eng
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2020-08-01
1
3
1
14
10.29252/hatef.jahla.1.3.1
113360
Original Article
From rings to minimal Hv-fields
T. Vougiouklis
tvougiou@eled.duth.gr
1
Emeritus Professor of Mathematics, Democritus University of Thrace, Greece
The class of Hv-structures is the largest class of hyperstructures defined on the same set. For this reason, they have applications in mathematics and in other sciences, which range from biology, hadronic physics, leptons, linguistics, sociology, to mention but a few. They satisfy the weak axioms where the non-empty intersection replaces equality. The fundamental relations connect, by quotients, the Hv-structures with the classical ones. In order to specify the appropriate hyperstructure as a model for an application which fulfill a number of properties, the researcher can start from the basic ones. Thus, the researcher must know the minimal hyperstructures. Hv-numbers are elements of Hv-field, and they are used in representation theory. In this presentation we focus on minimal Hv-fields derived from rings.
https://jahla.hatef.ac.ir/article_113360_b39c2a6fa92d72aa1cf7e95bdf0c1266.pdf
Hyperstructure
Hv -structure
hope
iso-numbers
hypernumbers
eng
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2020-08-01
1
3
15
29
10.29252/HATEF.JAHLA.1.3.2
113361
Original Article
A brief survey on algebraic hyperstructures: Theory and applications
B. Davvaz
davvaz@yazd.ac.ir
1
Department of Mathematics Yazd University, Yazd Iran
I am working on algebraic hyperstructures from 1995. During the last twenty years, I together with my students and co-authors studied and developed the theory of algebraic hyperstructures in many directions. In particular, we tried to find real examples of hyperstructures in nature. In this paper we review some parts of these works such as (1) Fundamental relations on hyperstructures; (2) Fuzzy sets and hyperstructures; (3) Rough sets and hyperstructures; (4) Topology and hyperstructures; (5) Number theory and hyperstructures; (6) n-ary hypergroups and there extension to hyperrings and hypermodules; (7) Applications of hyperstructures in biology, physics and chemistry.
https://jahla.hatef.ac.ir/article_113361_87b9f01d2154e1386c8dcb03d52ada1e.pdf
Hyperstructures
fundamental relations
Fuzzy Sets
rough sets
n-ary hypergroups
eng
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2020-08-01
1
3
31
50
10.29252/hatef.jahla.1.3.3
113363
Original Article
An overview of hyper logical algebras
R.A. Borzooei
borzooei@sbu.ac.ir
1
M. Aaly
mona4011@gmail.com
2
Shahid Beheshti University
Hatef University
Hyper logical algebras were first studied in 2000 by Borzooei et al. They applied the concept of hyperstructures to one of the logical algebraic structures known as the BCK-algebra, and introduced two generalizations of them called the hyper BCK-algebra and hyper K-algebra. Then many researchers in this field continued their research and used hyperstructures on other logical algebras and introduced the concepts of hyper residuated lattices, hyper BL-algebras, hyper MV-algebras, hyper EQ-algebras, hyper BE-algebras, hyper equality algebras, hyper hoops and etc. Moreover, they defined some new notions such as different kinds of hyper ideals, hyper filters and hyper congruence relations on these structures and studied some properties, the relation among them and the quotient structure. Now, in this paper, we review the definitions of all those hyper logical algebras and investigate relations among them.
