{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:54:09Z","timestamp":1740142449850,"version":"3.37.3"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T00:00:00Z","timestamp":1639353600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T00:00:00Z","timestamp":1639353600000},"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":["Comp. Appl. Math."],"published-print":{"date-parts":[[2022,2]]},"DOI":"10.1007\/s40314-021-01717-x","type":"journal-article","created":{"date-parts":[[2021,12,13]],"date-time":"2021-12-13T14:03:35Z","timestamp":1639404215000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Intuitionistic fuzzy multi-polygroups"],"prefix":"10.1007","volume":"41","author":[{"given":"Serkan","family":"Onar","sequence":"first","affiliation":[]},{"given":"Bayram Ali","family":"Ersoy","sequence":"additional","affiliation":[]},{"given":"Bijan","family":"Davvaz","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6425-2619","authenticated-orcid":false,"given":"Kostaq","family":"Hila","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,12,13]]},"reference":[{"key":"1717_CR1","first-page":"34","volume":"2","author":"IM Adamu","year":"2017","unstructured":"Adamu IM, Tella Y, Alkali AJ (2017) On normal and soft normal groups under multisets and soft multisets context. Mayfeb J Math 2:34\u201347","journal-title":"Mayfeb J Math"},{"issue":"2","key":"1717_CR2","doi-asserted-by":"publisher","first-page":"127","DOI":"10.22457\/apam.581v19n2a1","volume":"19","author":"IM Adamu","year":"2019","unstructured":"Adamu IM, Tella Y, Alkali AJ (2019) On normal sub-intuitionistic fuzzy multigroups. Ann Pure Appl Math 19(2):127\u2013139","journal-title":"Ann Pure Appl Math"},{"issue":"1","key":"1717_CR3","first-page":"17","volume":"28","author":"F Arabpur","year":"2020","unstructured":"Arabpur F, Jafarpour M, Aminizadeh M, Hoskova-Mayerova S (2020) On geometric polygroups. An. St. Univ. Ovidius Constanta 28(1):17\u201333","journal-title":"An. St. Univ. Ovidius Constanta"},{"key":"1717_CR4","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/S0165-0114(86)80034-3","volume":"20","author":"K Atanassov","year":"1986","unstructured":"Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87\u201396","journal-title":"Fuzzy Sets Syst"},{"key":"1717_CR5","first-page":"80","volume":"2","author":"A Baby","year":"2015","unstructured":"Baby A, Shinoj TK, Sunil JJ (2015) On Abelian fuzzy multi groups and orders of fuzzy multi groups. J New Theory 2:80\u201393","journal-title":"J New Theory"},{"issue":"1","key":"1717_CR6","first-page":"36","volume":"30","author":"WD Blizard","year":"1989","unstructured":"Blizard WD (1989) Multiset theory. Notre Dame J Formal Logic 30(1):36\u201366","journal-title":"Notre Dame J Formal Logic"},{"key":"1717_CR7","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0304-3975(93)90351-S","volume":"110","author":"WD Blizard","year":"1993","unstructured":"Blizard WD (1993) Dedekind multisets and function shells. Theor Comput Sci 110:79\u201398","journal-title":"Theor Comput Sci"},{"issue":"2","key":"1717_CR8","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1016\/0021-8693(84)90225-4","volume":"89","author":"SD Comer","year":"1984","unstructured":"Comer SD (1984) Polygroups derived from cogroups. J Algebra 89(2):397\u2013405","journal-title":"J Algebra"},{"key":"1717_CR9","volume-title":"Prolegomena of hypergroup theory","author":"P Corsini","year":"1993","unstructured":"Corsini P (1993) Prolegomena of hypergroup theory, 2nd edn. Aviani Editore, Italy","edition":"2"},{"issue":"Part