The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 1; peer review: 2 approved]
This paper introduces the concept of fuzzy filters and 2-fuzzy filters of a quasi-ordered residuated system K . This research explores comparative, normal, implicative and associative fuzzy filters within a quasi-ordered residuated system. It establishes the sufficient conditions under which a compa...
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| Format: | Article |
| Language: | English |
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F1000 Research Ltd
2025-06-01
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| Online Access: | https://f1000research.com/articles/14-566/v1 |
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| author | Teferi Getachew Alemayehu Yeshiwas Mebrat Gubena |
| author_facet | Teferi Getachew Alemayehu Yeshiwas Mebrat Gubena |
| author_sort | Teferi Getachew Alemayehu |
| collection | DOAJ |
| description | This paper introduces the concept of fuzzy filters and 2-fuzzy filters of a quasi-ordered residuated system K . This research explores comparative, normal, implicative and associative fuzzy filters within a quasi-ordered residuated system. It establishes the sufficient conditions under which a comparative fuzzy filter in K qualifies as a normal fuzzy filter and vice-versa. Furthermore, the study demonstrates that the collection of all comparative fuzzy filters in K constitutes a complete lattice. The notion of fuzzy filters of a pseudo quasi-ordered residuated system is introduced and the analysis extends to fantastic, comparative, associative and implicative fuzzy filters within a pseudo quasi-ordered residuated framework. Finally, it is proven that an associative fuzzy filter in K inherently satisfies the criteria for both implicative and comparative fuzzy filters. |
| format | Article |
| id | doaj-art-8542d3b2778b4e2c9ec2d022f452d89f |
| institution | Matheson Library |
| issn | 2046-1402 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | F1000 Research Ltd |
| record_format | Article |
| series | F1000Research |
| spelling | doaj-art-8542d3b2778b4e2c9ec2d022f452d89f2025-07-10T01:00:00ZengF1000 Research LtdF1000Research2046-14022025-06-0114181869The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 1; peer review: 2 approved]Teferi Getachew Alemayehu0https://orcid.org/0000-0001-9832-9522Yeshiwas Mebrat Gubena1https://orcid.org/0000-0002-8399-288XMathematics, Debre Berhan University, Debre Birhan, Amhara, EthiopiaMathematics, Bahir Dar University Department of Mathematics, Bahir Dar, Amhara, EthiopiaThis paper introduces the concept of fuzzy filters and 2-fuzzy filters of a quasi-ordered residuated system K . This research explores comparative, normal, implicative and associative fuzzy filters within a quasi-ordered residuated system. It establishes the sufficient conditions under which a comparative fuzzy filter in K qualifies as a normal fuzzy filter and vice-versa. Furthermore, the study demonstrates that the collection of all comparative fuzzy filters in K constitutes a complete lattice. The notion of fuzzy filters of a pseudo quasi-ordered residuated system is introduced and the analysis extends to fantastic, comparative, associative and implicative fuzzy filters within a pseudo quasi-ordered residuated framework. Finally, it is proven that an associative fuzzy filter in K inherently satisfies the criteria for both implicative and comparative fuzzy filters.https://f1000research.com/articles/14-566/v1associative fuzzy filter; pseudo quasi-order residuated system; Comparative fuzzy filter; fantastic fuzzy filter; Quasi- order residuated system.eng |
| spellingShingle | Teferi Getachew Alemayehu Yeshiwas Mebrat Gubena The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 1; peer review: 2 approved] F1000Research associative fuzzy filter; pseudo quasi-order residuated system; Comparative fuzzy filter; fantastic fuzzy filter; Quasi- order residuated system. eng |
| title | The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 1; peer review: 2 approved] |
| title_full | The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 1; peer review: 2 approved] |
| title_fullStr | The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 1; peer review: 2 approved] |
| title_full_unstemmed | The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 1; peer review: 2 approved] |
| title_short | The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 1; peer review: 2 approved] |
| title_sort | notions of fuzzy set on pseudo quasi ordered residuated systems version 1 peer review 2 approved |
| topic | associative fuzzy filter; pseudo quasi-order residuated system; Comparative fuzzy filter; fantastic fuzzy filter; Quasi- order residuated system. eng |
| url | https://f1000research.com/articles/14-566/v1 |
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