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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| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Fuzzy Systems |
| Online Access: | http://dx.doi.org/10.1155/2018/8464295 |
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| author | Venus Amjid Faisal Yousafzai Kostaq Hila |
| author_facet | Venus Amjid Faisal Yousafzai Kostaq Hila |
| author_sort | Venus Amjid |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-e7aeeb8d5d594515b0da6baa7ab7b867 |
| institution | Kabale University |
| issn | 1687-7101 1687-711X |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Fuzzy Systems |
| spelling | doaj-art-e7aeeb8d5d594515b0da6baa7ab7b8672025-02-03T05:44:33ZengWileyAdvances 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 |
| 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 |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/2018/8464295 |
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