In this paper, we consider join hyperlattices and we define ordered join hyperlattices. Then, we ... more In this paper, we consider join hyperlattices and we define ordered join hyperlattices. Then, we consider product of two orderd join hyperlattices and we study prime ideals on them. Moreover, we define semiprime ideals on ordered join hyperlattices and prove some results about them. Also, we define a regular relation on ordered join hyperlattice L such that the quotient of L is an ordered join hyperlattice. Then, we investigate isomorphism on product of two ordered join hyperlattices with such regular relations.
International Journal of Analysis and Applications, 2016
In this paper, the relation between two definitions of a fuzzy topological polygroup is discussed... more In this paper, the relation between two definitions of a fuzzy topological polygroup is discussed. The collection of all fuzzy continuous functions from a fuzzy topological space Y to a fuzzy topological polygroup Z, denoted by FC(Y,Z) induces a polygroup structure from that of Z. Moreover, we study (fuzzy) topological polygroup of the polygroup FC(Y,Z) when it is equipped with various known topologies and fuzzy topologies. Also, a few properties of fuzzy topological polygroups are established and a category CFTP is formed with objects as FTP and morphisms as the fuzzy topological homomorphisms. The category CTP is seen to be a full subcategory of CFTP.
International Journal of Analysis and Applications, 2016
The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the not... more The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. Intuitionistic fuzzy topological spaces were introduced by Coker. This paper provides a new connection between algebraic hyperstructures and intuitionistic fuzzy sets. In this paper, we introduce and study the concept of intuitionistic fuzzy subpolygroup and intuitionistic fuzzy topological polygroup. We also investigate some interesting properties of an intuitionistic fuzzy subpolygroup and intuitionistic fuzzy normal subpolygroup.
International Journal of Neutrosophic Science, 2020
The aim of this paper is to combine the notions of ordered algebraic structures and neutrosophy. ... more The aim of this paper is to combine the notions of ordered algebraic structures and neutrosophy. In this regard, we define for the first time single valued neutrosophic sets in ordered groupoids. More precisely, we study single valued neutrosophic subgroupoids of ordered groupoids, single valued neutrosophic ideals of ordered groupoids, and single valued neutrosophic filters of ordered groupoids. Finally, we present some remarks on single valued neutrosophic subgroups (ideals) of ordered groups.
International Journal of Neutrosophic Science, 2020
In this paper, we find a relationship between SVNS and neutrosophic N-structures and study it. Mo... more In this paper, we find a relationship between SVNS and neutrosophic N-structures and study it. Moreover, we apply our results to algebraic structures (hyperstructures) and prove that the results on neutrosophic N-substructure (subhyperstructure) of a given algebraic structure (hyperstructure) can be deduced from single valued neutrosophic algebraic structure (hyperstructure) and vice versa.
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2017
In this paper, by considering the notion of congruences on hyper- lattices we define almost princ... more In this paper, by considering the notion of congruences on hyper- lattices we define almost principal ideals on hyperlattices. We investigate some properties and prove some results about them. Also, we define compatible functions on hyperlattices and investigate connection between these functions and almost principal ideals. Then, we define tensor product of two hyperlattices and present several properties such as completeness and distributivity on tensor product of hyperlattices.
The concept of ordered semihypergroups is a generalization of the concept of ordered semigroups. ... more The concept of ordered semihypergroups is a generalization of the concept of ordered semigroups. In this paper, we study some aspects of hyperideals, bi-hyperideals and quasi-hyperideals of ordered semihypergroups. We investigate the notions of regular, intra-regular and completely regular ordered semihypergroups and give their characterizations in terms of hyperideals, bi-hyperideals and quasi-hyperideals. Also, the notion of duo ordered semihypergroups is introduced and some related results are discussed.
In a multiplicative hyperring, the multiplication is a hyperoperation, while the addition is a bi... more In a multiplicative hyperring, the multiplication is a hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is in- troduced and some related properties are investigated.
In this paper, we extend the notion of 2-absorbing ideal on rings to Krasner hyperrings. In fact... more In this paper, we extend the notion of 2-absorbing ideal on rings to Krasner hyperrings. In fact, we give a characterization of new generalization of prime hyperideals in Krasner hyperrings by introducing 2-absorbing hyperideals. We present some illustrative examples. Also, we study fundamental properties of 2-absorbing hyperideals on Krasner hyperrings and investigate some related results.
In this paper, we first introduce the concept of fuzzy interior hyperideals of an ordered semihyp... more In this paper, we first introduce the concept of fuzzy interior hyperideals of an ordered semihypergroup S by the ordered fuzzy points of S; and investigate its related properties. In particular, we give the characterization of fuzzy interior hyperideal generated by a fuzzy subset in an ordered semihypergroup. Furthermore, the idea of normal fuzzy interior hyperideals in ordered semihypergroups is given and several related characterization theorems are provided. Finally, some new characterizations of semisimple ordered semihypergroups by the properties of fuzzy interior hyperideals are given.
