Topological Polygroups Heidari, D.; Davvaz, B.; Modarres, S. M. S.
Bulletin of the Malaysian Mathematical Sciences Society,
04/2016, Volume:
39, Issue:
2
Journal Article
Peer reviewed
This paper deals with certain algebraic systems called polygroups. A polygroup is a completely regular, reversible in itself hypergroup. The concept of topological polygroups is a generalization of ...the concept of topological groups. In this paper, we present the concept of topological hypergroups and prove some properties. Then, we define the notion of topological polygroups. By considering the relative topology on subpolygroups we prove some properties of them. Finally, the topological isomorphism theorems of topological polygroups are proved.
On geometric polygroups Arabpur, F.; Jafarpour, M.; Aminizadeh, M. ...
Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică,
03/2020, Volume:
28, Issue:
1
Journal Article
Peer reviewed
Open access
In this paper, we introduce a geodesic metric space called generalized Cayley graph (gCay(P,S)) on a finitely generated polygroup. We define a hyperaction of polygroup on gCayley graph and give some ...properties of this hyperaction. We show that gCayley graphs of a polygroup by two different generators are quasi-isometric. Finally, we express a connection between finitely generated polygroups and geodesic metric spaces.
gK-algebra associated to polygroups Naghibi, R.; Anvariyeh, S. M.; Davvaz, B.
Afrika mathematica,
11/2021, Volume:
32, Issue:
7-8
Journal Article
Peer reviewed
In this paper, we first introduce a generalized
K
-algebra (briefly, gK-algebra)
(
P
,
·
,
⊙
,
e
,
-
1
)
which is constructed on a non-symmetric polygroup
(
P
,
·
,
e
,
-
1
)
, by adjoining binary ...hyperoperation
⊙
defined by
x
⊙
y
=
x
·
y
-
1
, for all
x
,
y
∈
P
. Then, we show that every
gK
-algebra associated to a canonical hypergroup is a hyper
B
-algebra with constant
e
. Finally, we define generalized
gK
-subalgebras, (prime) generalized
gK
-ideals, homomorphisms of
(
P
,
·
,
⊙
,
e
,
-
1
)
and quotient generalized
gK
-algebras.
In this paper first, we define the notions of left and right soft int-hypergroups and derive some of their basic properties. Second, we study these concepts in the context of complete hypergroups and ...polygroups. Then, we introduce the notions of left and right soft int-additive hyperrings and soft int-hyperideal. In special case we study these notions for the class of Krasner hyperrings. Finally, a characterization of soft int-hyperideal for the class of Krasner hyperfields is investigated.
Using the triangular norm
T
(conorm
S
) in the context of
n
-ary polygroups, we introduce the concept of an interval-valued (anti) fuzzy
n
-ary subpolygroup with respect to
T
(
S
respectively). A ...necessary and sufficient condition for an interval-valued fuzzy subset in order to be an interval-valued (anti) fuzzy
n
-ary subpolygroup is established and some important results are presented. This study is useful for the most computational part of fuzzy control, which is the defuzzification.
Fuzzy Krasner ( m , n ) -hyperrings Davvaz, B.
Computers & mathematics with applications (1987),
06/2010, Volume:
59, Issue:
12
Journal Article
Peer reviewed
Open access
Recently, Krasner
(
m
,
n
)
-hyperrings were introduced and analyzed by Mirvakili and Davvaz. Krasner
(
m
,
n
)
-hyperrings are a suitable generalization of Krasner hyperrings. This paper concerns a ...relationship between fuzzy sets and hyperstructure theory. It is a continuation of the ideas presented by Davvaz et al. (2009) B. Davvaz, P. Corsini, V. Leoreanu-Fotea, Fuzzy
n
-ary subpolygroups, Computers & Mathematics with Applications 57 (2009) 141–152. The aim of the paper is to introduce the notion of a fuzzy hyperideal of a Krasner
(
m
,
n
)
-hyperring and to extend the fuzzy results to Krasner
(
m
,
n
)
-hyperrings.
In this paper, we prove various inclusion relationships among different classes of algebraic structures and hyperstructures of type
U
on the right of finite size. In particular, we consider in detail ...the inclusion properties
G
n
⊆
PUR
n
⊆
HUR
n
⊆
SUR
n
between the classes of groups
G
n
, polygroups
PUR
n
, hypergroups
HUR
n
and semihypergroups
SUR
n
of type
U
on the right of size
n
and provide conditions such that the equality holds. As a particular result, we prove that every polygroup of type
U
on the right is a group.
Fuzzy n -ary subpolygroups Davvaz, B.; Corsini, P.; Leoreanu-Fotea, V.
Computers & mathematics with applications (1987),
2009, 2009-01-00, 20090101, Volume:
57, Issue:
1
Journal Article
Peer reviewed
Open access
Recently,
n
-ary hypergroups were introduced and analyzed by Davvaz and Vougiouklis.
n
-ary polygroups are suitable generalizations of polygroups and a special case of
n
-ary hypergroups. The aim of ...this paper is to introduce the notion of a fuzzy
n
-ary subpolygroup of an
n
-ary polygroup and to extend the fuzzy results of fundamental equivalence relations to
n
-ary polygroups.
In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. By using a certain type of ...equivalence relations, we can connect semihypergroups to semigroups and hypergroups (polygroups) to groups. These equivalence relations are called strongly regular relations. In this paper, we review some strongly regular relations on hyperstructures and we give some their applications.
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