{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T00:22:00Z","timestamp":1770510120522,"version":"3.49.0"},"reference-count":33,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2018,9,25]],"date-time":"2018-09-25T00:00:00Z","timestamp":1537833600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2018,10,27]]},"abstract":"<jats:p>\n                    An\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">AG<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -groupoid can be referred to as a non-associative semigroup, as the main difference between a semigroup and an\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">AG<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -groupoid is the switching of an associative law. In this paper, we define the smallest one-sided ideals in an\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">AG<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -groupoid and use them to characterize a strongly regular class of a unitary\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">AG<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -groupoid along with its semilattices and\n                    <jats:italic>SI<\/jats:italic>\n                    -\n                    <jats:italic>l<\/jats:italic>\n                    -ideals (\n                    <jats:italic>SI<\/jats:italic>\n                    -\n                    <jats:italic>r<\/jats:italic>\n                    -ideals) and\n                    <jats:italic>SI<\/jats:italic>\n                    -bi-ideals. As an application, we get some interesting and new characterizations which we usually do not find in semigroups. Finally we give the concept of an\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:msup>\n                          <mml:mi mathvariant=\"script\">AG<\/mml:mi>\n                          <mml:mrow>\n                            <mml:mo>*<\/mml:mo>\n                            <mml:mo>*<\/mml:mo>\n                            <mml:mo>*<\/mml:mo>\n                          <\/mml:mrow>\n                        <\/mml:msup>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -groupoid and give an example to show that this class is the generalization of a unitary\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi mathvariant=\"script\">AG<\/mml:mi>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    -groupoid.\n                  <\/jats:p>","DOI":"10.3233\/jifs-18873","type":"journal-article","created":{"date-parts":[[2018,9,29]],"date-time":"2018-09-29T07:22:10Z","timestamp":1538205730000},"page":"4837-4847","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["Non-associative semigroups in terms of semilattices via soft ideals"],"prefix":"10.1177","volume":"35","author":[{"given":"Faisal","family":"Yousafzai","sequence":"first","affiliation":[{"name":"Military College of Engineering, National University of Sciences and Technology (NUST), Islamabad, Pakistan"}]},{"given":"Arshad","family":"Ali","sequence":"additional","affiliation":[{"name":"Military College of Engineering, National University of Sciences and Technology (NUST), Islamabad, Pakistan"}]},{"given":"Shamsul","family":"Haq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Abbottabad, Pakistan and Department of Mathematics, Hazara University, Mansehra, Pakistan"}]},{"given":"Kostaq","family":"Hila","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, University of Gjirokastra, Albania"}]}],"member":"179","published-online":{"date-parts":[[2018,9,25]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2008.11.009"},{"key":"e_1_3_2_3_2","article-title":"A study of ordered AGgroupoids in terms of ilattices via smallest (fuzzy) ideals","author":"Amjid V.","unstructured":"V.Amjid, F.Yousafzai, K.HILA, A study of ordered AGgroupoids in terms of ilattices via smallest (fuzzy) ideals, Adv Fuzzy Syst. 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