B","key":"1717_CR10","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1016\/j.ejc.2014.08.005","volume":"44","author":"P Corsini","year":"2015","unstructured":"Corsini P (2015) Fuzzy multiset hyper structures. Eur J Combin 44(Part B):198\u2013207","journal-title":"Eur J Combin"},{"key":"1717_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3714-1","volume-title":"Applications of hyperstructure theory. Advances in mathematics","author":"P Corsini","year":"2003","unstructured":"Corsini P, Leoreanu V (2003) Applications of hyperstructure theory. Advances in mathematics. Kluwer Academic Publishers, Dordrecht"},{"key":"1717_CR12","unstructured":"Davvaz B (2016) Semihypergroup theory. Elsevier\/Academic Press, Amsterdam (ISBN 978-0-12-809815-8\/pbk; 978-0-12-809925-4\/ebook), vol viii, p 156"},{"key":"1717_CR13","first-page":"67","volume":"8","author":"B Davvaz","year":"2000","unstructured":"Davvaz B (2000) Fuzzy hyperideals in semihypergroups. Ital J Pure Appl Math 8:67\u201374","journal-title":"Ital J Pure Appl Math"},{"issue":"4","key":"1717_CR14","first-page":"21","volume":"6","author":"B Davvaz","year":"2009","unstructured":"Davvaz B (2009) Fuzzy hyperideals in ternary semihyperrings. Iran J Fuzzy Syst 6(4):21\u201336","journal-title":"Iran J Fuzzy Syst"},{"issue":"1","key":"1717_CR15","first-page":"37","volume":"27","author":"B Davvaz","year":"2010","unstructured":"Davvaz B (2010) A survey of fuzzy algebraic hyperstructures. Algebra Groups Geometr 27(1):37\u201362","journal-title":"Algebra Groups Geometr"},{"key":"1717_CR16","first-page":"viii+200","volume-title":"Polygroup theory and related systems","author":"B Davvaz","year":"2013","unstructured":"Davvaz B (2013) Polygroup theory and related systems. World Scientific Publishing Co Pte Ltd., Hackensack, p viii+200 (ISBN: 978-981-4425-30-8)"},{"key":"1717_CR17","volume-title":"Hyperring theory and applications","author":"B Davvaz","year":"2007","unstructured":"Davvaz B, Leoreanu-Fotea V (2007) Hyperring theory and applications. International Academic Press, New York"},{"key":"1717_CR18","unstructured":"Davvaz B, Cristea I (2015) Fuzzy algebraic hyperstructures. An introduction. Studies in fuzziness and soft computing, vol 321. Springer, Cham, p x:242 (ISBN 978-3-319-14761-1\/hbk; 978-3-319-14762-8\/ebook)"},{"issue":"3","key":"1717_CR19","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1016\/S0165-0114(98)00191-2","volume":"114","author":"SK De","year":"2000","unstructured":"De SK, Biswas R, Roy AR (2000) Some operations on intuitionistic fuzzy sets. Fuzzy Sets Syst 114(3):477\u2013484","journal-title":"Fuzzy Sets Syst"},{"issue":"1","key":"1717_CR20","first-page":"114","volume":"13","author":"PA Ejegwa","year":"2018","unstructured":"Ejegwa PA (2018) Homomorphism of fuzzy multigroups and some of its properties. Appl Appl Math 13(1):114\u2013129","journal-title":"Appl Appl Math"},{"issue":"2","key":"1717_CR21","doi-asserted-by":"publisher","first-page":"189","DOI":"10.34198\/ejms.4220.189210","volume":"4","author":"PA Ejegwa","year":"2020","unstructured":"Ejegwa PA, Agbetayo JM (2020) On commutators of fuzzy multigroups. Earthline J Math Sci 4(2):189\u2013210","journal-title":"Earthline J Math Sci"},{"issue":"1","key":"1717_CR22","first-page":"64","volume":"8","author":"PA Ejegwaa","year":"2018","unstructured":"Ejegwaa PA (2018) On normal fuzzy submultigroups of a fuzzy multigroup. Theory Appl Math Comput Sci 8(1):64\u201380","journal-title":"Theory Appl Math Comput Sci"},{"key":"1717_CR23","first-page":"1","volume":"13","author":"K Hayat","year":"2021","unstructured":"Hayat K, Tariq Z, Lughofer E, Aslam MF (2021) New