{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:44:37Z","timestamp":1740149077126,"version":"3.37.3"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,9,2]],"date-time":"2018-09-02T00:00:00Z","timestamp":1535846400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Fuzzy Systems"],"published-print":{"date-parts":[[2018,9,2]]},"abstract":"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 orderedA<\/mml:mi>G<\/mml:mi><\/mml:mrow>\u204e<\/mml:mo>\u204e<\/mml:mo>\u204e<\/mml:mo><\/mml:mrow><\/mml:msup><\/mml:math>-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.<\/jats:p>","DOI":"10.1155\/2018\/8464295","type":"journal-article","created":{"date-parts":[[2018,9,2]],"date-time":"2018-09-02T23:35:12Z","timestamp":1535931312000},"page":"1-8","source":"Crossref","is-referenced-by-count":1,"title":["A Study of Ordered Ag-Groupoids in terms of Semilattices via Smallest (Fuzzy) Ideals"],"prefix":"10.1155","volume":"2018","author":[{"given":"Venus","family":"Amjid","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, University of Science and Technology of China, Hefei, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Faisal","family":"Yousafzai","sequence":"additional","affiliation":[{"name":"Military College of Engineering, National University of Sciences and Technology (NUST), Islamabad, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6425-2619","authenticated-orcid":true,"given":"Kostaq","family":"Hila","sequence":"additional","affiliation":[{"name":"Department of Mathematics & Computer Science, University of Gjirokastra, Gjirokastra, Albania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"19","first-page":"338","volume":"8","year":"1965","journal-title":"Information and Computation"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(71)90199-5"},{"issue":"1","key":"8","first-page":"17","volume":"28","year":"1980","journal-title":"Commentarii Mathematici Universitatis Sancti Pauli"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-37125-0"},{"issue":"3","key":"1","first-page":"473","volume":"9","year":"2015","journal-title":"Annals of Fuzzy Mathematics and Informatics"},{"key":"16","series-title":"Series A. 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