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In this article, we introduce the concept of fuzzy (n-fold) obstinate filter on hoop algebras and study some of the properties. We define and study fuzzy prime filter and fuzzy n-fold implicative filter on hoop algebras. Also, the relationship between fuzzy obstinate filter and some other fuzzy filters likeness fuzzy prime and fuzzy positive implicative filters are investigated. Then we show that the quotient of this structure is a Boolean algebra and obtained some condition equivalent with fuzzy n-fold implicative filter. Finally we show that every fuzzy n-fold obstinate filter with some conditions is a fuzzy n-fold implicative filter.

In this paper, we define modal operators in residuated skew lattices and prove some fundamental properties of monotone modal operators on residuated skew lattices (RSL). We prove that the composition of two modal operators is a modal operator if and only if they commute. We investigate strong modal operators in RSL and get a characterization of them. Deductive systems under a modal operator are investigated.

In this paper we introduce Sheffer stroke BE-algebras (briefly, SBE-algebras) 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 SBE-subalgebra 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.

In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It is indicated that the axioms of a Sheffer stroke BCK-algebra are independent. The relationship between a Sheffer stroke BCK-algebra and a BCK-algebra is stated. After describing a commutative, an implicative and an involutory Sheffer stroke BCK-algebras, some of important properties are proved. The relationship of this structures is demonstrated. A Sheffer stroke BCK-algebra with condition (S) is described and the connection with other structures is shown. Finally, it is proved that for a Sheffer stroke BCK-algebra to be a Boolean lattice, it must be an implicative Sheffer stroke BCK-algebra.

The notions of intuitionistic fuzzy quasi-subalgebras and intuitionistic fuzzy (ultra) filters are defined and examined on Sheffer stroke BL-algebras in detail. Then we characterize the properties of these intuitionistic fuzzy structures, and show the relationships between intuitionistic fuzzy quasi-subalgebras and intuitionistic fuzzy (ultra) filters. Also, it is stated that the affiliations between aforementioned intuitionistic fuzzy structures and ordinary fuzzy structures on Sheffer stroke BL-algebras, and that the upper and lower level sets defining intuitionistic fuzzy (ultra) filters are (ultra) filters on these algebraic structures. At the end of the study, the process of building new intuitionistic fuzzy filters is presented by means of homomorphisms of Sheffer stroke BL-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we introduce Sheffer Stroke UP-algebra (in short, SUP-algebra) and study its properties. We demonstrate that the Cartesian product of two SUP-algebras is a SUP-algebra. After presenting SUP-subalgebras, we define SUP-homomorphisms between SUP-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 paper, we study some of the properties fuzzy soft tri-quasi ideals of a semiring. Tri-quasi ideals generalize, bi-ideals, quasi-ideals and interior ideals. We characterize regular semiring using fuzzy soft tri-quasi ideals and prove that, if (η,A) is a fuzzy soft tri-quasi ideal over a regular semiring M, then (η,A) is a fuzzy soft tri-ideal over M. [ABSTRACT FROM AUTHOR]

In this paper, congruences and (order, prime and compatible) filters are introduced in Sheffer stroke basic algebras. They are interrelated with each other. Also some relationships between filters and congruences by focusing on their properties in these structures are given. In addition to these, a basic algebra is constructed by the help of compatible filter and 𝒜/ Θ (F). Moreover, a representation theorem for Sheffer stroke basic algebra by using prime filters and 𝒜/ Θ (F) is stated and proved.

In this paper, we define residuated skew lattice as non-commutative generalization of residuated lattice and investigate its properties. We show that Green’s relation 𝔻 is a congruence relation on residuated skew lattice and its quotient algebra is a residuated lattice. Deductive system and skew deductive system in residuated skew lattices are defined and relationships between them are given and proved. We define branchwise residuated skew lattice and show that a conormal distributive residuated skew lattice is equivalent with a branchwise residuated skew lattice under a condition.

Hilbert algebras are important tools for certain investigations in algebraic logic since they can be considered as fragments of any propositional logic containing a logical connective implication and the constant 1 which is considered as the logical value “true” and as a generalization of this was defined the notion of g-Hilbert algebra. In this paper, we investigate the relationship between g-Hilbert algebras, gi-algebras, implication gruopoid and BE-algebras. In fact, we show that every g-Hilbert algebra is a self distributive BE-algebras and conversely. We show cannot remove the condition self distributivity. Therefore we show that any self distributive commutative BE-algebras is a gi-algebra and any gi-algebra is strong and transitive if and only if it is a commutative BE-algebra. We prove that the MV -algebra is equivalent to the bounded commutative BE-algebra.

