University of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001320200801From rings to minimal Hv-fields11411336010.29252/hatef.jahla.1.3.1ENT. VougiouklisEmeritus Professor of Mathematics, Democritus University of Thrace, Greece0000-0002-4076-8853Journal Article20200829The 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.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001320200801A brief survey on algebraic hyperstructures: Theory and applications152911336110.29252/HATEF.JAHLA.1.3.2ENB. DavvazDepartment of Mathematics Yazd University, Yazd IranJournal Article20200829I 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.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001320200801An overview of hyper logical algebras315011336310.29252/hatef.jahla.1.3.3ENR.A. BorzooeiShahid Beheshti University0000-0001-7538-7885M. AalyHatef UniversityJournal Article20200829Hyper 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.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001320200801On strong-inverse elements516011336410.29252/hatef.jahla.1.3.4ENT. Kaplani1Fotada, 42100 Trikala, Greece,T. VougiouklisEmeritus Professor of Mathematics, Democritus University of Thrace, Greece0000-0002-4076-8853Journal Article19991130Hyperstructures 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 classichttps://jahla.hatef.ac.ir/article_113364_3cf745d5f9b805172718a085ddbc2cbc.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001320200801Hyper vector spaces over Krasner hyperfields617211336610.29252/hatef.jahla.1.3.5ENM. Al-TahanDepartment of Mathematics, Lebanese International University, Bekaa, CZ-961, LebanonB. DavvazDepartment of Mathematics Yazd University, Yazd IranJournal Article20200829In 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.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001320200801Hyperstructures on bar of V & V in pieces737911336710.29252/hatef.jahla.1.3.6ENP. NikolaidouDemocritus University of Thrace, Orestiada, 68200, GreeceJournal Article20200829An 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 of<br />Likert 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.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001320200801Hyperoperations defined on sets of S -helix matrices819011336810.29252/hatef.jahla.1.3.7ENS. VougioukliAristotle University of ThessalonikiJournal Article20200829A 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.pdfUniversity of Hatef (Hatef College University)Journal of Algebraic Hyperstructures and Logical Algebras2676-60001320200801Cyclicity in some classes of Hv-groups919711336910.29252/hatef.jahla.1.3.8ENP. KamporoudiDemocritus University of Thrace, Panagathou 44B, Alexandroupoli 68131, Greece
2T. VougiouklisEmeritus Professor of Mathematics, Democritus University of Thrace, Greece0000-0002-4076-8853Journal Article20200829The 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