Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making
Molodtsov’s soft set theory is a newly emerging mathematical tool to handle uncertainty. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. This paper aims to extend the classical soft sets to hesitant fuzzy soft sets which are combined by the soft sets...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/643785 |
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| _version_ | 1850171350573907968 |
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| author | Fuqiang Wang Xihua Li Xiaohong Chen |
| author_facet | Fuqiang Wang Xihua Li Xiaohong Chen |
| author_sort | Fuqiang Wang |
| collection | DOAJ |
| description | Molodtsov’s soft set theory is a newly emerging mathematical tool to handle uncertainty. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. This paper aims to extend the classical soft sets to hesitant fuzzy soft sets which are combined by the soft sets and hesitant fuzzy sets. Then, the complement, “AND”, “OR”, union and intersection operations are defined on hesitant fuzzy soft sets. The basic properties such as DeMorgan’s laws and the relevant laws of hesitant fuzzy soft sets are proved. Finally, with the help of level soft set, the hesitant fuzzy soft sets are applied to a decision making problem and the effectiveness is proved by a numerical example. |
| format | Article |
| id | doaj-art-9cf23bc5abfb44dc9e05d5fdf4ab1c74 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9cf23bc5abfb44dc9e05d5fdf4ab1c742025-08-20T02:20:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/643785643785Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision MakingFuqiang Wang0Xihua Li1Xiaohong Chen2School of Business, Central South University, Changsha, Hunan 410083, ChinaSchool of Business, Central South University, Changsha, Hunan 410083, ChinaSchool of Business, Central South University, Changsha, Hunan 410083, ChinaMolodtsov’s soft set theory is a newly emerging mathematical tool to handle uncertainty. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. This paper aims to extend the classical soft sets to hesitant fuzzy soft sets which are combined by the soft sets and hesitant fuzzy sets. Then, the complement, “AND”, “OR”, union and intersection operations are defined on hesitant fuzzy soft sets. The basic properties such as DeMorgan’s laws and the relevant laws of hesitant fuzzy soft sets are proved. Finally, with the help of level soft set, the hesitant fuzzy soft sets are applied to a decision making problem and the effectiveness is proved by a numerical example.http://dx.doi.org/10.1155/2014/643785 |
| spellingShingle | Fuqiang Wang Xihua Li Xiaohong Chen Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making Journal of Applied Mathematics |
| title | Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making |
| title_full | Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making |
| title_fullStr | Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making |
| title_full_unstemmed | Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making |
| title_short | Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making |
| title_sort | hesitant fuzzy soft set and its applications in multicriteria decision making |
| url | http://dx.doi.org/10.1155/2014/643785 |
| work_keys_str_mv | AT fuqiangwang hesitantfuzzysoftsetanditsapplicationsinmulticriteriadecisionmaking AT xihuali hesitantfuzzysoftsetanditsapplicationsinmulticriteriadecisionmaking AT xiaohongchen hesitantfuzzysoftsetanditsapplicationsinmulticriteriadecisionmaking |