeast University Nanjing, Jiangsu 211189, ChinaIn recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type 𝑛 fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, use a notion of nested interval to reflect their common ground, then propose an extension principle of DHFSs. Additionally, we give an example to illustrate the application of DHFSs in group forecasting.http://dx.doi.org/10.1155/2012/879629 |
| spellingShingle | Bin Zhu Zeshui Xu Meimei Xia Dual Hesitant Fuzzy Sets Journal of Applied Mathematics |
| title | Dual Hesitant Fuzzy Sets |
| title_full | Dual Hesitant Fuzzy Sets |
| title_fullStr | Dual Hesitant Fuzzy Sets |
| title_full_unstemmed | Dual Hesitant Fuzzy Sets |
| title_short | Dual Hesitant Fuzzy Sets |
| title_sort | dual hesitant fuzzy sets |
| url | http://dx.doi.org/10.1155/2012/879629 |
| work_keys_str_mv | AT binzhu dualhesitantfuzzysets AT zeshuixu dualhesitantfuzzysets AT meimeixia dualhesitantfuzzysets |