A Hesitant Soft Fuzzy Rough Set and its Applications
The difficulty of establishing a common membership degree is not because there is a margin of error or some possibility distribution values, but because there is a set of possible values. Based on hesitant fuzzy sets and soft sets, a hesitant soft fuzzy rough set model is proposed in this paper. Bas...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2019-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8906022/ |
| _version_ | 1818323709304242176 |
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| author | Ting Xie Zengtai Gong |
| author_facet | Ting Xie Zengtai Gong |
| author_sort | Ting Xie |
| collection | DOAJ |
| description | The difficulty of establishing a common membership degree is not because there is a margin of error or some possibility distribution values, but because there is a set of possible values. Based on hesitant fuzzy sets and soft sets, a hesitant soft fuzzy rough set model is proposed in this paper. Basic properties of hesitant soft fuzzy rough sets are investigated in detail. We obtain a decomposition theorem for a hesitant fuzzy binary relation, which states that every typical hesitant fuzzy binary relation on a set can be represented by a well-structured family of fuzzy binary relations on that set. Indeed, a hesitant fuzzy soft set can induce a hesitant fuzzy binary relation. Then we give the relationship between hesitant fuzzy rough sets and hesitant soft fuzzy rough sets. In addition, we prove a characterization theorem for the hesitant soft fuzzy rough set model, which shows that the lower and upper hesitant soft fuzzy rough approximations can be equivalently defined by using level sets of the hesitant fuzzy soft set. Finally, by analyzing the limitations and advantages in the existing literatures, we establish an approach to decision making problem based on the hesitant soft fuzzy rough set model proposed in this paper and give a practical example to illustrate the validity of the novel method. |
| first_indexed | 2024-12-13T11:17:00Z |
| format | Article |
| id | doaj.art-d2eb65e517294202937b63b7ae42e490 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-13T11:17:00Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-d2eb65e517294202937b63b7ae42e4902022-12-21T23:48:36ZengIEEEIEEE Access2169-35362019-01-01716776616778310.1109/ACCESS.2019.29541798906022A Hesitant Soft Fuzzy Rough Set and its ApplicationsTing Xie0https://orcid.org/0000-0002-0336-3662Zengtai Gong1https://orcid.org/0000-0001-5878-1506College of Mathematics and Statistics, Northwest Normal University, Lanzhou, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou, ChinaThe difficulty of establishing a common membership degree is not because there is a margin of error or some possibility distribution values, but because there is a set of possible values. Based on hesitant fuzzy sets and soft sets, a hesitant soft fuzzy rough set model is proposed in this paper. Basic properties of hesitant soft fuzzy rough sets are investigated in detail. We obtain a decomposition theorem for a hesitant fuzzy binary relation, which states that every typical hesitant fuzzy binary relation on a set can be represented by a well-structured family of fuzzy binary relations on that set. Indeed, a hesitant fuzzy soft set can induce a hesitant fuzzy binary relation. Then we give the relationship between hesitant fuzzy rough sets and hesitant soft fuzzy rough sets. In addition, we prove a characterization theorem for the hesitant soft fuzzy rough set model, which shows that the lower and upper hesitant soft fuzzy rough approximations can be equivalently defined by using level sets of the hesitant fuzzy soft set. Finally, by analyzing the limitations and advantages in the existing literatures, we establish an approach to decision making problem based on the hesitant soft fuzzy rough set model proposed in this paper and give a practical example to illustrate the validity of the novel method.https://ieeexplore.ieee.org/document/8906022/Rough setshesitant fuzzy setssoft setsfuzzy binary relationslevel sets |
| spellingShingle | Ting Xie Zengtai Gong A Hesitant Soft Fuzzy Rough Set and its Applications IEEE Access Rough sets hesitant fuzzy sets soft sets fuzzy binary relations level sets |
| title | A Hesitant Soft Fuzzy Rough Set and its Applications |
| title_full | A Hesitant Soft Fuzzy Rough Set and its Applications |
| title_fullStr | A Hesitant Soft Fuzzy Rough Set and its Applications |
| title_full_unstemmed | A Hesitant Soft Fuzzy Rough Set and its Applications |
| title_short | A Hesitant Soft Fuzzy Rough Set and its Applications |
| title_sort | hesitant soft fuzzy rough set and its applications |
| topic | Rough sets hesitant fuzzy sets soft sets fuzzy binary relations level sets |
| url | https://ieeexplore.ieee.org/document/8906022/ |
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