https://jahla.hatef.ac.ir/article_113363_988394cc10f3520c0df8c4cec7f11f2f.pdf
Hyper BCK-algebra
hyper K-algebra
hyper I-algebra
hyper BCC-algebra
hyper MV-algebra
Hyper residuated lattice
hyper hoop
hyper EQ-algebra
hyper equality algebra
hyper BL-algebra
eng
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2020-08-01
1
3
51
60
10.29252/hatef.jahla.1.3.4
113364
Original Article
On strong-inverse elements
T. Kaplani
dorakikaplani@gmail.com
1
T. Vougiouklis
tvougiou@eled.duth.gr
2
1Fotada, 42100 Trikala, Greece,
Emeritus Professor of Mathematics, Democritus University of Thrace, Greece
Hyperstructures have applications in mathematics and in other sciences. For this, the largest class of the hyperstructures, the Hv-structures, is used. They satisfy the weak axioms where the non-empty intersection replaces equality. The fundamental relations connect, by quotients, the Hv-structures with the classic
https://jahla.hatef.ac.ir/article_113364_3cf745d5f9b805172718a085ddbc2cbc.pdf
Hyperstructure
hope
H_{v}-structure
strong inverse element
eng
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2020-08-01
1
3
61
72
10.29252/hatef.jahla.1.3.5
113366
Original Article
Hyper vector spaces over Krasner hyperfields
M. Al-Tahan
madeline.tahan@liu.edu.lb
1
B. Davvaz
davvaz@yazd.ac.ir
2
Department of Mathematics, Lebanese International University, Bekaa, CZ-961, Lebanon
Department of Mathematics Yazd University, Yazd Iran
In this paper, we study hyper vector spaces over Krasner hyperfields. First, we introduce the notions of linearly independence (dependence) and basis for a hyper vector space. Second, we investigate their properties and prove some results for hyper vector spaces that are similar to that of vector spaces over fields. Then, we define linear transformations over hyper vector spaces and investigate their properties. Finally, we prove the dimension theorem for linear transformations.
https://jahla.hatef.ac.ir/article_113366_284ecb4e5f42e74f8f524aba5ec6ea4b.pdf
Krasner hyperfield
hyper vector space
subhyperspace
linearly independent
basis
linear transformation
eng
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2020-08-01
1
3
73
79
10.29252/hatef.jahla.1.3.6
113367
Original Article
Hyperstructures on bar of V & V in pieces
P. Nikolaidou
pnikolai@eled.duth.gr
1
Democritus University of Thrace, Orestiada, 68200, Greece
An application of hyperstructure theory on social sciences is presented. In social sciences when questionnaires are used, there is a new tool, the bar instead of Likert scale. The bar has been suggested by Vougiouklis & Vougiouklis in 2008, who have proposed the replacement ofLikert scales, usually used in questionnaires, with a bar. This new tool, gives the opportunity to researchers to elaborate the questionnaires in different ways, depending on the filled questionnaires and of course on the problem. We study these filled questionnaires using hyperstructure theory. The hyperstructure theory is being related with questionnaires and we study the obtained hyperstructures which are used as an organized device of the problem and we focus on special problems.
https://jahla.hatef.ac.ir/article_113367_bb54572f949e1f62c7dd5ce53caa0f68.pdf
Hyperstructures
Questionnaires
Hv -structure
V & V bar
eng
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2020-08-01
1
3
81
90
10.29252/hatef.jahla.1.3.7
113368
Original Article
Hyperoperations defined on sets of S -helix matrices
S. Vougioukli
elsouvou@gmail.com
1
Aristotle University of Thessaloniki
A hyperproduct on non-square ordinary matrices can be defined by using the helix-hyperoperation. Therefore, the helix-hyperoperation (abbreviated hope ) is based on a classical operation and was introduced in order to overcome the non-existing cases. We study the helixhyperstructures on the special type of matrices, the Shelix matrices, used on the small dimension representations. In this paper, we introduce and focus our study on the class of S-helix matrices called k-overlap helix matrices. The reason is that their hyper-vector spaces can represent n-dimensional spaces which have independent both, single valued dimensions and multivalued dimensions.
https://jahla.hatef.ac.ir/article_113368_ce91454aaad50f755fa4775236257e8c.pdf
Hyperstructures
Hv -structures
hope
helix-hopes
eng
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2020-08-01
1
3
91
97
10.29252/hatef.jahla.1.3.8
113369
Original Article
Cyclicity in some classes of Hv-groups
P. Kamporoudi
pkamporoudi@gmail.com
1
T. Vougiouklis
tvougiou@eled.duth.gr
2
Democritus University of Thrace, Panagathou 44B, Alexandroupoli 68131, Greece 2
Emeritus Professor of Mathematics, Democritus University of Thrace, Greece
The study of cyclicity in hyperstructures was started very early, almost from the beginning of the introduction of a hypergroup by F. Marty in 1934. New concepts appeared in hyperstructures the main of which are the period of a generator and the single power cyclicity. These terms have no meaning in the classical structures as groups. We study the cyclicity in special large classes of Hv-groups.
https://jahla.hatef.ac.ir/article_113369_6bbb11134cf8d28e802db02252311671.pdf
Hv-group
hope
cyclicity
single power cyclicity
generator