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. 2025 Jul 24:14:566.
doi: 10.12688/f1000research.165259.2. eCollection 2025.

The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems

Yeshiwas Mebrat Gubena  1 , Teferi Getachew Alemayehu  2
Affiliations

The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems

Yeshiwas Mebrat Gubena et al. F1000Res. .

Abstract

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.

Keywords: associative fuzzy filter; pseudo quasi-order residuated system; Comparative fuzzy filter; fantastic fuzzy filter; Quasi- order residuated system..

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Conflict of interest statement

No competing interests were disclosed.

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