{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T07:29:55Z","timestamp":1750663795047,"version":"3.37.3"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int. J. Mach. Learn. & Cyber."],"published-print":{"date-parts":[[2021,8]]},"DOI":"10.1007\/s13042-021-01314-8","type":"journal-article","created":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T12:03:06Z","timestamp":1617278586000},"page":"2339-2348","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Multipolar fuzzy a-ideals in BCI-algebras"],"prefix":"10.1007","volume":"12","author":[{"given":"Rajab Ali","family":"Borzooei","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gholam Reza","family":"Rezaei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5596-5841","authenticated-orcid":false,"given":"G.","family":"Muhiuddin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Young Bae","family":"Jun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,1]]},"reference":[{"key":"1314_CR1","doi-asserted-by":"publisher","first-page":"1220","DOI":"10.1016\/j.jksus.2018.10.002","volume":"31","author":"A Al-Masarwah","year":"2019","unstructured":"Al-Masarwah A, Ahmad AG (2019) $m$-polar fuzzy ideals of BCK\/BCI-algebras. J King Saud Univ Sci 31:1220\u20131226","journal-title":"J King Saud Univ Sci"},{"key":"1314_CR2","doi-asserted-by":"publisher","first-page":"44","DOI":"10.3390\/sym11010044","volume":"11","author":"A Al-Masarwah","year":"2019","unstructured":"Al-Masarwah A, Ahmad AG (2019) $m$-polar $(\\alpha, \\beta )$-fuzzy ideals in BCK\/BCI-algebras. Symmetry 11:44. https:\/\/doi.org\/10.3390\/sym11010044","journal-title":"Symmetry"},{"issue":"1","key":"1314_CR3","first-page":"88","volume":"3","author":"D Al-Kadi","year":"2020","unstructured":"Al-Kadi D, Muhiuddin G (2020) Bipolar fuzzy BCI-implicative ideals of BCI-algebras. Ann Commun Math 3(1):88\u201396","journal-title":"Ann Commun Math"},{"key":"1314_CR4","first-page":"416","volume":"2014","author":"J Chen","year":"2014","unstructured":"Chen J, Li S, Ma S, Wang X (2014) $m$-polar fuzzy sets: an extension of bipolar fuzzy sets. Sci World J 2014:416\u2013530","journal-title":"Sci World J"},{"key":"1314_CR5","volume-title":"BCI-Algebra","author":"Y Huang","year":"2006","unstructured":"Huang Y (2006) BCI-Algebra. Science Press, Beijing"},{"key":"1314_CR6","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1007\/s10012-000-0243-y","volume":"24","author":"YL Liu","year":"2000","unstructured":"Liu YL, Meng J, Zhang XH, Yue ZC (2000) $q$-ideals and $a$-ideals in BCI-algebras. Southeast Asian Bull Math 24:243\u2013253","journal-title":"Southeast Asian Bull Math"},{"key":"1314_CR7","volume-title":"BCK-algebras","author":"J Meng","year":"1994","unstructured":"Meng J, Jun YB (1994) BCK-algebras. Kyungmoonsa Co., Seoul"},{"issue":"6","key":"1314_CR8","doi-asserted-by":"publisher","first-page":"2803","DOI":"10.1016\/j.jksus.2020.07.001","volume":"32","author":"G Muhiuddin","year":"2020","unstructured":"Muhiuddin G, Takallo MM, Borzooei RA, Jun YB (2020) $m$-polar fuzzy $q$-ideals in BCI-algebras. J King Saud Univ Sci 32(6):2803\u20132809","journal-title":"J King Saud Univ Sci"},{"doi-asserted-by":"publisher","unstructured":"Muhiuddin G, Al-Kadi D (2021) Bipolar fuzzy implicative ideals of BCK-algebras. J Math 2021, Article ID 6623907. https:\/\/doi.org\/10.1155\/2021\/6623907","key":"1314_CR9","DOI":"10.1155\/2021\/6623907"},{"issue":"5","key":"1314_CR10","first-page":"859","volume":"18","author":"G Muhiuddin","year":"2020","unstructured":"Muhiuddin G, Al-Kadi D, Mehboob A, Shum KP (2020) New types of bipolar fuzzy ideals of BCK-algebras. Int J Anal Appl 18(5):859\u2013875","journal-title":"Int J Anal Appl"},{"doi-asserted-by":"crossref","unstructured":"Muhiuddin G, Harizavi H, Jun YB (2020) Bipolar-valued fuzzy soft hyper BCK ideals in hyper BCK algebras. Discret Math Algorithms Appl 12(02):2050018. https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830920500184","key":"1314_CR11","DOI":"10.1142\/S1793830920500184"},{"issue":"3","key":"1314_CR12","first-page":"409","volume":"8","author":"G Muhiuddin","year":"2014","unstructured":"Muhiuddin G (2014) Bipolar fuzzy KU-subalgebras\/ideals of KU-algebras. Ann Fuzzy Math Inform 8(3):409\u2013418","journal-title":"Ann Fuzzy Math Inform"},{"doi-asserted-by":"crossref","unstructured":"Muhiuddin G, Kim SJ, Jun YB (2019) Implicative N-ideals of BCK-algebras