A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals

A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals

An ordered AG-groupoid can be referred to as an ordered left almost semigroup, as the main difference between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we define the smallest one-sided ideals in an ordered AG-groupoid and use them to chara...

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Main Authors: Venus Amjid, Faisal Yousafzai, Kostaq Hila
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in Fuzzy Systems
Online Access:http://dx.doi.org/10.1155/2018/8464295
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spelling doaj-e7aeeb8d5d594515b0da6baa7ab7b8672020-11-24T22:13:49ZengHindawi LimitedAdvances in Fuzzy Systems1687-71011687-711X2018-01-01201810.1155/2018/84642958464295A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) IdealsVenus Amjid0Faisal Yousafzai1Kostaq Hila2School of Mathematical Sciences, University of Science and Technology of China, Hefei, ChinaMilitary College of Engineering, National University of Sciences and Technology (NUST), Islamabad, PakistanDepartment of Mathematics & Computer Science, University of Gjirokastra, Gjirokastra, AlbaniaAn ordered AG-groupoid can be referred to as an ordered left almost semigroup, as the main difference between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we define the smallest one-sided ideals in an ordered AG-groupoid and use them to characterize a strongly regular class of a unitary ordered AG-groupoid along with its semilattices and fuzzy one-sided ideals. We also introduce the concept of an ordered AG⁎⁎⁎-groupoid and investigate its structural properties by using the generated ideals and fuzzy one-sided ideals. These concepts will verify the existing characterizations and will help in achieving more generalized results in future works.http://dx.doi.org/10.1155/2018/8464295
collection DOAJ
language English
format Article
sources DOAJ
author Venus Amjid
Faisal Yousafzai
Kostaq Hila
spellingShingle Venus Amjid
Faisal Yousafzai
Kostaq Hila
A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals
Advances in Fuzzy Systems
author_facet Venus Amjid
Faisal Yousafzai
Kostaq Hila
author_sort Venus Amjid
title A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals
title_short A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals
title_full A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals
title_fullStr A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals
title_full_unstemmed A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals
title_sort study of ordered ag-groupoids in terms of semilattices via smallest (fuzzy) ideals
publisher Hindawi Limited
series Advances in Fuzzy Systems
issn 1687-7101
1687-711X
publishDate 2018-01-01
description An ordered AG-groupoid can be referred to as an ordered left almost semigroup, as the main difference between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we define the smallest one-sided ideals in an ordered AG-groupoid and use them to characterize a strongly regular class of a unitary ordered AG-groupoid along with its semilattices and fuzzy one-sided ideals. We also introduce the concept of an ordered AG⁎⁎⁎-groupoid and investigate its structural properties by using the generated ideals and fuzzy one-sided ideals. These concepts will verify the existing characterizations and will help in achieving more generalized results in future works.
url http://dx.doi.org/10.1155/2018/8464295
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AT kostaqhila astudyoforderedaggroupoidsintermsofsemilatticesviasmallestfuzzyideals
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AT faisalyousafzai studyoforderedaggroupoidsintermsofsemilatticesviasmallestfuzzyideals
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