aggregation operators on group-based generalized intuitionistic fuzzy soft sets. Soft Comput 13:1\u201312","journal-title":"Soft Comput"},{"key":"1717_CR24","first-page":"1","volume":"38","author":"AM Ibrahim","year":"2016","unstructured":"Ibrahim AM, Ejegwa PA (2016) A survey on the concept of multigroups. J Niger Assoc Math Phys 38:1\u20138","journal-title":"J Niger Assoc Math Phys"},{"key":"1717_CR25","unstructured":"Knuth D (1981) The art of computer programming, vol 2: seminumerical algorithms. Addison-Wesley, Berlin"},{"key":"1717_CR26","unstructured":"Marty F (1934) Surune generalization de la notion de groupe. In: 8$$^{iem}$$ Congres Math. Scandinaves, Stockholm, Sweden, pp 45\u201349"},{"issue":"12","key":"1717_CR27","first-page":"2637","volume":"21","author":"F Mehmood","year":"2020","unstructured":"Mehmood F, Shi F, Hayat K (2020) A new approach to the fuzzification of rings. J Nonlinear Convex Anal 21(12):2637\u20132646","journal-title":"J Nonlinear Convex Anal"},{"issue":"411","key":"1717_CR28","first-page":"1","volume":"8","author":"F Mehmood","year":"2020","unstructured":"Mehmood F, Shi F, Hayat K, Yang X (2020) The Homomorphism theorems of $$M$$-Hazy rings and their induced fuzzifying convexities. Mathematics 8(411):1\u201314","journal-title":"Mathematics"},{"key":"1717_CR29","unstructured":"Miyamoto S (1996) Fuzzy multisets and applications to rough approximation of fuzzy sets. In: Proc. Fourth Intern. workshop on rough sets, fuzzy sets, and machine discovery, RSFD\u201996, pp 255\u2013260"},{"key":"1717_CR30","unstructured":"Miyamoto S (1999) Two images and two cuts in fuzzy multisets. In: Proc. eight intern. fuzzy systems ass. world congress, IFSA\u201999, pp 1047\u20131051"},{"key":"1717_CR31","unstructured":"Miyamoto S (2000) Fuzzy multisets and their generalizations. In: Calude CS, P\u0102un G, Rozenberg G, Salomaa A (eds) Multiset processing. WMC 2000. Lecture notes in computer science, vol 2235. Springer, Berlin, Heidelberg"},{"issue":"3","key":"1717_CR32","first-page":"643","volume":"6","author":"SK Nazmul","year":"2013","unstructured":"Nazmul SK, Majumdar P, Samanta SK (2013) On multisets and multigroups. Ann Fuzzy Math Inform 6(3):643\u2013656","journal-title":"Ann Fuzzy Math Inform"},{"issue":"3","key":"1717_CR33","first-page":"213","volume":"26","author":"BO Onasanya","year":"2018","unstructured":"Onasanya BO, Hoskova-Mayerova S (2018) Some topological and algebraic properties of $$\\alpha $$-level subsets\u2019 topology of a fuzzy subset. An Stiint Univ Ovidius Constanta-Ser Mat 26(3):213\u2013227","journal-title":"An Stiint Univ Ovidius Constanta-Ser Mat"},{"key":"1717_CR34","first-page":"597","volume":"41","author":"BO Onasanya","year":"2019","unstructured":"Onasanya BO, Hoskova-Mayerova S (2019) Multi-fuzzy group induced by multisets. Ital J Pure Appl Math 41:597\u2013604","journal-title":"Ital J Pure Appl Math"},{"key":"1717_CR35","unstructured":"Rado R (1974) Multisets and multicardinals. In: Lecture to the London Mathematical Society"},{"key":"1717_CR36","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1016\/0022-247X(71)90199-5","volume":"35","author":"A Rosenfeld","year":"1971","unstructured":"Rosenfeld A (1971) Fuzzy groups. J Math Anal Appl 35:512\u2013517","journal-title":"J Math Anal Appl"},{"key":"1717_CR37","first-page":"34","volume":"6","author":"TK Shinoj","year":"2012","unstructured":"Shinoj TK, John SJ (2012) Intuitionistic fuzzy multiset and its application in medical diagnosis. Int J Math Comput Sci World Acad Sci Eng Technol (WASET) 6:34\u201338","journal-title":"Int J Math Comput