University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2
2
2021
05
01
On nilpotent and solvable pair of polygroups
1
12
EN
E.
Mohammadzadeh
Department of Mathematics, Faculty of Science, Payame Noor University, Tehran, Iran
mohamadzadeh36@gmail.com
F.
Mohammadzadeh
Department of Mathematics, Faculty of Science, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
mohamadzadef464@gmail.com
10.52547/HATEF.JAHLA.2.2.1
In this paper, we introduce nilpotent and solvable pair of polygroups. By a pair of polygroups $(P,N)$, we mean a polygroup $P$ with a normal sub-polygroup $N$ of $P$. In addition, we obtain a necessary and sufficient condition between nilpotency (solvability) of pair of polygroups and pair of groups. In particular, we extend the theory of groups to a pair of polygroups. Finally, we study the relationship between nilpotent and solvable pair of polygroups.
Polygroups,pair of polygroups,solvable pair of polygroups,nilpotent pair of polygroups
https://jahla.hatef.ac.ir/article_132752.html
https://jahla.hatef.ac.ir/article_132752_25a4e513e6f078240488ffe232dbbb3e.pdf
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2
2
2021
05
01
On neutro-d-subalgebras
13
23
EN
M.
Hamidi
0000-0002-8686-6942
Payam nor university, Kashan
m.hamidi@pnu.ac.ir
10.52547/HATEF.JAHLA.2.2.13
This paper introduces the novel concept of neutro-d-algebra. In neutro-d-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: Appurtenance, non-appurtenance, or indeterminate and for an axiom: Equal, non-equal, or indeterminate. This study investigates the neutro-d-algebra and shows that neutro-d-algebra is different from d-algebra. The notation of neutro-d-algebra generates a new concept of neutro poset. Finally, we introduce a notation of neutro d-homomorphism and extend the structure of neutro-d-algebras.
Neutro-d-algebra,neutro poset,neutro transitive d-algebra,neutro d-homomorphism
https://jahla.hatef.ac.ir/article_132753.html
https://jahla.hatef.ac.ir/article_132753_9c0fb81103d4b9d49aa9d2853a861f7a.pdf
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2
2
2021
05
01
On S-prime hyperideals in multiplicative hyperrings
25
34
EN
P.
Ghiasvand
Department of Mathematics, Payame Noor University, Tehran, Iran
p_ghiasvand@pnu.ac.ir
F.
Farzalipour
Department of Mathematics, Payame Noor University, P.O.BOX 19395-3697 Tehran, Iran,
f_farzalipour@pnu.ac.ir
10.52547/HATEF.JAHLA.2.2.25
Let R be a multiplicative hyperring and S be a subset of R be a multiplicatively closed subset of R. In this paper, we introduce and study the concept of S-prime hyperideals which is a generalization of prime hyperideals. Some properties of S-prime hyperideals in multiplicative hyperring are presented. Then we investigate the behaviour of S-prime hyperideals under homomorphism hyperrings, in factor hyperrings, Cartesian products of hyperrings, and the fundamental relation in the context of multiplicative hyperring.
Multiplicative hyperring,prime hyperideal,S-prime hyperideal
https://jahla.hatef.ac.ir/article_132754.html
https://jahla.hatef.ac.ir/article_132754_ef2846382691bd2ac9e5ed4a756dca85.pdf
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2
2
2021
05
01
On $\alpha$-solvable fundamental groups
35
46
EN
F.
Mohammadzadeh
Department of Mathematics, Faculty of Science, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran
mohamadzadef464@gmail.com
E.
Mohammadzadeh
Department of Mathematics, Faculty of Science, Payame Noor University, Tehran, Iran
mohamadzadeh36@gmail.com
10.52547/HATEF.JAHLA.2.2.35
We introduce a specific kind of equivalence relation ${\xi^*}_n^{\alpha}$ on a fuzzy hypergroup S such that the quotient $S/ {\xi^*}_n^{\alpha}$, the set of all equivalence classes, is an $\alpha$-solvable group. This helps us to introduce the $\alpha$-solvable fundamental relation $\xi^{*\alpha}$. In particular, we obtain an equivalent condition with transitivity of $\xi^\alpha$.
