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The relationship between a transitive GE-algebra and a belligerent GE-algebra (also, between an antisymmetric GE-algebra and a left exchangeable GE-algebra) is displayed. A condition for the trivial GE-filter to be a belligerent GE-filter is provided. The least GE-filter containing a given GE-filter and one element is formed. Conditions under which any set can be turned into a GE-filter are described. The notions of $$\odot $$ -GE-algebras and prominent GE-filters are introduced, and their properties are investigated. The relationship between a prominent GE-filter and a GE-filter are considered, and conditions for a GE-filter and the trivial GE-filter to be a prominent GE-filter are given. The conditions under which the upset of an element will be a prominent GE-filter are examined, and the extension property for the prominent GE-filter is established. The notion of GE-morphism is introduced, and the GE-morphism theorem is considered. Conditions for the kernel of a GE-morphism to be a belligerent GE-filter are provided, and the condition that if the kernel of a GE-morphism is a belligerent GE-filter, then the trivial GE-filter becomes a belligerent GE-filter is given. A condition for the kernel of a GE-morphism to be a belligerent GE-filter is discussed, and the vice versa is also considered.

A complex intuitionistic fuzzy set (CIFS) has an ability to represent the problems with intuitionistic uncertainty and periodicity, simultaneously. In this paper, we present a new framework for handling complex intuitionistic fuzzy information by combining the CIFSs with competition graphs. We first introduce the concept of complex intuitionistic fuzzy competition graphs along with its two worthwhile extensions, namely, complex intuitionistic fuzzy k-competition and complex intuitionistic fuzzy p-competition graphs. Further, we present complex intuitionistic fuzzy neighborhood graphs and m-step complex intuitionistic fuzzy competition graphs with some of their remarkable results. We also describe an application of complex intuitionistic fuzzy competition graphs along with an algorithm which finds the competition among the applicants competing for the particular jobs possessing the two-dimensional information. Moreover, we provide a comparison analysis of proposed competition graphs with existing graphs to find the validity and superiority of proposed competition graphs.

In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of Sheffer stroke and a Hilbert algebra. After it is shown that the axioms of Sheffer stroke Hilbert algebra are independent, it is given some properties of this algebraic structure. Then it is stated the relationship between Sheffer stroke Hilbert algebra and Hilbert algebra by defining a unary operation on Sheffer stroke Hilbert algebra. Also, it is presented deductive system and ideal of this algebraic structure. It is defined an ideal generated by a subset of a Sheffer stroke Hilbert algebra, and it is constructed a new ideal of this algebra by adding an element of this algebra to its ideal., Ege University Scientific Research Projects DirectorateEge University [20772], The authors would like to express their sincere thanks to the referee for their valuable suggestions and comments. This study is partially funded by Ege University Scientific Research Projects Directorate with the Project Number 20772.

We introduce and investigate central lifting property (CLP) for orthomodular lattices as a property whereby all central elements can be lifted modulo every p-ideal. It is shown that prime ideals, maximal ideals and finite p-ideals have CLP. Also Boolean algebras, simple chain finite orthomodular lattices, subalgebras of an orthomodular lattices generated by two elements and finite orthomodular lattices have CLP. The main results of the present paper include the investigation of CLP for principal p-ideals and finite direct products of orthomodular lattices.

Inspired by the analysis of soft sets and fuzzy sets, in this paper, we study the relevance and interrelationship of the equivalence and congruence relation of lattice ordered fuzzy soft groups(l-FSGs). Moreover, we analyze some of the innate algebraic results accrued out of it theoretically. We construct l-FSG congruence class and l-FSG quotient set on a group X. We analyze the relationship between l-FSG congruence relation and l-FSG normal subgroups. In particular, we prove that in a group X, l-FSG normal subgroups form a modular lattice.

In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators. After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras. By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras and characterize simple and subdirectly irreducible monadic MTL-algebras. Moreover, present monadic monoidal t-norm based logic (MMT L), a system of many valued logic capturing the tautologies of monadic MTL-algebras and prove a completeness theorem.AMS Classification: 08A72, 03G25, 03B50, 03C05.

The main objective of this study is to introduce a neutrosophic N- subalgebra (ideal) of L-algebras and to investigate some properties. It is shown that the level-set of a neutrosophic N- subalgebra (ideal) of an L-algebra is its subalgebra (ideal), and the family of all neutrosophic N- subalgebras of an L-algebra forms a complete distributive modular lattice. Additionally, it is proved that every neutrosophic N- ideal of an L-algebra is the neutrosophic N- subalgebra but the inverse of the statement may not be true in general. As the concluding part, some special cases are provided as ideals which are particular subsets of an L-algebra defined due to N- functions. © 2022, The Author(s) under exclusive license to Università degli Studi di Ferrara.

The aim of this study is to present (sup-hesitant) fuzzy SUP-subalgebras and fuzzy duplex SUP-sets on Sheffer stroke UP-algebra (in short, SUP-algebra). After defining (sup-hesitant) fuzzy SUP-subalgebras and fuzzy duplex SUP-sets of a SUP-algebra, we give their some properties and analyse whether the intersection or union of these subalgebras is a (sup-hesitant) fuzzy SUP-subalgebra of a SUP-algebra. It is shown that the level sets of (sup-hesitant) fuzzy SUP-subalgebras of a SUP-algebra are its SUP-subalgebras. Also, fuzzy duplex SUP-sets of a SUP-algebra are determined and studied the cases which these sets are SUP-algebras. Finally, the relationships between aforementioned structures are investigated.

