{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:29:20Z","timestamp":1777703360455,"version":"3.51.4"},"reference-count":13,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2016,11,8]],"date-time":"2016-11-08T00:00:00Z","timestamp":1478563200000},"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":[[2017,1,13]]},"abstract":"<jats:p>\n                    The notions of hesitant fuzzy translations and hesitant fuzzy extensions of a hesitant fuzzy set on\n                    <jats:italic>BCK<\/jats:italic>\n                    \/\n                    <jats:italic>BCI<\/jats:italic>\n                    -algebras are introduced, and related properties are investigated. We prove that every hesitant fuzzy translation of a hesitant fuzzy subalgebra (ideal) is a hesitant fuzzy subalgebra (ideal). Conditions for a hesitant fuzzy set to be a hesitant fuzzy subalgebra (ideal) are provided. We show that if a hesitant fuzzy set is a hesitant fuzzy subalgebra (ideal), then its support is a subalgebra (ideal), and also prove that if the support of a hesitant fuzzy set is a subalgebra (ideal), then its hesitant fuzzy translation is a hesitant fuzzy subalgebra (ideal).\n                  <\/jats:p>","DOI":"10.3233\/jifs-151031","type":"journal-article","created":{"date-parts":[[2016,11,8]],"date-time":"2016-11-08T11:11:26Z","timestamp":1478603486000},"page":"43-48","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":18,"title":["Hesitant fuzzy translations and extensions\u00a0of subalgebras and ideals in\u00a0\n                    <i>BCK<\/i>\n                    \/\n                    <i>BCI<\/i>\n                    -algebras"],"prefix":"10.1177","volume":"32","author":[{"given":"G.","family":"Muhiuddin","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hee Sik","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seok Zun","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jeju National University, Jeju, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Young Bae","family":"Jun","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Gyeongsang National University, Jinju, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2016,11,8]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"HuangY. 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