scholarly journals Involution Abel–Grassmann’s Groups and Filter Theory of Abel–Grassmann’s Groups

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 553 ◽  
Author(s):  
Xiaohong Zhang ◽  
Xiaoying Wu
Keyword(s):  
Congruence Relation ◽  
Filter Theory ◽  
Basic Properties ◽  
New Concepts ◽  
Structure Theorems

In this paper, some basic properties and structure characterizations of AG-groups are further studied. First, some examples of infinite AG-groups are given, and weak commutative, alternative and quasi-cancellative AG-groups are discussed. Second, two new concepts of involution AG-group and generalized involution AG-group are proposed, the relationships among (generalized) involution AG-groups, commutative groups and AG-groups are investigated, and the structure theorems of (generalized) involution AG-groups are proved. Third, the notion of filter of an AG-group is introduced, the congruence relation is constructed from arbitrary filter, and the corresponding quotient structure and homomorphism theorems are established.

scholarly journals States and Measures on Hyper BCK-Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiao-Long Xin ◽  
Pu Wang
Keyword(s):  
Congruence Relation ◽  
Basic Properties ◽  
Mv Algebra ◽  
Regular Congruence ◽  
Bosbach State

We define the notions of Bosbach states and inf-Bosbach states on a bounded hyper BCK-algebra(H,∘,0,e)and derive some basic properties of them. We construct a quotient hyper BCK-algebra via a regular congruence relation. We also define a∘-compatibledregular congruence relationθand aθ-compatibledinf-Bosbach stateson(H,∘,0,e). By inducing an inf-Bosbach states^on the quotient structureH/[0]θ, we show thatH/[0]θis a bounded commutative BCK-algebra which is categorically equivalent to an MV-algebra. In addition, we introduce the notions of hyper measures (states/measure morphisms/state morphisms) on hyper BCK-algebras, and present a relation between hyper state-morphisms and Bosbach states. Then we construct a quotient hyper BCK-algebraH/Ker(m)by a reflexive hyper BCK-idealKer(m). Further, we prove thatH/Ker(m)is a bounded commutative BCK-algebra.

scholarly journals Anti Fuzzy Equivalence Relation on Rings with Respect to t-conorm C

2019 ◽  
pp. 1-19 ◽  
Author(s):  
Rasul Rasuli
Keyword(s):  
Equivalence Relation ◽  
Congruence Relation ◽  
Basic Properties ◽  
Fuzzy Congruence

In this paper, by using t-conorms, we define the concept of anti fuzzy equivalence relation and anti fuzzy congruence relation on ring R and we investigate some of their basic properties. Also we define fuzzy ideals of ring R under t-conorms and compare this with fuzzy equivalence relation and fuzzy congruence relation on ring R such that we define new introduced ring. Next we investigate this concept under homomorphism of new introduced ring.

scholarly journals Ordered Convex Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Ismat Beg
Keyword(s):  
Metric Spaces ◽  
Basic Properties ◽  
New Concepts ◽  
Convex Metric Spaces

The aim of this article is to introduce a new notion of ordered convex metric spaces and study some basic properties of these spaces. Several characterizations of these spaces are proven that allow making geometric interpretations of the new concepts.

scholarly journals Symmetry in Hyperstructure: Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1217 ◽  
Author(s):  
Xiaohong Zhang ◽  
Florentin Smarandache ◽  
Yingcang Ma
Keyword(s):  
Disjoint Union ◽  
Basic Properties ◽  
New Concepts

The symmetry of hyperoperation is expressed by hypergroup, more extensive hyperalgebraic structures than hypergroups are studied in this paper. The new concepts of neutrosophic extended triplet semihypergroup (NET- semihypergroup) and neutrosophic extended triplet hypergroup (NET-hypergroup) are firstly introduced, some basic properties are obtained, and the relationships among NET- semihypergroups, regular semihypergroups, NET-hypergroups and regular hypergroups are systematically are investigated. Moreover, pure NET-semihypergroup and pure NET-hypergroup are investigated, and a strucuture theorem of commutative pure NET-semihypergroup is established. Finally, a new notion of weak commutative NET-semihypergroup is proposed, some important examples are obtained by software MATLAB, and the following important result is proved: every pure and weak commutative NET-semihypergroup is a disjoint union of some regular hypergroups which are its subhypergroups.

scholarly journals Almost Periodic Time Scales and Almost Periodic Functions on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yongkun Li ◽  
Bing Li
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Basic Properties ◽  
New Concepts ◽  
Almost Periodic Time Scales

We propose some new concepts of almost periodic time scales and almost periodic functions on time scales and give some basic properties of these new types of almost periodic time scales and almost periodic functions on time scales. We also give some comments on a recent paper by Wang and Agarwal (2014) concerning a new almost periodic time scale.

