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The Notions of Fuzzy Set on Pseudo Quasi Ordered Residuated Systems
Yeshiwas Mebrat Gubena1, Teferi Getachew Alemayehu2
1Mathematics, Bahir Dar University Department of Mathematics, Bahir Dar, Amhara, Ethiopia.
Abstract:
This paper introduces the concept of fuzzy filters and 2-fuzzy filters of a quasi-ordered residuated system . 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 qualifies as a normal fuzzy filter and vice-versa. Furthermore, the study demonstrates that the collection of all comparative fuzzy filters in 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 inherently satisfies the criteria for both implicative and comparative fuzzy filters.
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