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Akbar Rezaei

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Akbar Rezaei received his Ph. D. in Mathematics, Iran in 2014. He is currently an associate professor and academic member at the Department of Mathematics in Payame Noor University, Tehran, Iran. His current research interests include algebraic logic, algebraic structures, fuzzy sets and applications, fuzzy logic, neutrosophic sets.

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Kansas State University

Homi Bhabha National Institute (HBNI, BARC, MUMBAI)

Ahmed A . Salama

Port Said University

Florentin Smarandache

University of New Mexico

Dominique Raynaud

Université Grenoble Alpes

Srinivasa Rao Gadde

The University of Dodoma, Tanzania

Francisco Gallego Lupiañez

Universidad Complutense de Madrid

University of Gaziantep

Eduardo Araujo-Pradere

Miami Dade College

University of East London

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Papers by Akbar Rezaei

Extensions of BCK-algebras

Rms: Research In Mathematics & Statistics, Dec 29, 2016

In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the... more

States on Pseudo-BCK Algebras

J. Multiple Valued Log. Soft Comput., 2008

The notion of a state is an analogue of a probability measure and was first introduced by Kôpka a... more The notion of a state is an analogue of a probability measure and was first introduced by Kôpka and Chovanec for MV-algebras and by Riecan for BLalgebras. The states have also been studied for different types of non-commutative fuzzy structures such as pseudo-MV algebras, pseudo-BL algebras, bounded Rmonoids, residuated lattices and pseudo-BCK semilattices. In this paper we investigate the states on pseudo-BCK algebras and show that Georgescu's original problem in [10] for pseudo-BL algebras has a negative solution for good pseudo-BCK algebras. We prove that every Bosbach state on a pseudo-BCK algebra is a Riecan state and that every Riecan state on a good pseudo-BCK algebra with pseudo-double negation is a Bosbach state. In contrast to the case of pseudo-BL algebras, we show that there exist linearly ordered pseudo-BCK algebras having no Bosbach states.

PURE MATHEMATICS | RESEARCH ARTICLE Extensions of BCK-algebras

In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the... more

Independence concepts for groupoids

Annales Universitatis Paedagogicae Cracoviensis, 2023

In this paper, for getting more results in groupoids, we consider a set and introduce the notion ... more In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset. Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.

Left rays of groupoids

Asian-european Journal of Mathematics, May 7, 2022

In this paper, we introduce and study the notion of a [Formula: see text]positive implicative[For... more In this paper, we introduce and study the notion of a [Formula: see text]positive implicative[Formula: see text] left ray in groupoids, and we show that every normal subgroup of a group is a left ray of a group, and in every finite group, left rays are normal subgroups. Further, left absorptive subsets of groupoids are discussed and several examples for these definitions provided. The relationship between left rays and zero semigroups is discussed.

Interval-valued hesitant fuzzy filters in BE-algebras

Journal of Intelligent and Fuzzy Systems, Jun 22, 2017

In this paper, we develop fuzzy filter theory on a BE-algebra and apply the concept of interval-v... more In this paper, we develop fuzzy filter theory on a BE-algebra and apply the concept of interval-valued hesitant fuzzy filter to BE-algebras. Moreover, some types of interval-valued hesitant fuzzy filters such as interval-valued hesitant fuzzy implicative filter and interval-valued hesitant fuzzy fantastic filter are introduced and some of properties are investigated.

A generalization of groups

Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Mar 18, 2018

In this article we introduce the notion of e-group as a new generalization of a group. The condit... more In this article we introduce the notion of e-group as a new generalization of a group. The condition for a group to be an e-group is given. The characterization of some properties is established and some results follow. * 2 a b c d a a a a a b a b c d c c c a d d b d b c Then (G; * 1 , A) satisfies (G1) and (eG2) but does not satisfy (eG3). In addition, (G; * 2 ; A) satisfies (eG2) and (eG3) but does not satisfy (G1), since

Decision making on consistent customer centric inventory model with quality sustenance and smart warehouse management cost parameters