In this paper, with the aim of further investigating on B L-algebras, we introduced the concept of the annihilator of complement elements of a non-empty subset X of a B L-algebra, (⊥(X−)), and we proved that this set is a filter. Then we examined and studied ⊥(X−) completely and showed under what conditions it becomes the prime and maximal filter. Next, with the help of ⊥(X−), we obtained an equivalence condition for fantastic filters, and since fantastic filters are directly related to MValgebras, we were able to find an equivalence condition for checking MV-algebras. Also, we studied ⊥(X−) in various types of BL-algebras, including linearly ordered BL-algebras, Boolean algebra, Godel algebra, integral and special BL-algebras. In the last part of this article, with the help of the spectrum of fantastic filters, (FS(L)), we introduced a new BL-algebra and examined some of its features. [ABSTRACT FROM AUTHOR]

In this paper, we are going to introduce a fundamental relation on HvBE-algebra and investigate some of properties, also construct new (Hv)BE-algebras via this relation. We show that quotient of any HvBE-algebra via a regular regulation is an HvBE-algebra and this quotient, via any strongly relation is a BE-algebra. Furthermore, we investigate that under what conditions some relations on HvBEalgebra are transitive relations. [ABSTRACT FROM AUTHOR]

The main objective of the study is to introduce a hesitant fuzzy structures on Sheffer stroke BCK-algebras related to their subsets (subalgebras as possible as). Then it is proved that every hesitant fuzzy ideal of a Sheffer stroke BCK-algebra related to the subset is the hesitant fuzzy subalgebra. By defining a hesitant fuzzy maximal ideal in this algebra, relationships between aforementioned structures, subalgebras and ideals on Sheffer stroke BCK-algebras are shown in detail. Finally, it is illustrated that a subset of a Sheffer stroke BCK-algebra defined by a certain element and a hesitant fuzzy (maximal) ideal on the algebra is a (maximal) ideal but the inverse is usually not true. [ABSTRACT FROM AUTHOR]

The concept of ₦-structures was initiated by Jun et al. in 2009. Later, Young Bae Jun extended this concept as ₦-hyper sets and dealt its associated outcomes. In particular, four types of ₦-substructures with relevant properties have been investigated which leads to the introduction of the notion of ₦-hyper β − subalgebra in this study. Further, it was proved that the intersection of two ₦-hyper β − subalgebras is again an ₦-hyper β − subalgebra. In addition to that, the properties based on the homomorphism and Cartesian product were discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new algebra, called a BI-algebra, which is a generalization of a (dual) implication algebra and we discuss the basic properties of BI-algebras, and investigate ideals and congruence relations.

The main objective of this study is to introduce Sheffer stroke R0-algebra (for short, SR0-algebra). Then it is stated that the axiom system of a Sheffer stroke R0-algebra is independent. It is indicated that every Sheffer stroke R0-algebra is R0-algebra but specific conditions are necessarily for the inverse. Afterward, various ideals of a Sheffer stroke R0-algebra are defined, a congruence relation on a Sheffer stroke R0-algebra is determined by the ideal and quotient Sheffer stroke R0-algebra is built via this congruence relation. It is proved that quotient Sheffer stroke R0-algebra constructed by a prime ideal of this algebra is totally ordered and the cardinality is less than or equals to 2. After all, important conclusions are obtained for totally ordered Sheffer stroke R0-algebras by applying various properties of prime ideals. [ABSTRACT FROM AUTHOR]

The purpose of this paper is the study of prime ideals and prime filters in hyperlattices. I-filter and the filter generated by a ∈ L are introduced. Moreover, we introduce dual distributive hyperlattices, and I-filter in dual distributive hyperlattices. Some properties of hyperlat- tices are studied and the relationship between prime ideals and prime filters in hyperlattices is discussed.

The aim of this work is to introduce some types of filters in Hilbert algebras. Some theorems are stated and proved which determine the relationship between these notions and other filters of Hilbert algebra and by some examples we show that these concepts are different. The relationships between these filters and quotient algebras that are constructed via these filters are described.

The main goal of this paper is to investigate very true MTL-algebras and prove the completeness of the very true MTL-logic. In this paper, the concept of very true operators on MTL-algebras is introduced and some related properties are investigated. Also, conditions for an MTL-algebra to be an MV-algebra and a Gödel algebra are given via this operator. Moreover, very true filters on very true MTL-algebras are studied. In particular, subdirectly irreducible very true MTL-algebras are characterized and an analogous of representation theorem for very true MTL-algebras is proved. Then, the left and right stabilizers of very true MTL-algebras are introduced and some related properties are given. As applications of stabilizer of very true MTL-algebras, we produce a basis for a topology on very true MTL-algebras and show that the generated topology by this basis is Baire, connected, locally connected and separable. Finally, the corresponding logic very true MTL-logic is constructed and the soundness and completeness of this logic are proved based on very true MTL-algebras.

In this paper, we introduce the notions of N- subalgebras and N-filters based on Smarandache CI-algebra and give a number of their properties. The relationship between N(Q; f)-subalgebras(filters) and N-subalgebras(filters) are also in- vestigated