A note on operations of hesitant fuzzy sets
In this paper, properties of operations and algebraic structures of hesitant fuzzy sets are investigated. Semilattices of hesitant fuzzy sets with union and intersection are discussed, respectively. By using ⊕ and ⊗ operators, the commutative monoid of hesitant fuzzy sets is pro...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2015-04-01
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| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/25868592.pdf |
| _version_ | 1818543406790475776 |
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| author | Zheng Pei Liangzhong Yi |
| author_facet | Zheng Pei Liangzhong Yi |
| author_sort | Zheng Pei |
| collection | DOAJ |
| description | In this paper, properties of operations and algebraic structures of hesitant fuzzy sets are investigated. Semilattices of hesitant fuzzy sets with union and intersection are discussed, respectively. By using ⊕ and ⊗ operators, the commutative monoid of hesitant fuzzy sets is provided, moreover, the lattice and distributive lattice of hesitant fuzzy sets are defined on the equivalence class of hesitant fuzzy sets. Based on the distributive lattice of hesitant fuzzy sets, the residuated lattices of hesitant fuzzy sets are constructed by residual implications, which are induced by intersection and ⊗, respectively. From the theoretical point of view, algebraic structures of hesitant fuzzy sets are useful for approximate reasoning and decision making to deal with hesitancy of information. |
| first_indexed | 2024-12-11T22:34:58Z |
| format | Article |
| id | doaj.art-b986e712ba074034af36546f7844c39f |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-12-11T22:34:58Z |
| publishDate | 2015-04-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-b986e712ba074034af36546f7844c39f2022-12-22T00:48:00ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832015-04-018210.1080/18756891.2015.1001947A note on operations of hesitant fuzzy setsZheng PeiLiangzhong YiIn this paper, properties of operations and algebraic structures of hesitant fuzzy sets are investigated. Semilattices of hesitant fuzzy sets with union and intersection are discussed, respectively. By using ⊕ and ⊗ operators, the commutative monoid of hesitant fuzzy sets is provided, moreover, the lattice and distributive lattice of hesitant fuzzy sets are defined on the equivalence class of hesitant fuzzy sets. Based on the distributive lattice of hesitant fuzzy sets, the residuated lattices of hesitant fuzzy sets are constructed by residual implications, which are induced by intersection and ⊗, respectively. From the theoretical point of view, algebraic structures of hesitant fuzzy sets are useful for approximate reasoning and decision making to deal with hesitancy of information.https://www.atlantis-press.com/article/25868592.pdfhesitant fuzzy setsoperationsthe latticethe residuated lattice |
| spellingShingle | Zheng Pei Liangzhong Yi A note on operations of hesitant fuzzy sets International Journal of Computational Intelligence Systems hesitant fuzzy sets operations the lattice the residuated lattice |
| title | A note on operations of hesitant fuzzy sets |
| title_full | A note on operations of hesitant fuzzy sets |
| title_fullStr | A note on operations of hesitant fuzzy sets |
| title_full_unstemmed | A note on operations of hesitant fuzzy sets |
| title_short | A note on operations of hesitant fuzzy sets |
| title_sort | note on operations of hesitant fuzzy sets |
| topic | hesitant fuzzy sets operations the lattice the residuated lattice |
| url | https://www.atlantis-press.com/article/25868592.pdf |
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