Decision Making: Applications in Management and Engineering

Customer acquaintance and the quality of the products decide the survival span of all the busines... more Customer acquaintance and the quality of the products decide the survival span of all the business sectors. Every production firm attempts to manufacture novel products with attractive and compatible features to satisfy the demands of different types of customers, especially with a special preference for the consistent kind of customers. A decision-making inventory model compassing the initiatives taken by the production firm for consistent customers is developed with the inclusion of costs associated with quality conservation and warehouse management. The reliability of the model is validated with numerical examples and inferences on parametric variations are made by comparing the results employing MATLAB software. The proposed model shall be further discussed in a fuzzy environment

J o u r n a l of Mathematics and Applications

This paper is devoted to the study of some structural properties of bounded and involutory BE-alg... more This paper is devoted to the study of some structural properties of bounded and involutory BE-algebras and investigate the relationship between them. We construct a commutative monoid by definition of proper operation in an involutory BE-algebra. Some rules of calculus for BE-algebras with a semi-lattice structure are provided. Many results related to the natural order of a BE-algebras were found. Finally, we show that an involutory bounded BE-algebra X is semi-simple.

On filters in eBE-algebras

Afrika Matematika

On Neutro-LA-semihypergroups and Neutro-Hv-LA-semigroups

In this paper, we extend the notion of LA-semihypergroups (resp. Hv-LA-semigroups) to neutro-LA-s... more In this paper, we extend the notion of LA-semihypergroups (resp. Hv-LA-semigroups) to neutro-LA-semihypergroups (respectively, neutro-Hv-LA-semigroups). Anti-LA-semihypergroups (respectively, anti-Hv-LA-semigroups) are studied and investigated some of their properties. We show that these new concepts are di fferent from classical concepts by several examples. These are particular cases of the classical algebraic structures generalized to neutroalgebraic structures and antialgebraic structures (Smarandache, 2019). 2000 Mathematics subject classification: 20N20, 20N99.

Applications of states to BI-algebras

Journal of algebraic hyperstructures and logical algebras, Aug 1, 2022

This paper aims is to introduce states, Bosbach states and state-morphism operators on BI-algebra... more This paper aims is to introduce states, Bosbach states and state-morphism operators on BI-algebras. We define state ideals on BI-algebras and give a characterization of the least state ideal of a BI-algebra. It is proved that the kernel of a Bosbach state on a BI-algebra X is an ideal of X. Further, by these concepts, we introduce the notions of state BI-algebras and state-morphism BIalgebras. The notion of complement pairs of a BI-algebra X is defined, and proves that under suitable conditions, there is a one-to-one correspondence between complement pairs of BI-algebras and state-morphism operators on BI-algebras.

On Neutrosophic RM-algebras

The Educational Publisher Inc., 2021

Intuitionistic (T,S)-fuzzy CI-algebras

Computers & Mathematics with Applications, 2012

In this paper, we introduce the notion of intuitionistic (T , S)-fuzzy subalgebras in CIalgebras ... more In this paper, we introduce the notion of intuitionistic (T , S)-fuzzy subalgebras in CIalgebras and study their fundamental properties. We get a fuzzy subalgebra from an intuitionistic (T , S)-fuzzy subalgebra. Also the notion of intuitionistic (T , S)-fuzzy (closed) filters of CI-algebras is introduced. We investigate the relationship between intuitionistic (T , S)-fuzzy subalgebras and intuitionistic (T , S)-fuzzy (closed) filters of CI-algebras.

ON S mBE-ALGEBRAS

In this article, class of all bounded commutative self distributive modal BE-algebras mBE S is in... more

Distributive Pseudo Be-Algebras

Fasciculi Mathematici, 2015

In this paper, we introduce the notion of distributive pseudo BE-algebra and show that the relate... more In this paper, we introduce the notion of distributive pseudo BE-algebra and show that the related relation defined on this structure is transitive and prove that every pseudo upper set is a pseudo filter. Also, the pseudo filter generated by a set is define and show that the set of all pseudo filters is distributive complete lattice but it is not complemented. the notion of prime and irreducible subset and prove that every irreducible subset is prime.

Journal of Algebraic Hyperstructures and Logical Algebras

In this paper, we introduce the notion of a ringoid, and we obtain left distributive ringoids ove... more In this paper, we introduce the notion of a ringoid, and we obtain left distributive ringoids over a field which are not rings. We introduce several different types of ringoids, and also we discuss on (r, s)-ringoids. Moreover, we discuss geometric observations of the parallelism of vectors in several ringoids.