Fuzzy hypergroup,fundamental relation,$alpha$-solvable group
https://jahla.hatef.ac.ir/article_132755.html
https://jahla.hatef.ac.ir/article_132755_745d49519fe12905cc1c482af9c1f924.pdf
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2
2
2021
05
01
Connections between fuzzy multi-groups and fuzzy multi-graphs
47
60
EN
S.
Mirvakili
https://orcid.org/00
Department of mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran
saeed_mirvakili@pnu.ac.ir
H.
Naraghi
Department Mathematics, Payame Noor University, Tehran, Iran.
ho.naraghi@pnu.ac.ir
M.
Shirvani
Department of Mathematics, Payame Noor University, Tehran, Iran
maryam.shirvani81@gmail.com
10.52547/HATEF.JAHLA.2.2.47
In this paper, we introduce the concept of fuzzy multi-graphs and a type of isomorphism on fuzzy multi-graphs and study their properties. We show that how to assign a fuzzy multi-graph to the appropriate fuzzy multi-groups. We also prove that every fuzzy multi-group of group $G$ can be embedded into the fuzzy multi-group of the group $Aut(\Gamma_\wedge^\sigma)$, where $Aut(\Gamma_\wedge^\sigma)$ is a group of automorphisms of the fuzzy multi-graph $\Gamma_\wedge^\sigma$.
Fuzzy multi-graph,fuzzy multi-group,Fuzzy graph,automorphism
https://jahla.hatef.ac.ir/article_132756.html
https://jahla.hatef.ac.ir/article_132756_7382afd644e1739b8c65062932f52474.pdf
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2
2
2021
05
01
K-nilpotent groups based on hypergroups
61
72
EN
A.
Mosayebi Dorcheh
0000-0001-7665-7859
Department of Mathematics, Payame Noor University (PNU), Iran
alimosayebi@chmail.ir
10.52547/HATEF.JAHLA.2.2.61
Fundamental relations are one of the main tools in connection relation between hyperstructures theory and structures theory. In this paper, we introduce a general fundamental relation on any hypergroup in such a way that all fundamental relations are a special case of this relation. Also, this study considered the notation of the relation on the derivation of $k$-nilpotent groups from any hypergroups.
Hypergroup,relation-part,$k$-nilpotent group
https://jahla.hatef.ac.ir/article_132757.html
https://jahla.hatef.ac.ir/article_132757_093c7be3aa633259973965b246420407.pdf
University of Hatef (Hatef College University)
Journal of Algebraic Hyperstructures and Logical Algebras
2676-6000
2676-6019
2
2
2021
05
01
Irregular vague graphs
73
90
EN
S.
Banitalebi
Department of Knowledge and Cognitive Intelligence‎‎‎, ‎Imam Hossein University‎, ‎Tehran‎, ‎Iran
krbanitalebi@ihu.ac.ir
10.52547/HATEF.JAHLA.2.2.73
A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, the new concepts of (totally) irregular, strongly (totally) irregular, highly totally irregular, neighborly totally irregular, edge-irregular of vague graphs are introduced and generalized, and some properties and related results are investigated. Then, we present the concepts of homomorphism, weak isomorphism, co-weak isomorphism and isomorphism of irregular vague graphs and some results on (total) domination number, (total) 2-domination number, (total) cobondage number and (total) 2-cobondage number. Finally, one of their applications related to location map of Fire Stations and Emergency Medical centers in urban regions of a metropolis is presented.
Vague graph,irregular vague graph,homomorphism,isomorphim
https://jahla.hatef.ac.ir/article_132758.html
https://jahla.hatef.ac.ir/article_132758_85a9d5a9da971941bbe394cc5276ff32.pdf