based on neutrosophic N-structures. Discret Math Algorithms Appl 11(01):1950011 https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500113","key":"1314_CR13","DOI":"10.1142\/S1793830919500113"},{"issue":"1","key":"1314_CR14","first-page":"48","volume":"2","author":"G Muhiuddin","year":"2019","unstructured":"Muhiuddin G, Jun YB (2019) Sup-hesitant fuzzy subalgebras and its translations and extensions. Ann Commun Math 2(1):48\u201356","journal-title":"Ann Commun Math"},{"issue":"7","key":"1314_CR15","first-page":"2293","volume":"43","author":"G Muhiuddin","year":"2017","unstructured":"Muhiuddin G, Al-roqi AM, Aldhafeeri Shuaa (2017) Filter theory in MTL-algebras based on uni-soft property. Bull Iran Math Soc 43(7):2293\u20132306","journal-title":"Bull Iran Math Soc"},{"issue":"1","key":"1314_CR16","doi-asserted-by":"publisher","first-page":"43","DOI":"10.3233\/JIFS-151031","volume":"32","author":"G Muhiuddin","year":"2017","unstructured":"Muhiuddin G, Kim HS, Song SZ, Jun YB (2017) Hesitant fuzzy translations and extensions of subalgebras and ideals in BCK\/BCI-algebras. J Intell Fuzzy Syst 32(1):43\u201348","journal-title":"J Intell Fuzzy Syst"},{"issue":"2","key":"1314_CR17","first-page":"291","volume":"8","author":"G Muhiuddin","year":"2014","unstructured":"Muhiuddin G, Al-roqi AM (2014) Cubic soft sets with applications in BCK\/BCI-algebras. Ann Fuzzy Math Inform 8(2):291\u2013304","journal-title":"Ann Fuzzy Math Inform"},{"doi-asserted-by":"publisher","unstructured":"Muhiuddin G, Feng F, Jun Young Bae (2014) Subalgebras of BCK\/BCI-algebras based on cubic soft sets. Sci World J 7(11):1094. Article ID 458638.  https:\/\/doi.org\/10.3390\/math7111094","key":"1314_CR18","DOI":"10.3390\/math7111094"},{"key":"1314_CR19","doi-asserted-by":"publisher","first-page":"1094","DOI":"10.3390\/math7111094","volume":"7","author":"MM Takallo","year":"2019","unstructured":"Takallo MM, Ahn SS, Borzooei RA, Jun YB (2019) Multipolar fuzzy $p$-ideals of BCI-algebras. Mathematics 7:1094","journal-title":"Mathematics"},{"key":"1314_CR20","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/j.knosys.2012.01.001","volume":"35","author":"HL Yang","year":"2012","unstructured":"Yang HL, Lia SG, Wang S, Wang J (2012) Bipolar fuzzy rough set model on two different universes and its application. Knowl Based Syst 35:94\u2013101","journal-title":"Knowl Based Syst"},{"key":"1314_CR21","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.knosys.2011.07.012","volume":"27","author":"HL Yang","year":"2012","unstructured":"Yang HL, Lia SG, Guo ZL, Ma CH (2012) Transformation of bipolar fuzzy rough set models. Knowl Based Syst 27:60\u201368","journal-title":"Knowl Based Syst"},{"key":"1314_CR22","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8:338\u2013353","journal-title":"Inf Control"},{"key":"1314_CR23","first-page":"121","volume":"27","author":"XH Zhang","year":"1994","unstructured":"Zhang XH, Hao J, Bhatti SA (1994) On $p$-ideals of a BCI-algebra. Punjab Univ J Math (Lahore) 27:121\u2013128","journal-title":"Punjab Univ J Math (Lahore)"},{"unstructured":"Zhang WR (1994) Bipolar fuzzy sets and relations: a computational framework for cognitive and modeling and multiagent decision analysis. In: Proceedings of the fuzzy information processing society biannual conference, San Antonio, TX, USA, vol 18\u201321, pp 305\u2013309","key":"1314_CR24"}],"container-title":["International Journal of Machine Learning and Cybernetics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-021-01314-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13042-021-01314-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13042-021-01314-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,13]],"date-time":"2021-07-13T02:29:55Z","timestamp":1626143395000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13042-021-01314-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,1]]},"references-count":24,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["1314"],"URL":"https:\/\/doi.org\/10.1007\/s13042-021-01314-8","relation":{},"ISSN":["1868-8071","1868-808X"],"issn-type":[{"type":"print","value":"1868-8071"},{"type":"electronic","value":"1868-808X"}],"subject":[],"published":{"date-parts":[[2021,4,1]]},"assertion":[{"value":"7 February 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 April 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}]}}