On eGE-algebras

Discussiones Mathematicae - General Algebra and Applications

A new algebraic structure was introduced, called an eGE-algebra, which is a generalisation of a G... more

Neutrosophic N−Ideals on Sheffer Stroke BCK-Algebras

Journal of the Indonesian Mathematical Society

In this study, a neutrosophic N −subalgebra and neutrosophic N−ideal of a Sheffer stroke BCK-alge... more In this study, a neutrosophic N −subalgebra and neutrosophic N−ideal of a Sheffer stroke BCK-algebras are defined. It is shown that the level-set of a neutrosophic N−subalgebra (ideal) of a Sheffer stroke BCK-algebra is a subalgebra (ideal) of this algebra and vice versa. Then we present that the family of all neutrosophic N−subalgebras of a Sheffer stroke BCK-algebra forms a complete distributive modular lattice and that every neutrosophic N−ideal of a Sheffer stroke BCK-algebra is the neutrosophic N −subalgebra but the inverse does not usually hold. Also, relationships between neutrosophic N−ideals of Sheffer stroke BCK-algebras and homomorphisms are analyzed. Finally, we determine special subsets of a Sheffer stroke BCK-algebra by means of N−functions on this algebraic structure and examine the cases in which these subsets are its ideals.

Neutrosophic N −structures on Sheffer stroke BCH-algebras

CERN European Organization for Nuclear Research - Zenodo, Jun 29, 2022

The aim of the study is to introduce a neutrosophic N −subalgebra and neutrosophic N −ideal of a ... more The aim of the study is to introduce a neutrosophic N −subalgebra and neutrosophic N −ideal of a Sheffer stroke BCH-algebras. We prove that the level-set of a neutrosophic N −subalgebra (neutrosophic N −ideal) of a Sheffer stroke BCH-algebra is its subalgebra (ideal) and vice versa. Then it is shown that the family of all neutrosophic N −subalgebras of a Sheffer stroke BCH-algebra forms a complete distributive modular lattice. Also, we state that every neutrosophic N −ideal of a Sheffer stroke BCH-algebra is its neutrosophic N −subalgebra but the inverse is generally not true. We examine relationships between neutrosophic N −ideals of Sheffer stroke BCH-algebras by means of a surjective homomorphism between these algebras. Finally, certain subsets of a Sheffer stroke BCH-algebra are defined by means of N −functions on this algebraic structure and some properties are investigated.

Extensions of BCK-algebras

Rms: Research In Mathematics & Statistics, Dec 29, 2016

In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the... more

States on Pseudo-BCK Algebras

J. Multiple Valued Log. Soft Comput., 2008

The notion of a state is an analogue of a probability measure and was first introduced by Kôpka a... more The notion of a state is an analogue of a probability measure and was first introduced by Kôpka and Chovanec for MV-algebras and by Riecan for BLalgebras. The states have also been studied for different types of non-commutative fuzzy structures such as pseudo-MV algebras, pseudo-BL algebras, bounded Rmonoids, residuated lattices and pseudo-BCK semilattices. In this paper we investigate the states on pseudo-BCK algebras and show that Georgescu's original problem in [10] for pseudo-BL algebras has a negative solution for good pseudo-BCK algebras. We prove that every Bosbach state on a pseudo-BCK algebra is a Riecan state and that every Riecan state on a good pseudo-BCK algebra with pseudo-double negation is a Bosbach state. In contrast to the case of pseudo-BL algebras, we show that there exist linearly ordered pseudo-BCK algebras having no Bosbach states.

PURE MATHEMATICS | RESEARCH ARTICLE Extensions of BCK-algebras

In this paper, we introduce the notion of sBCI/sBCK/eBCI/eBCK-algebras as a generalization of the... more

Independence concepts for groupoids

Annales Universitatis Paedagogicae Cracoviensis, 2023

In this paper, for getting more results in groupoids, we consider a set and introduce the notion ... more In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset. Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.

