Bi-Fuzzy S-Approximation Spaces
The S-approximation spaces are significant extension of the rough set model and have been widely applied in intelligent decision-making. However, traditional S-approximation spaces are limited to two crisp universes, whereas bi-fuzzy universes (i.e., two distinct fuzzy domains) are more prevalent in...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/2/324 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588011090477056 |
|---|---|
| author | Ronghai Wang Xiaojie Xie Huilai Zhi |
| author_facet | Ronghai Wang Xiaojie Xie Huilai Zhi |
| author_sort | Ronghai Wang |
| collection | DOAJ |
| description | The S-approximation spaces are significant extension of the rough set model and have been widely applied in intelligent decision-making. However, traditional S-approximation spaces are limited to two crisp universes, whereas bi-fuzzy universes (i.e., two distinct fuzzy domains) are more prevalent in practical applications. To bridge this gap, this study introduces the bi-fuzzy S-approximation spaces (BFS approximation spaces) as an advancement of knowledge space theory’s fuzzy extension. Upper and lower approximation operators are formally defined, and the properties of BFS approximation spaces under various operations, such as complement, intersection and union are systematically explored. Special attention is given to a significant form of these operators, under which the monotonicity and complementary compatibility of BFS approximation spaces are rigorously analyzed. These results not only extend the theoretical framework of S-approximation spaces but also pave the way for further exploration of fuzzy extensions within knowledge space theory. |
| format | Article |
| id | doaj-art-aea7e283f3e447f3b4947bfaf24f0fe1 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-aea7e283f3e447f3b4947bfaf24f0fe12025-01-24T13:40:11ZengMDPI AGMathematics2227-73902025-01-0113232410.3390/math13020324Bi-Fuzzy S-Approximation SpacesRonghai Wang0Xiaojie Xie1Huilai Zhi2School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, ChinaSchool of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, ChinaSchool of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, ChinaThe S-approximation spaces are significant extension of the rough set model and have been widely applied in intelligent decision-making. However, traditional S-approximation spaces are limited to two crisp universes, whereas bi-fuzzy universes (i.e., two distinct fuzzy domains) are more prevalent in practical applications. To bridge this gap, this study introduces the bi-fuzzy S-approximation spaces (BFS approximation spaces) as an advancement of knowledge space theory’s fuzzy extension. Upper and lower approximation operators are formally defined, and the properties of BFS approximation spaces under various operations, such as complement, intersection and union are systematically explored. Special attention is given to a significant form of these operators, under which the monotonicity and complementary compatibility of BFS approximation spaces are rigorously analyzed. These results not only extend the theoretical framework of S-approximation spaces but also pave the way for further exploration of fuzzy extensions within knowledge space theory.https://www.mdpi.com/2227-7390/13/2/324S-approximation spacesrough setsfuzzy setsbi-fuzzy S-approximation spaces (BFS approximation spaces)monotonicitycomplementary compatibility |
| spellingShingle | Ronghai Wang Xiaojie Xie Huilai Zhi Bi-Fuzzy S-Approximation Spaces Mathematics S-approximation spaces rough sets fuzzy sets bi-fuzzy S-approximation spaces (BFS approximation spaces) monotonicity complementary compatibility |
| title | Bi-Fuzzy S-Approximation Spaces |
| title_full | Bi-Fuzzy S-Approximation Spaces |
| title_fullStr | Bi-Fuzzy S-Approximation Spaces |
| title_full_unstemmed | Bi-Fuzzy S-Approximation Spaces |
| title_short | Bi-Fuzzy S-Approximation Spaces |
| title_sort | bi fuzzy s approximation spaces |
| topic | S-approximation spaces rough sets fuzzy sets bi-fuzzy S-approximation spaces (BFS approximation spaces) monotonicity complementary compatibility |
| url | https://www.mdpi.com/2227-7390/13/2/324 |
| work_keys_str_mv | AT ronghaiwang bifuzzysapproximationspaces AT xiaojiexie bifuzzysapproximationspaces AT huilaizhi bifuzzysapproximationspaces |