The study of hypernear-rings is extremely challenging, offering curiously beautiful results to on... more The study of hypernear-rings is extremely challenging, offering curiously beautiful results to one who is willing to look for structure where symmetry is not so abundant. The purpose of this paper is to present certain results arising from a study of hypernear-rings. In particular, we define the notion of hyper R-subgroup of a hypernear-ring and we investigate some properties of hypernear-rings with respect to the hyper R-subgroups.
In this paper, we introduce the notion of derivation on Krasner hyperrings as follows: the functi... more In this paper, we introduce the notion of derivation on Krasner hyperrings as follows: the function d : R R isa derivation on a Krasner hyperring R if for all , , Ry x ) ( ) ( = ) ( y d x d y x d andd (x y) d (x) y x d ( y). Then, we investigate some fundamental properties of derivation on Krasnerhyperings and prime Krasner hyperrings. Also, we introduce differential Krasner hyperingsand discuss some relatedproperties.
In this paper, we study various strongly convex hyper S-subposets of hyper S-posets in detail. To... more In this paper, we study various strongly convex hyper S-subposets of hyper S-posets in detail. To begin with, we consider the decomposition of hyper S-posets. A unique decomposition theorem for hyper S-posets is given based on strongly convex indecomposable hyper S-subposets. Furthermore, we discuss the properties of minimal and maximal strongly convex hyper S-subposets of hyper S-posets. In the sequel, the concept of hyper C-subposets of a hyper S-poset is introduced, and several related properties are investigated. In particular, we discuss the relationship between greatest strongly convex hyper S-subposets and hyper C-subposets of hyper S-posets. Moreover, we introduce the concept of bases of a hyper S-poset and give out the sufficient and necessary conditions of the existence of the greatest hyper C-subposets of a hyper S-poset by the properties of bases.
In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in d... more In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208–217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.
We introduce the concept of(f,g)-derivations ofBCI-algebras and we investigate some fundamental p... more We introduce the concept of(f,g)-derivations ofBCI-algebras and we investigate some fundamental properties and establish some results on(f,g)-derivations. Also, we treat to generalization of right derivation and left derivation ofBCI-algebras and consider some related properties.
In this paper, we consider join hyperlattices and we define ordered join hyperlattices. Then, we ... more In this paper, we consider join hyperlattices and we define ordered join hyperlattices. Then, we consider product of two orderd join hyperlattices and we study prime ideals on them. Moreover, we define semiprime ideals on ordered join hyperlattices and prove some results about them. Also, we define a regular relation on ordered join hyperlattice L such that the quotient of L is an ordered join hyperlattice. Then, we investigate isomorphism on product of two ordered join hyperlattices with such regular relations.
International Journal of Analysis and Applications, 2016
In this paper, the relation between two definitions of a fuzzy topological polygroup is discussed... more In this paper, the relation between two definitions of a fuzzy topological polygroup is discussed. The collection of all fuzzy continuous functions from a fuzzy topological space Y to a fuzzy topological polygroup Z, denoted by FC(Y,Z) induces a polygroup structure from that of Z. Moreover, we study (fuzzy) topological polygroup of the polygroup FC(Y,Z) when it is equipped with various known topologies and fuzzy topologies. Also, a few properties of fuzzy topological polygroups are established and a category CFTP is formed with objects as FTP and morphisms as the fuzzy topological homomorphisms. The category CTP is seen to be a full subcategory of CFTP.
International Journal of Analysis and Applications, 2016
The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the not... more The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. Intuitionistic fuzzy topological spaces were introduced by Coker. This paper provides a new connection between algebraic hyperstructures and intuitionistic fuzzy sets. In this paper, we introduce and study the concept of intuitionistic fuzzy subpolygroup and intuitionistic fuzzy topological polygroup. We also investigate some interesting properties of an intuitionistic fuzzy subpolygroup and intuitionistic fuzzy normal subpolygroup.
International Journal of Neutrosophic Science, 2020
The aim of this paper is to combine the notions of ordered algebraic structures and neutrosophy. ... more The aim of this paper is to combine the notions of ordered algebraic structures and neutrosophy. In this regard, we define for the first time single valued neutrosophic sets in ordered groupoids. More precisely, we study single valued neutrosophic subgroupoids of ordered groupoids, single valued neutrosophic ideals of ordered groupoids, and single valued neutrosophic filters of ordered groupoids. Finally, we present some remarks on single valued neutrosophic subgroups (ideals) of ordered groups.
International Journal of Neutrosophic Science, 2020
In this paper, we find a relationship between SVNS and neutrosophic N-structures and study it. Mo... more In this paper, we find a relationship between SVNS and neutrosophic N-structures and study it. Moreover, we apply our results to algebraic structures (hyperstructures) and prove that the results on neutrosophic N-substructure (subhyperstructure) of a given algebraic structure (hyperstructure) can be deduced from single valued neutrosophic algebraic structure (hyperstructure) and vice versa.
