The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems [version 1; peer review: 2 approved] - Teferi Getachew Alemayehu; Yeshiwas Mebrat Gubena (F1000Research, 2025)
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.