Sci World Acad Sci Eng Technol (WASET)"},{"key":"1717_CR38","unstructured":"Shinoj TK, John SJ (2013a) Intutionistic fuzzy multisets. Int J Eng Sci Innov Technol (IJESIT) 2(6):1\u201324"},{"key":"1717_CR39","unstructured":"Shinoj TK, John SJ (2013b) Accuracy in collaborative robotics: an intuitionistic fuzzy multiset approach. Glob J Sci Front Res (GJSFR) 13(10):20\u201328"},{"issue":"1","key":"1717_CR40","first-page":"131","volume":"9","author":"TK Shinoj","year":"2015","unstructured":"Shinoj TK, Sunil JJ (2015) Intuitionistic fuzzy multigroups. Ann Pure Appl Math 9(1):131\u2013143","journal-title":"Ann Pure Appl Math"},{"issue":"1","key":"1717_CR41","first-page":"77","volume":"9","author":"TK Shinoj","year":"2015","unstructured":"Shinoj TK, Baby A, Sunil JJ (2015) On some algebraic structures of fuzzy multisets. Ann Fuzzy Math Inform 9(1):77\u201390","journal-title":"Ann Fuzzy Math Inform"},{"key":"1717_CR42","first-page":"73","volume":"37","author":"D Singh","year":"2007","unstructured":"Singh D, Ibrahim AM, Yohanna T, Singh JN (2007) An overview of the applications of multisets. Novi Sad J Math 37:73\u201392","journal-title":"Novi Sad J Math"},{"key":"1717_CR43","doi-asserted-by":"publisher","unstructured":"Syropoulos A (2001) Mathematics of Multisets. Springer, Berlin, Heidelberg, pp 347\u2013358. https:\/\/doi.org\/10.1007\/3-540-45523-X_17","DOI":"10.1007\/3-540-45523-X_17"},{"issue":"3\u20134","key":"1717_CR44","first-page":"393","volume":"6","author":"A Syropoulos","year":"2003","unstructured":"Syropoulos A (2003) Categorical models of multisets. Roman J Inf Sci Technol 6(3\u20134):393\u2013400","journal-title":"Roman J Inf Sci Technol"},{"issue":"2","key":"1717_CR45","doi-asserted-by":"publisher","first-page":"2337","DOI":"10.3233\/JIFS-191262","volume":"38","author":"MAI Tahan","year":"2020","unstructured":"Tahan MAI, Hoskova-Mayerova S, Davvaz B (2020) Fuzzy multi-polygroups. J Intell Fuzzy Syst 38(2):2337\u20132345","journal-title":"J Intell Fuzzy Syst"},{"key":"1717_CR46","volume-title":"Hyperstructures and their representations","author":"T Vougiouklis","year":"1994","unstructured":"Vougiouklis T (1994) Hyperstructures and their representations. Hadronic Press, Palm Harbor"},{"key":"1717_CR47","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1080\/03081078608934952","volume":"13","author":"RR Yager","year":"1986","unstructured":"Yager RR (1986) On theory of bags. Int J Gen Syst 13:23\u201327","journal-title":"Int J Gen Syst"},{"key":"1717_CR48","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"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01717-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01717-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01717-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,10]],"date-time":"2022-02-10T18:42:19Z","timestamp":1644518539000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01717-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,13]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,2]]}},"alternative-id":["1717"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01717-x","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,12,13]]},"assertion":[{"value":"16 December 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 October 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 November 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 December 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"All authors declare that they have no conflict of interest.","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"}}],"article-number":"12"}}