The aim of this study is to introduce fuzzy filters of Sheffer stroke Hilbert algebra. After defining fuzzy filters of Sheffer stroke Hilbert algebra, it is shown that a quotient structure of this algebra is described by its fuzzy filter. In addition to this, the level filter of a Sheffer stroke Hilbert algebra is determined by its fuzzy filter. Some fuzzy filters of a Sheffer stroke Hilbert algebra are defined by a homomorphism. Normal and maximal fuzzy filters of a Sheffer stroke Hilbert algebra and the relation between them are presented. By giving the Cartesian product of fuzzy filters of a Sheffer stroke Hilbert algebra, various properties are examined.
Abstract:In this work, we introduce Wajsberg algebras which are equivalent structures to MV-algebras in their implicational version, and then we define new notions and give new solutions to the set-theoretical Yang-Baxter equation by using Wajsberg algebras.
In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved.
In this study, a neutrosophic N-subalgebra, a (implicative) neutrosophic N-filter, level sets of these neutrosophic N-structures and their properties are introduced on a Sheffer stroke BE-algebras (briefly, SBE-algebras). It is proved that the level set of neutrosophic N-subalgebras ((implicative) neutrosophic N-filter) of this algebra is the SBE-subalgebra ((implicative) SBE-filter) and vice versa. Then it is proved that the family of all neutrosophic N-subalgebras of a SBE-algebra forms a complete distributive modular lattice. We present relationships between upper sets and neutrosophic N-filters of this algebra. Also, it is given that every neutrosophic N-filter of a SBE-algebra is its neutrosophic N-subalgebra but the inverse is generally not true. It is demonstrated that a neutrosophic N-structure on a SBE-algebra defi ned by a (implicative) neutrosophic N-filter of another SBE-algebra and a surjective SBE-homomorphism is a (implicative) neutrosophic N-filter. We present relationships between a neutrosophic N-filter and an implicative neutrosophic N-filter of a SBE-algebra in detail. Finally, certain subsets of a SBE-algebra are determined by means of N-functions and some properties are examined.
In this paper we introduce Sheffer stroke BE-algebras (briefly, SBEalgebras) and investigate a relationship between SBE-algebras and BE-algebras. By presenting a SBE-filter, an upper set and a SBE-subalgebra on a SBE-algebra, it is shown that any SBE-filter of a SBE-algebra is a SBEsubalgebra but the converse of this statement is not true. Besides we construct quotient SBE-algebras via a congruence relation defined by a special SBE-filter. We discuss SBE-homomorphisms and their properties between SBE-algebras. Finally, a relation between Sheffer stroke Hilbert algebras and SBE-algebras is established.
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