Left rays of groupoids

Asian-european Journal of Mathematics, May 7, 2022

In this paper, we introduce and study the notion of a [Formula: see text]positive implicative[For... more In this paper, we introduce and study the notion of a [Formula: see text]positive implicative[Formula: see text] left ray in groupoids, and we show that every normal subgroup of a group is a left ray of a group, and in every finite group, left rays are normal subgroups. Further, left absorptive subsets of groupoids are discussed and several examples for these definitions provided. The relationship between left rays and zero semigroups is discussed.

Interval-valued hesitant fuzzy filters in BE-algebras

Journal of Intelligent and Fuzzy Systems, Jun 22, 2017

In this paper, we develop fuzzy filter theory on a BE-algebra and apply the concept of interval-v... more In this paper, we develop fuzzy filter theory on a BE-algebra and apply the concept of interval-valued hesitant fuzzy filter to BE-algebras. Moreover, some types of interval-valued hesitant fuzzy filters such as interval-valued hesitant fuzzy implicative filter and interval-valued hesitant fuzzy fantastic filter are introduced and some of properties are investigated.

A generalization of groups

Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, Mar 18, 2018

In this article we introduce the notion of e-group as a new generalization of a group. The condit... more In this article we introduce the notion of e-group as a new generalization of a group. The condition for a group to be an e-group is given. The characterization of some properties is established and some results follow. * 2 a b c d a a a a a b a b c d c c c a d d b d b c Then (G; * 1 , A) satisfies (G1) and (eG2) but does not satisfy (eG3). In addition, (G; * 2 ; A) satisfies (eG2) and (eG3) but does not satisfy (G1), since

Decision making on consistent customer centric inventory model with quality sustenance and smart warehouse management cost parameters

Decision Making: Applications in Management and Engineering

Customer acquaintance and the quality of the products decide the survival span of all the busines... more Customer acquaintance and the quality of the products decide the survival span of all the business sectors. Every production firm attempts to manufacture novel products with attractive and compatible features to satisfy the demands of different types of customers, especially with a special preference for the consistent kind of customers. A decision-making inventory model compassing the initiatives taken by the production firm for consistent customers is developed with the inclusion of costs associated with quality conservation and warehouse management. The reliability of the model is validated with numerical examples and inferences on parametric variations are made by comparing the results employing MATLAB software. The proposed model shall be further discussed in a fuzzy environment

J o u r n a l of Mathematics and Applications

This paper is devoted to the study of some structural properties of bounded and involutory BE-alg... more This paper is devoted to the study of some structural properties of bounded and involutory BE-algebras and investigate the relationship between them. We construct a commutative monoid by definition of proper operation in an involutory BE-algebra. Some rules of calculus for BE-algebras with a semi-lattice structure are provided. Many results related to the natural order of a BE-algebras were found. Finally, we show that an involutory bounded BE-algebra X is semi-simple.

On filters in eBE-algebras

Afrika Matematika

On Neutro-LA-semihypergroups and Neutro-Hv-LA-semigroups

In this paper, we extend the notion of LA-semihypergroups (resp. Hv-LA-semigroups) to neutro-LA-s... more In this paper, we extend the notion of LA-semihypergroups (resp. Hv-LA-semigroups) to neutro-LA-semihypergroups (respectively, neutro-Hv-LA-semigroups). Anti-LA-semihypergroups (respectively, anti-Hv-LA-semigroups) are studied and investigated some of their properties. We show that these new concepts are di fferent from classical concepts by several examples. These are particular cases of the classical algebraic structures generalized to neutroalgebraic structures and antialgebraic structures (Smarandache, 2019). 2000 Mathematics subject classification: 20N20, 20N99.

Applications of states to BI-algebras

Journal of algebraic hyperstructures and logical algebras, Aug 1, 2022

This paper aims is to introduce states, Bosbach states and state-morphism operators on BI-algebra... more This paper aims is to introduce states, Bosbach states and state-morphism operators on BI-algebras. We define state ideals on BI-algebras and give a characterization of the least state ideal of a BI-algebra. It is proved that the kernel of a Bosbach state on a BI-algebra X is an ideal of X. Further, by these concepts, we introduce the notions of state BI-algebras and state-morphism BIalgebras. The notion of complement pairs of a BI-algebra X is defined, and proves that under suitable conditions, there is a one-to-one correspondence between complement pairs of BI-algebras and state-morphism operators on BI-algebras.

