{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:33:01Z","timestamp":1777703581554,"version":"3.51.4"},"reference-count":14,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2017,2,15]],"date-time":"2017-02-15T00:00:00Z","timestamp":1487116800000},"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":[[2017,2,24]]},"abstract":"<jats:p>\n                    The concept of hesitant union (\u22d3) is introduced. Using this, the notions of \u22d3-hesitant fuzzy subalgebras and \u22d3-hesitant fuzzy ideals are introduced and several properties are investigated. Relations between \u222a-hesitant fuzzy subalgebras (resp. ideals) and \u22d3-hesitant fuzzy subalgebras (resp. ideals) are considered. Relations between a \u22d3-hesitant fuzzy subalgebra\/ideal and its lower level set are investigated. Characterizations of \u222a-hesitant fuzzy subalgebras\/ideals are discussed. Given a subalgebra (resp., ideal)\n                    <jats:italic>A<\/jats:italic>\n                    of a\n                    <jats:italic>BCK<\/jats:italic>\n                    \/\n                    <jats:italic>BCI<\/jats:italic>\n                    -algebra\n                    <jats:italic>X<\/jats:italic>\n                    , a \u22d3-hesitant fuzzy subalgebra (resp., ideal) is established.\n                  <\/jats:p>","DOI":"10.3233\/jifs-161601","type":"journal-article","created":{"date-parts":[[2017,2,17]],"date-time":"2017-02-17T10:35:42Z","timestamp":1487327742000},"page":"2009-2016","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":7,"title":["A new type of hesitant fuzzy subalgebras and ideals in\n                    <i>BCK<\/i>\n                    \/\n                    <i>BCI<\/i>\n                    -algebras"],"prefix":"10.1177","volume":"32","author":[{"given":"Seok-Zun","family":"Song","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jeju National University, Jeju, Republic of Korea"}]},{"given":"Hashem","family":"Bordbar","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, Statistics and Computer Science Shahid Bahonar University, Kerman, Iran"}]},{"given":"Young Bae","family":"Jun","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, Gyeongsang National University, Jinju, Republic of Korea"}]}],"member":"179","published-online":{"date-parts":[[2017,2,15]]},"reference":[{"key":"e_1_3_2_2_2","unstructured":"HuangY. BCI-algebra Science Press Beijing 2006."},{"issue":"4","key":"e_1_3_2_3_2","first-page":"635","article-title":"Hesitant fuzzy set theory applied to BCK\/BCI-algebras","volume":"20","author":"Jun Y.B.","year":"2016","unstructured":"JunY.B. and AhnS.S. Hesitant fuzzy set theory applied to BCK\/BCI-algebras, J Comput Anal Appl 20(4) (2016), 635\u2013646.","journal-title":"J Comput Anal Appl"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.5831\/HMJ.2014.36.4.813"},{"issue":"11","key":"e_1_3_2_5_2","first-page":"515","article-title":"Hesitant fuzzy prefilters and filters of EQ-algebras","volume":"9","author":"Jun Y.B.","year":"2015","unstructured":"JunY.B. and SongS.Z. Hesitant fuzzy prefilters and filters of EQ-algebras, Appl Math Sci 9(11) (2015), 515\u2013532.","journal-title":"Appl Math Sci"},{"key":"e_1_3_2_6_2","unstructured":"MengJ. JunY.B. BCK-algebras Kyungmoon Sa Co. Seoul 1994."},{"issue":"2","key":"e_1_3_2_7_2","first-page":"394","article-title":"Hesitant fuzzy filters and hesitant fuzzy G-filters in residuated attices","volume":"21","author":"Muhiuddin G.","year":"2016","unstructured":"MuhiuddinG., Hesitant fuzzy filters and hesitant fuzzy G-filters in residuated attices, J Comput Anal Appl 21(2) (2016), 394\u2013404.","journal-title":"J Comput Anal Appl"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2011.2170076"},{"key":"e_1_3_2_9_2","first-page":"529","article-title":"Hesitant fuzzy sets","volume":"25","author":"Torra V.","year":"2010","unstructured":"TorraV., Hesitant fuzzy sets, Int J Intell Syst 25 (2010), 529\u2013539.","journal-title":"Int J Intell Syst"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/FUZZY.2009.5276884"},{"key":"e_1_3_2_11_2","first-page":"10","article-title":"Hesitant fuzzy soft set and its applications in multicriteria decision making","volume":"2014","author":"Wang F.Q.","unstructured":"WangF.Q., LiX. and ChenX.H. Hesitant fuzzy soft set and its applications in multicriteria decision making, J Appl Math 2014, 10. Article ID 643785.","journal-title":"J Appl Math"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.knosys.2012.03.011"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2010.09.002"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2011.01.028"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1002\/int.20474"}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-161601","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.3233\/JIFS-161601","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/JIFS-161601","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:39:00Z","timestamp":1777455540000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/JIFS-161601"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,15]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,2,24]]}},"alternative-id":["10.3233\/JIFS-161601"],"URL":"https:\/\/doi.org\/10.3233\/jifs-161601","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,15]]}}}