{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:29:56Z","timestamp":1777703396049,"version":"3.51.4"},"reference-count":15,"publisher":"SAGE Publications","issue":"5","license":[{"start":{"date-parts":[[2015,7,29]],"date-time":"2015-07-29T00:00:00Z","timestamp":1438128000000},"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":[[2015,7,29]]},"abstract":"<jats:p>\n                    In this paper, we are going to introduce a fundamental relation \u201c\u03b4\u201d on (hyper\n                    <jats:italic>BE<\/jats:italic>\n                    -algebra) dual hyper\n                    <jats:italic>K<\/jats:italic>\n                    -algebra and investigate some properties. We show that quotient of any dual hyper\n                    <jats:italic>K<\/jats:italic>\n                    -algebra via a regular relation is a hyper\n                    <jats:italic>BE<\/jats:italic>\n                    -algebra and this quotient, via any strongly regular relation is a\n                    <jats:italic>BE<\/jats:italic>\n                    -algebra. Furthermore, it shows that \u201c\u03b4\u201d under some condition is transitive and quotient of any weak commutative dual hyper\n                    <jats:italic>K<\/jats:italic>\n                    -algebra via \u201c\u03b4\n                    <jats:sup>*<\/jats:sup>\n                    \u201d is a dual\n                    <jats:italic>BCK<\/jats:italic>\n                    -algebra.\n                  <\/jats:p>","DOI":"10.3233\/ifs-151667","type":"journal-article","created":{"date-parts":[[2015,11,10]],"date-time":"2015-11-10T11:35:43Z","timestamp":1447155343000},"page":"1889-1900","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":5,"title":["\u03b4-relation on dual hyper\n                    <i>K<\/i>\n                    \u2013algebras"],"prefix":"10.1177","volume":"29","author":[{"given":"Mohammad","family":"Hamidi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Payame Noor University (PNU), Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Akbar","family":"Rezaei","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Payame Noor University (PNU), Tehran, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arsham","family":"Borumand Saeid","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,8,4]]},"reference":[{"key":"e_1_3_1_2_2","first-page":"113","article-title":"On hyper K-algebras","volume":"52","author":"Borzooei RA","year":"2000","unstructured":"Borzooei RA, Hasankhani A, Zahedi MM, Jun YB 2000 On hyper K-algebras Sci, Math Jpn 52 113 121","journal-title":"Sci, Math Jpn"},{"issue":"4","key":"e_1_3_1_3_2","first-page":"65","article-title":"Fundamental 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1934 Sur une generalization de la notion de group 8th Congress Math Scandinaves, Stockholm 45 49","journal-title":"8th Congress Math Scandinaves, Stockholm"},{"issue":"2","key":"e_1_3_1_11_2","first-page":"137","article-title":"Hyper BE-algebras","volume":"44","author":"Radfar A","year":"2014","unstructured":"Radfar A, Rezaei A, Borumand Saeid A 2014 Hyper BE-algebras Novi Sad J Math 44 2 137 147","journal-title":"Novi Sad J Math"},{"key":"e_1_3_1_12_2","doi-asserted-by":"publisher","DOI":"10.5666\/KMJ.2012.52.4.483"},{"issue":"2","key":"e_1_3_1_13_2","first-page":"573","article-title":"Relation between Hilbert algebras and BE-algebras","volume":"8","author":"Rezaei A","year":"2013","unstructured":"Rezaei A, Borumand Saeid A, Borzooei RA 2013 Relation between Hilbert algebras and BE-algebras Applic Applic Math 8 2 573 584","journal-title":"Applic Applic 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