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2017
In this paper, by considering the notion of congruences on hyper- lattices we define almost princ... more In this paper, by considering the notion of congruences on hyper- lattices we define almost principal ideals on hyperlattices. We investigate some properties and prove some results about them. Also, we define compatible functions on hyperlattices and investigate connection between these functions and almost principal ideals. Then, we define tensor product of two hyperlattices and present several properties such as completeness and distributivity on tensor product of hyperlattices.
The concept of ordered semihypergroups is a generalization of the concept of ordered semigroups. ... more The concept of ordered semihypergroups is a generalization of the concept of ordered semigroups. In this paper, we study some aspects of hyperideals, bi-hyperideals and quasi-hyperideals of ordered semihypergroups. We investigate the notions of regular, intra-regular and completely regular ordered semihypergroups and give their characterizations in terms of hyperideals, bi-hyperideals and quasi-hyperideals. Also, the notion of duo ordered semihypergroups is introduced and some related results are discussed.
In a multiplicative hyperring, the multiplication is a hyperoperation, while the addition is a bi... more In a multiplicative hyperring, the multiplication is a hyperoperation, while the addition is a binary operation. In this paper, the notion of derivation on multiplicative hyperrings is in- troduced and some related properties are investigated.
In this paper, we extend the notion of 2-absorbing ideal on rings to Krasner hyperrings. In fact... more In this paper, we extend the notion of 2-absorbing ideal on rings to Krasner hyperrings. In fact, we give a characterization of new generalization of prime hyperideals in Krasner hyperrings by introducing 2-absorbing hyperideals. We present some illustrative examples. Also, we study fundamental properties of 2-absorbing hyperideals on Krasner hyperrings and investigate some related results.
In this paper, we first introduce the concept of fuzzy interior hyperideals of an ordered semihyp... more In this paper, we first introduce the concept of fuzzy interior hyperideals of an ordered semihypergroup S by the ordered fuzzy points of S; and investigate its related properties. In particular, we give the characterization of fuzzy interior hyperideal generated by a fuzzy subset in an ordered semihypergroup. Furthermore, the idea of normal fuzzy interior hyperideals in ordered semihypergroups is given and several related characterization theorems are provided. Finally, some new characterizations of semisimple ordered semihypergroups by the properties of fuzzy interior hyperideals are given.
The study of hypernear-rings is extremely challenging, offering curiously beautiful results to on... more The study of hypernear-rings is extremely challenging, offering curiously beautiful results to one who is willing to look for structure where symmetry is not so abundant. The purpose of this paper is to present certain results arising from a study of hypernear-rings. In particular, we define the notion of hyper R-subgroup of a hypernear-ring and we investigate some properties of hypernear-rings with respect to the hyper R-subgroups.
In this paper, we introduce the notion of derivation on Krasner hyperrings as follows: the functi... more In this paper, we introduce the notion of derivation on Krasner hyperrings as follows: the function d : R R isa derivation on a Krasner hyperring R if for all , , Ry x ) ( ) ( = ) ( y d x d y x d andd (x y) d (x) y x d ( y). Then, we investigate some fundamental properties of derivation on Krasnerhyperings and prime Krasner hyperrings. Also, we introduce differential Krasner hyperingsand discuss some relatedproperties.
In this paper, we study various strongly convex hyper S-subposets of hyper S-posets in detail. To... more In this paper, we study various strongly convex hyper S-subposets of hyper S-posets in detail. To begin with, we consider the decomposition of hyper S-posets. A unique decomposition theorem for hyper S-posets is given based on strongly convex indecomposable hyper S-subposets. Furthermore, we discuss the properties of minimal and maximal strongly convex hyper S-subposets of hyper S-posets. In the sequel, the concept of hyper C-subposets of a hyper S-poset is introduced, and several related properties are investigated. In particular, we discuss the relationship between greatest strongly convex hyper S-subposets and hyper C-subposets of hyper S-posets. Moreover, we introduce the concept of bases of a hyper S-poset and give out the sufficient and necessary conditions of the existence of the greatest hyper C-subposets of a hyper S-poset by the properties of bases.
In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in d... more In this paper, we study the ordered regular equivalence relations on ordered semihypergroups in detail. To begin with, we introduce the concept of weak pseudoorders on an ordered semihypergroup, and investigate several related properties. In particular, we construct an ordered regular equivalence relation on an ordered semihypergroup by a weak pseudoorder. As an application of the above result, we completely solve the open problem on ordered semihypergroups introduced in [B. Davvaz, P. Corsini and T. Changphas, Relationship between ordered semihypergroups and ordered semigroups by using pseuoorders, European J. Combinatorics 44 (2015), 208–217]. Furthermore, we establish the relationships between ordered regular equivalence relations and weak pseudoorders on an ordered semihypergroup, and give some homomorphism theorems of ordered semihypergroups, which are generalizations of similar results in ordered semigroups.
We introduce the concept of(f,g)-derivations ofBCI-algebras and we investigate some fundamental p... more We introduce the concept of(f,g)-derivations ofBCI-algebras and we investigate some fundamental properties and establish some results on(f,g)-derivations. Also, we treat to generalization of right derivation and left derivation ofBCI-algebras and consider some related properties.
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