ℒ-Fuzzy Cosets of ℒ-Fuzzy Filters of Residuated Multilattices
This paper mainly focuses on building the ℒ-fuzzy filter theory of residuated multilattices. Firstly, we introduce the concepts of ℒ-fuzzy filter and ℒ-fuzzy deductive system of residuated multilattices. Then, we highlight their properties and show how they are linked. Secondly, we introduce the con...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/6833943 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832563523151986688 |
|---|---|
| author | Pierre Carole Kengne Blaise Bleriot Koguep Njionou Daquin Cèdric Awouafack Luc Eméry Diékouam Fotso |
| author_facet | Pierre Carole Kengne Blaise Bleriot Koguep Njionou Daquin Cèdric Awouafack Luc Eméry Diékouam Fotso |
| author_sort | Pierre Carole Kengne |
| collection | DOAJ |
| description | This paper mainly focuses on building the ℒ-fuzzy filter theory of residuated multilattices. Firstly, we introduce the concepts of ℒ-fuzzy filter and ℒ-fuzzy deductive system of residuated multilattices. Then, we highlight their properties and show how they are linked. Secondly, we introduce the concept of prime ℒ-fuzzy filter and propose some illustrative examples. Then, we bring out their properties and show how they are related to the concept of ℒ-fuzzy prime filter. Thirdly, we characterize ℒ-fuzzy maximal filter and maximal ℒ-fuzzy filter by atoms and coatoms. In the case where ℒ is a distributive lattice, we prove that maximal ℒ-fuzzy filters are prime. Finally, we are interested in ℒ-fuzzy cosets of an ℒ-fuzzy filter, and we prove that the set of all ℒ-fuzzy cosets of any ℒ-fuzzy filter of a residuated multilattice is a residuated multilattice. |
| format | Article |
| id | doaj-art-cabe15ca76f843ba920c2ef9083cff8d |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-cabe15ca76f843ba920c2ef9083cff8d2025-02-03T01:19:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/6833943ℒ-Fuzzy Cosets of ℒ-Fuzzy Filters of Residuated MultilatticesPierre Carole Kengne0Blaise Bleriot Koguep Njionou1Daquin Cèdric Awouafack2Luc Eméry Diékouam Fotso3Department of Mathematics and Computer ScienceDepartment of Mathematics and Computer ScienceDepartment of Mathematics and Computer ScienceDepartment of MathematicsThis paper mainly focuses on building the ℒ-fuzzy filter theory of residuated multilattices. Firstly, we introduce the concepts of ℒ-fuzzy filter and ℒ-fuzzy deductive system of residuated multilattices. Then, we highlight their properties and show how they are linked. Secondly, we introduce the concept of prime ℒ-fuzzy filter and propose some illustrative examples. Then, we bring out their properties and show how they are related to the concept of ℒ-fuzzy prime filter. Thirdly, we characterize ℒ-fuzzy maximal filter and maximal ℒ-fuzzy filter by atoms and coatoms. In the case where ℒ is a distributive lattice, we prove that maximal ℒ-fuzzy filters are prime. Finally, we are interested in ℒ-fuzzy cosets of an ℒ-fuzzy filter, and we prove that the set of all ℒ-fuzzy cosets of any ℒ-fuzzy filter of a residuated multilattice is a residuated multilattice.http://dx.doi.org/10.1155/2022/6833943 |
| spellingShingle | Pierre Carole Kengne Blaise Bleriot Koguep Njionou Daquin Cèdric Awouafack Luc Eméry Diékouam Fotso ℒ-Fuzzy Cosets of ℒ-Fuzzy Filters of Residuated Multilattices International Journal of Mathematics and Mathematical Sciences |
| title | ℒ-Fuzzy Cosets of ℒ-Fuzzy Filters of Residuated Multilattices |
| title_full | ℒ-Fuzzy Cosets of ℒ-Fuzzy Filters of Residuated Multilattices |
| title_fullStr | ℒ-Fuzzy Cosets of ℒ-Fuzzy Filters of Residuated Multilattices |
| title_full_unstemmed | ℒ-Fuzzy Cosets of ℒ-Fuzzy Filters of Residuated Multilattices |
| title_short | ℒ-Fuzzy Cosets of ℒ-Fuzzy Filters of Residuated Multilattices |
| title_sort | l fuzzy cosets of l fuzzy filters of residuated multilattices |
| url | http://dx.doi.org/10.1155/2022/6833943 |
| work_keys_str_mv | AT pierrecarolekengne lfuzzycosetsoflfuzzyfiltersofresiduatedmultilattices AT blaisebleriotkoguepnjionou lfuzzycosetsoflfuzzyfiltersofresiduatedmultilattices AT daquincedricawouafack lfuzzycosetsoflfuzzyfiltersofresiduatedmultilattices AT lucemerydiekouamfotso lfuzzycosetsoflfuzzyfiltersofresiduatedmultilattices |