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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
F1000 Research Ltd
2025-06-01
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| Series: | F1000Research |
| Subjects: | |
| Online Access: | https://f1000research.com/articles/14-566/v1 |
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| Summary: | 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. |
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| ISSN: | 2046-1402 |