The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems
Following the idea of L-fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L-fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L-fu...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/5523822 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849693140411219968 |
|---|---|
| author | Qiao-Ling Song Hu Zhao Juan-Juan Zhang A. A. Ramadan Hong-Ying Zhang Gui-Xiu Chen |
| author_facet | Qiao-Ling Song Hu Zhao Juan-Juan Zhang A. A. Ramadan Hong-Ying Zhang Gui-Xiu Chen |
| author_sort | Qiao-Ling Song |
| collection | DOAJ |
| description | Following the idea of L-fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L-fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L-fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on L-fuzzy relations. Furthermore, if L satisfies the double negative law, then there exists an order isomorphic mapping between upper and lower approximation operators based on L-fuzzy generalized neighborhood systems; when L-fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on L-fuzzy relations are complete lattice isomorphism. |
| format | Article |
| id | doaj-art-377c8557f9364982b6fe335d1d10fb52 |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-377c8557f9364982b6fe335d1d10fb522025-08-20T03:20:30ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/55238225523822The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood SystemsQiao-Ling Song0Hu Zhao1Juan-Juan Zhang2A. A. Ramadan3Hong-Ying Zhang4Gui-Xiu Chen5School of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaSchool of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaSchool of Science, Xi’an Polytechnic University, Xi’an 710048, ChinaDepartment of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, EgyptSchool of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaSchool of Mathematics and Statistics, Qinghai Normal University, Xining 810008, ChinaFollowing the idea of L-fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L-fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L-fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on L-fuzzy relations. Furthermore, if L satisfies the double negative law, then there exists an order isomorphic mapping between upper and lower approximation operators based on L-fuzzy generalized neighborhood systems; when L-fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on L-fuzzy relations are complete lattice isomorphism.http://dx.doi.org/10.1155/2021/5523822 |
| spellingShingle | Qiao-Ling Song Hu Zhao Juan-Juan Zhang A. A. Ramadan Hong-Ying Zhang Gui-Xiu Chen The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems Complexity |
| title | The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems |
| title_full | The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems |
| title_fullStr | The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems |
| title_full_unstemmed | The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems |
| title_short | The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems |
| title_sort | lattice structures of approximation operators based on l fuzzy generalized neighborhood systems |
| url | http://dx.doi.org/10.1155/2021/5523822 |
| work_keys_str_mv | AT qiaolingsong thelatticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT huzhao thelatticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT juanjuanzhang thelatticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT aaramadan thelatticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT hongyingzhang thelatticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT guixiuchen thelatticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT qiaolingsong latticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT huzhao latticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT juanjuanzhang latticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT aaramadan latticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT hongyingzhang latticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems AT guixiuchen latticestructuresofapproximationoperatorsbasedonlfuzzygeneralizedneighborhoodsystems |