Utilization of Fermatean Fuzzy subsets to $Q$-Ideals
Keywords:
($AL$, $CL$, $\mathbb{J}$-coverd)$Q$-algebra, Fermatean fuzzy set, Fermatean fuzzy $Q$-algebra, Fermatean fuzzy $Q$-ideal.Abstract
This paper introduces the notions of $ALQ$-algebra and $CL$$Q$-algebra and shows that $ALQ$-algebras and $CL$$Q$-algebras are isomorphic. It is presented in the the notions of Fermatean fuzzy $Q$-algebras and ($3$-regular) Fermatean fuzzy $Q$-ideals as a generalization of fuzzy $Q$-algebras and fuzzy $Q$-ideals. It investigates the connection between Fermatean fuzzy $Q$-algebras and Fermatean fuzzy $Q$-ideals and is shown that Fermatean fuzzy $Q$-ideals are a subclass of Fermatean fuzzy $Q$-subalgebras and $3$-regular Fermatean fuzzy $Q$-subalgebras are Fermatean fuzzy $Q$-ideals.
In this study, the concepts of nil radical Fermatean fuzzy $Q$-subsets are introduced, and it is stabilized that nil radical Fermatean fuzzy $Q$-subsets are Fermatean fuzzy $Q$-subalgebra. Also, the Fermatean fuzzy $Q$-algebras(ideals) are extended by, intersection, union, combination, and isomorphisms and $\mathbb{J}$-coverd conditions in any given $Q$-algebra.
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