A ∗-prehomomorphism of a type B semigroup

2020 ◽  
pp. 2150222
Author(s):  
Chunhua Li ◽  
Zhi Pei ◽  
Baogen Xu
Keyword(s):  
New York ◽  
Inverse Semigroup ◽  
Partial Order ◽  
Inverse Semigroups ◽  
Natural Partial Order ◽  
Type B ◽  
Abundant Semigroup ◽  
Basic Properties ◽  
Structure Theorems

Type B semigroups are generalizations of inverse semigroups, and every inverse semigroup admits an [Formula: see text]-unitary cover (M. Petrich, Inverse Semigroups (Wiley, New York, 1984)). Motivated by studying [Formula: see text]-unitary cover for inverse semigroups, and as a continuation of Petrich’s works in inverse semigroups, in this paper, we first introduce the concept of ∗-prehomomorphism of a type B semigroup. After obtaining some basic properties, we get some structure theorems and give some conditions for a type B semigroup which is constructed by using the ∗-prehomomorphism to be proper. In particular, we introduce the notion of [Formula: see text]-unitary good cover for an abundant semigroup, and prove that every type B semigroup with compatible natural partial order admits an [Formula: see text]-unitary good cover.

Some New Concepts on int-soft Ideals in Ordered Semigroups

2021 ◽  
pp. 1-13
Author(s):  
G. Muhiuddina ◽  
Ebtehaj N. Alenzea ◽  
Ahsan Mahboobb ◽  
Anas Al-Masarwahc
Keyword(s):  
Soft Set ◽  
Ordered Semigroup ◽  
Ordered Semigroups ◽  
Basic Properties ◽  
New Concepts ◽  
Soft Point

In the present paper, we introduce some new notions on ordered semigroup. In fact, notion of a convex soft set in an ordered semigroup is introduced, and its basic properties are investigated. Moreover, we consider a characterization of a convex soft set. Furthermore, relations between a convex soft set and an int-soft [Formula: see text]-ideal (or, int-soft [Formula: see text]-ideal) are studied. Finally, int-soft [Formula: see text]-ideals (or, int-soft [Formula: see text]-ideals) generated by an ordered soft point are established.

scholarly journals Coloured Petri Nets Extended with Place Capacities, Test Arcs and Inhibitor Arcs

1992 ◽  
Vol 21 (398) ◽  
Author(s):  
Søren Christensen ◽  
Niels Damgaard Hansen
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
The Other ◽  
Coloured Petri Nets ◽  
Basic Properties ◽  
New Concepts ◽  
Special Cases ◽  
The One ◽  
Net Framework ◽  
Informal Description

In this paper we show how to extend Coloured Petri Nets (CP-nets), with three new modelling primitives - place capacities, test arcs and inhibitor arcs. The new modelling primitives are introduced to improve the possibilities of creating models that are on the one hand compact and comprehensive and on the other hand easy to develop, understand and analyse. A number of different place capacity and inhibitor concepts have been suggested earlier, e.g. integer and multi-set capacities and zero-testing and threshold inhibitors. These concepts can all be described as special cases of the more general place capacity and inhibitor concepts defined in this paper. We give an informal description of the new concepts and show how the concepts can be fonnally defined and integrated in the Petri net framework keeping the basic properties of CP-nets. In contrast to a number of the previously suggested extensions to CP-nets the new modelling primitives preserve the concurrency properties of CP-nets. We show how CP-nets with place capacities, test arcs and inhibitor arcs can be transformed into behaviourally equivalent CP-nets without these primitives. From this we conclude that the basic properties of CP-nets are preserved and that the theory developed for CP-nets can be applied to the extended CP-nets. Finally, we discuss how to generalise the analysis methods of CP-nets to cover the place capacities, test arcs and inhibitor arcs.

Weak and strong forms of fuzzy \(\alpha\)-open (closed) sets and its applications

2018 ◽  
Vol 9 (2) ◽  
Author(s):  
Hakeem Ahmed Ali ◽  
Alanod M. Sibih
Keyword(s):  
Topological Spaces ◽  
Connected Space ◽  
Basic Properties ◽  
Closed Sets ◽  
Continuous Mappings ◽  
New Concepts ◽  
Fuzzy Topological Spaces ◽  
Closed Mappings

In this paper, we generalize the concept of infra-\(\alpha\)-open (closed) and supra-\(\alpha\)-open (closed) sets to fuzzy topological spaces and basic properties of these new concepts have been introduced. Some applications on fuzzy (supra-) infra-\(\alpha\)-open (closed) sets, likely, fuzzy (supra-) infra-\(\alpha\)-continuous mappings, fuzzy (supra-) infra-\(\alpha\)-open (closed) mappings, fuzzy supra-\(\alpha\)- irresolute mapping and fuzzy supra-\(\alpha\)-connected space are introduced. The relations and converse relations between these new concepts and others kinds of fuzzy open sets and fuzzy continuous mappings are discussed. Special results about these new concepts are investigated and studied.

II. Basic properties

1962 ◽  
Vol 55 (7) ◽  
pp. 589-590
Author(s):  
Richard W. Feldmann
Keyword(s):  
Basic Properties ◽  
New Concepts

After Cayley published his expository articles on the theory of matrices, many mathematicians published papers expanding Cayley's ideas and developing new concepts, notations, and terminology. Some of these were fruitful and are still used, while others never turned up in print again.

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