{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:34:23Z","timestamp":1777703663604,"version":"3.51.4"},"reference-count":47,"publisher":"SAGE Publications","issue":"6","license":[{"start":{"date-parts":[[2018,6,22]],"date-time":"2018-06-22T00:00:00Z","timestamp":1529625600000},"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":[[2018,6,22]]},"abstract":"<jats:p>\n                    Cubic sets are generalized version of fuzzy sets, in which there are two representations, one is used for the degree of membership and other is used for the degree of non-membership. Membership function is handled in the form of intervals while non-membership is handled through ordinary fuzzy sets. Since the invention of fuzzy set many researchers applied this notion to different algebraic structures. Mostly, they focus on the associative structures. Here we concentrate on a useful non associative structure known as H\n                    <jats:sub>\n                      <jats:italic>v<\/jats:italic>\n                    <\/jats:sub>\n                    -LA-semigroup. Using this idea, we characterize an H\n                    <jats:sub>\n                      <jats:italic>v<\/jats:italic>\n                    <\/jats:sub>\n                    -LA-semigroup in terms of cubic ideals. We study the idea of cubic equivalence relations, cubic regular relations in H\n                    <jats:sub>\n                      <jats:italic>v<\/jats:italic>\n                    <\/jats:sub>\n                    -LA-semigroups and provide some related results.\n                  <\/jats:p>","DOI":"10.3233\/jifs-171744","type":"journal-article","created":{"date-parts":[[2018,6,26]],"date-time":"2018-06-26T15:01:37Z","timestamp":1530025297000},"page":"4161-4172","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":14,"title":["Extensions of cubic ideals in weak left almost semihypergroups"],"prefix":"10.1177","volume":"34","author":[{"given":"Muhammad","family":"Gulistan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hazara University, Mansehra, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Naveed","family":"Yaqoob","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Vougiouklis","sequence":"additional","affiliation":[{"name":"School of Education, Democritus University of Thrace, Alexandroupolis, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hafiz","family":"Abdul Wahab","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hazara University, Mansehra, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,6,22]]},"reference":[{"key":"e_1_3_2_2_2","first-page":"1","article-title":"On almost semigroups","volume":"2","author":"Kazim M.A.","year":"1972","unstructured":"KazimM.A. and NaseeruddinM., On almost semigroups, The Aligarh Bulletin of Mathematics 2 (1972), 1\u20137.","journal-title":"The Aligarh Bulletin of Mathematics"},{"key":"e_1_3_2_3_2","first-page":"65","article-title":"On LA-semigroups","volume":"8","author":"Mushtaq Q.","year":"1978","unstructured":"MushtaqQ. and YusufS.M., On LA-semigroups, The Aligarh Bulletin of Mathematics 8 (1978), 65\u201370.","journal-title":"The Aligarh Bulletin of Mathematics"},{"issue":"1","key":"e_1_3_2_4_2","first-page":"101","article-title":"Groupoids satisfying a simple invertive law","volume":"61","author":"Holgate P.","year":"1992","unstructured":"HolgateP., Groupoids satisfying a simple invertive law, The Mathematics Student 61(1-4) (1992), 101\u2013106.","journal-title":"The Mathematics Student"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022448218116"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.12988\/ams.2013.13195"},{"issue":"3","key":"e_1_3_2_7_2","first-page":"61","article-title":"Characterizations of left almost semigroups by their ideals","volume":"2","author":"Khan M.","year":"2010","unstructured":"KhanM. and AhmadN., Characterizations of left almost semigroups by their ideals, Journal of Advanced Research in Pure Mathematics 2(3) (2010), 61\u201373.","journal-title":"Journal of Advanced Research in Pure Mathematics"},{"issue":"1","key":"e_1_3_2_8_2","first-page":"57","article-title":"On locally associative LA semigroups","volume":"19","author":"Mushtaq Q.","year":"1979","unstructured":"MushtaqQ. and YusufS.M., On locally associative LA semigroups, The Journal of Natural Sciences and Mathematics 19(1) (1979), 57\u201362.","journal-title":"The Journal of Natural Sciences and Mathematics"},{"issue":"4","key":"e_1_3_2_9_2","first-page":"371","article-title":"AG-test and some general properties of Abel-Grassmann\u2019s groupoids","volume":"6","author":"Protic P.V.","year":"1995","unstructured":"ProticP.V. and StevanovicN., AG-test and some general properties of Abel-Grassmann\u2019s groupoids, Pure Mathematics and Applications 6(4) (1995), 371\u2013383.","journal-title":"Pure Mathematics and Applications"},{"issue":"2","key":"e_1_3_2_10_2","first-page":"175","article-title":"Composition of Abel-Grassmann\u2019s 3-bands","volume":"34","author":"Stevanovic N.","year":"2004","unstructured":"StevanovicN. and ProticP.V., Composition of Abel-Grassmann\u2019s 3-bands, Novi Sad Journal of Mathematics 34(2) (2004), 175\u2013182.","journal-title":"Novi Sad Journal of Mathematics"},{"key":"e_1_3_2_11_2","unstructured":"MartyF. 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