On Neutrosophic RM-algebras

The Educational Publisher Inc., 2021

Intuitionistic (T,S)-fuzzy CI-algebras

Computers & Mathematics with Applications, 2012

In this paper, we introduce the notion of intuitionistic (T , S)-fuzzy subalgebras in CIalgebras ... more In this paper, we introduce the notion of intuitionistic (T , S)-fuzzy subalgebras in CIalgebras and study their fundamental properties. We get a fuzzy subalgebra from an intuitionistic (T , S)-fuzzy subalgebra. Also the notion of intuitionistic (T , S)-fuzzy (closed) filters of CI-algebras is introduced. We investigate the relationship between intuitionistic (T , S)-fuzzy subalgebras and intuitionistic (T , S)-fuzzy (closed) filters of CI-algebras.

ON S mBE-ALGEBRAS

In this article, class of all bounded commutative self distributive modal BE-algebras mBE S is in... more

Distributive Pseudo Be-Algebras

Fasciculi Mathematici, 2015

In this paper, we introduce the notion of distributive pseudo BE-algebra and show that the relate... more In this paper, we introduce the notion of distributive pseudo BE-algebra and show that the related relation defined on this structure is transitive and prove that every pseudo upper set is a pseudo filter. Also, the pseudo filter generated by a set is define and show that the set of all pseudo filters is distributive complete lattice but it is not complemented. the notion of prime and irreducible subset and prove that every irreducible subset is prime.

Journal of Algebraic Hyperstructures and Logical Algebras

In this paper, we introduce the notion of a ringoid, and we obtain left distributive ringoids ove... more In this paper, we introduce the notion of a ringoid, and we obtain left distributive ringoids over a field which are not rings. We introduce several different types of ringoids, and also we discuss on (r, s)-ringoids. Moreover, we discuss geometric observations of the parallelism of vectors in several ringoids.

On eGE-algebras

Discussiones Mathematicae - General Algebra and Applications

A new algebraic structure was introduced, called an eGE-algebra, which is a generalisation of a G... more

Neutrosophic N−Ideals on Sheffer Stroke BCK-Algebras

Journal of the Indonesian Mathematical Society

In this study, a neutrosophic N −subalgebra and neutrosophic N−ideal of a Sheffer stroke BCK-alge... more In this study, a neutrosophic N −subalgebra and neutrosophic N−ideal of a Sheffer stroke BCK-algebras are defined. It is shown that the level-set of a neutrosophic N−subalgebra (ideal) of a Sheffer stroke BCK-algebra is a subalgebra (ideal) of this algebra and vice versa. Then we present that the family of all neutrosophic N−subalgebras of a Sheffer stroke BCK-algebra forms a complete distributive modular lattice and that every neutrosophic N−ideal of a Sheffer stroke BCK-algebra is the neutrosophic N −subalgebra but the inverse does not usually hold. Also, relationships between neutrosophic N−ideals of Sheffer stroke BCK-algebras and homomorphisms are analyzed. Finally, we determine special subsets of a Sheffer stroke BCK-algebra by means of N−functions on this algebraic structure and examine the cases in which these subsets are its ideals.

Neutrosophic N −structures on Sheffer stroke BCH-algebras

CERN European Organization for Nuclear Research - Zenodo, Jun 29, 2022

The aim of the study is to introduce a neutrosophic N −subalgebra and neutrosophic N −ideal of a ... more The aim of the study is to introduce a neutrosophic N −subalgebra and neutrosophic N −ideal of a Sheffer stroke BCH-algebras. We prove that the level-set of a neutrosophic N −subalgebra (neutrosophic N −ideal) of a Sheffer stroke BCH-algebra is its subalgebra (ideal) and vice versa. Then it is shown that the family of all neutrosophic N −subalgebras of a Sheffer stroke BCH-algebra forms a complete distributive modular lattice. Also, we state that every neutrosophic N −ideal of a Sheffer stroke BCH-algebra is its neutrosophic N −subalgebra but the inverse is generally not true. We examine relationships between neutrosophic N −ideals of Sheffer stroke BCH-algebras by means of a surjective homomorphism between these algebras. Finally, certain subsets of a Sheffer stroke BCH-algebra are defined by means of N −functions on this algebraic structure and some properties are investigated.