In this study, fuzzy subalgebras and ideals with t-conorms on Sheffer stroke Hilbert algebras are discussed. We state and prove relationships between the level-set of a fuzzy subalgebra with a t-conorm T (briefly, T-fuzzy subalgebra) and a subalgebra of a Sheffer stroke Hilbert algebra. Then the composition of T-fuzzy subalgebras and homomorphisms of Sheffer stroke Hilbert algebras are analyzed. By defining fuzzy subalgebras of Sheffer stroke Hilbert algebras, the relationships between fuzzy subalgebras and T-fuzzy subalgebras of this algebraic structure are investigated. Also, it is shown that every fuzzy ideal with t-conorm T (in short, T-fuzzy ideal) is a T-fuzzy subalgebra but the converse does not generally hold. As in T-fuzzy subalgebras of Sheffer stroke Hilbert algebras, some properties of the T-fuzzy ideals are proved.

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.

In this article, we introduce dual hesitant

Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algebra. We also characterize congruence kernels of transitive GE-algebras.

In this paper, we focus on investigating some types of (skew) filters such as weak (positive) implicative (skew) filters on pseudo residuated skew lattices and obtain some properties of these (skew) filters. The relationship between these (skew) filters and other types of (skew) filters are discussed. It is shown that any weak positive implicative filter is a weak implicative and strong filter if it is a normal filter. Moreover, we characterize some types of filters by the properties of corresponding quotient algebras. Some equivalent characterizations for some filters are obtained too. Finally, a new characterization of these filters in a pseudo residuated skew lattice by a diagram is given.

In this paper, we introduce the concept of fuzzy congruence relations on a pseudo BE-algebra and some of properties are investigated. We show that the set of all fuzzy congruence relations is a modular lattice and the quotient structure induced by fuzzy congruence relations is studied.

In this paper, pseudo residuated skew lattices are defined as a non-commutative generalization of residuated skew lattices and their properties are investigated. It is shown that the class of all conormal pseudo residuated skew lattices forms a variety under some conditions. Dense, regular and strong elements are studied in a pseudo residuated skew lattice and the relationships between them are discussed. We define and investigate different classes of pseudo residuated skew lattices and show that any pseudo residuated skew chain with element 0 is local and also, any locally finite pseudo residuated skew lattice is local. It is shown that any strong pseudo residuated skew lattice is good and any locally finite pseudo residuated skew lattice is good under an extra condition too.

We consider pseudofinite MV-algebras. As a main result, we show that an infinite MV-algebra is pseudofinite if and only if it is definably well founded, improving a result of a previous paper. Moreover, we show that the theory of pseudofinite MV-algebras has a partial form of elimination of quantifiers. Further, we show that the class of pseudofinite MV-chains and the class of pseudofinite MV-algebras are not finitely axiomatizable, we give some collapsing results for pseudofinite MV-algebras, we consider relative subalgebras of pseudofinite MV-algebras, and we study ideals of pseudofinite MV-algebras.

Knowing the applications of logical algebras in various fields, such as artificial intelligence or coding theory, in this paper, we study some properties of a special class of such algebras, namely finite Wajsberg algebras. For this purpose, we give a representation theorem for finite Wajsberg algebras and give a formula for the number of non-isomorphic Wajsberg algebras of order n; also we give the total number of finite Wajsberg algebras of order n. Since a big value of n involves a lot of computations, as examples, we present and describe all finite Wajsberg algebras of order $$n\le 9$$ .

The notions of $$(\in ,\in \vee q)$$-cubic p- (a- and q-) ideals of BCI-algebras are introduced and some related properties are investigated. Several characterization for these generalized $$(\in ,\in \vee q)$$-cubic ideals are defined and relationship between $$(\in ,\in \vee q)$$-cubic p-ideals, $$(\in ,\in \vee q)$$-cubic q-deals and $$(\in ,\in \vee q)$$-cubic a-ideals of BCI-algebras are discussed.

As generalizations and alternatives of classical algebraic structures there have been introduced in 2019 the NeutroAlgebraic structures (or NeutroAlgebras) and AntiAlgebraic structures (or AntiAlgebras). Unlike the classical algebraic structures, where all operations are well defined and all axioms are totally true, in NeutroAlgebras and AntiAlgebras, the operations may be partially well defined and the axioms partially true or, respectively, totally outer-defined and the axioms totally false. These NeutroAlgebras and AntiAlgebras form a new field of research, which is inspired from our real world. In this paper, we study neutrosophic quadruple algebraic structures and NeutroQuadrupleAlgebraicStructures. NeutroQuadrupleGroup is studied in particular and several examples are provided. It is shown that $$(NQ({\mathbb {Z}}),\div )$$ ( N Q ( Z ) , ÷ ) is a NeutroQuadrupleGroup. Substructures of NeutroQuadrupleGroups are also presented with examples.