{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T16:42:28Z","timestamp":1778776948020,"version":"3.51.4"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T00:00:00Z","timestamp":1760486400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T00:00:00Z","timestamp":1760486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171294"],"award-info":[{"award-number":["12171294"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2026,3]]},"DOI":"10.1007\/s40314-025-03402-9","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T05:17:27Z","timestamp":1760505447000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Migrativity of grouping functions over fuzzy implications"],"prefix":"10.1007","volume":"45","author":[{"given":"Peng","family":"Yu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huxiong","family":"Song","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,15]]},"reference":[{"key":"3402_CR1","doi-asserted-by":"crossref","unstructured":"M. Baczy\u0144ski, B. Jayaram, S. Massanet, J. Torrens,(2015) Fuzzy implications: past, present, and future. Springer Handbook of Computational Intelligence, 183-202","DOI":"10.1007\/978-3-662-43505-2_12"},{"key":"3402_CR2","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.ins.2020.04.033","volume":"531","author":"M Baczy\u0144ski","year":"2020","unstructured":"Baczy\u0144ski M, Jayaram B, Mesiar R (2020) Fuzzy implication: alpha migrativity and generalised laws of importation. Inf Sci 531:87\u201396","journal-title":"Inf Sci"},{"key":"3402_CR3","unstructured":"Baczy\u0144ski M, Jayaram B,(2008) Fuzzy Implications. Studies in Fuzziness and Soft Computing"},{"key":"3402_CR4","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1016\/j.ins.2013.05.004","volume":"249","author":"B Bedregal","year":"2013","unstructured":"Bedregal B, Dimuro GP, Bustince H, Barrenechea E (2013) New results on overlap and grouping functions. Inf Sci 249:148\u2013170","journal-title":"Inf Sci"},{"key":"3402_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ijar.2017.07.001","volume":"90","author":"B Bedregal","year":"2017","unstructured":"Bedregal B, Bustince H, Palmeira E, Dimuro G, Fernandez J (2017) Generalized interval-valued OWA operators with interval weights derived from interval-valued overlap functions. Int J Approx Reason 90:1\u201316","journal-title":"Int J Approx Reason"},{"key":"3402_CR6","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1016\/j.fss.2008.09.018","volume":"160","author":"H Bustince","year":"2009","unstructured":"Bustince H, Montero J, Mesiar R (2009) Migrativity of aggregation functions. Fuzzy Sets Syst 160:766\u2013777","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR7","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.ins.2011.12.019","volume":"191","author":"H Bustince","year":"2012","unstructured":"Bustince H, De Baets B, Fernandez J, Mesiar R, Montero J (2012) A generalization of the migrativity property of aggregation functions. Inf Sci 191:76\u201385","journal-title":"Inf Sci"},{"issue":"3","key":"3402_CR8","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1109\/TFUZZ.2011.2173581","volume":"20","author":"H Bustince","year":"2012","unstructured":"Bustince H, Pagola M, Mesiar R, Hullermeier E, Herrera F (2012) Grouping, overlap, and generalized bientropic functions for fuzzy modeling of pairwise comparisons. IEEE Trans Fuzzy Syst 20(3):405\u2013415","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"3402_CR9","unstructured":"Bustince H, Fern\u00e1ndez J, Mesiar R, Montero J, Orduna R, (2009) Overlap index, overlap functions and migrativity. in: Proceedings of IFSA\/EUSFLAT Conference, pp. 300-305"},{"key":"3402_CR10","doi-asserted-by":"crossref","unstructured":"De Baets B, (1997) Fuzzy morphology: a logical approach, in: Uncertainty Analysis in Engineering and Sciences: Fuzzy Logic, Statistics, and Neural Network Approach, Kluwer, Norwell, MA, USA, pp. 53-68","DOI":"10.1007\/978-1-4615-5473-8_4"},{"key":"3402_CR11","doi-asserted-by":"crossref","unstructured":"Dimuro GP, Bedregal B, Bustince H, Mesiar R, Asi\u00e1in MJ, (2014) On additive generators of grouping functions, International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer, Chain, pp. 252-261","DOI":"10.1007\/978-3-319-08852-5_26"},{"key":"3402_CR12","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.ins.2015.03.049","volume":"312","author":"GP Dimuro","year":"2015","unstructured":"Dimuro GP, Bedregal B (2015) On residual implications derived from overlap functions. Inf Sci 312:78\u201388","journal-title":"Inf Sci"},{"key":"3402_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.ins.2014.04.021","volume":"279","author":"GP Dimuro","year":"2014","unstructured":"Dimuro GP, Bedregal B, Santiago RHN (2014) On (G, N )-implications derived from grouping functions. Inf Sci 279:1\u201317","journal-title":"Inf Sci"},{"key":"3402_CR14","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.fss.2015.02.008","volume":"287","author":"GP Dimuro","year":"2016","unstructured":"Dimuro GP, Bedregal B, Bustince H, Asi\u00e1in MJ, Mesiar R (2016) On additive generators of overlap functions. Fuzzy Sets Syst 287:76\u201396","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR15","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1016\/j.ijar.2016.12.013","volume":"82","author":"GP Dimuro","year":"2017","unstructured":"Dimuro GP, Bedregal B, Bustince H, Jurio A, Baczy\u0144ski M, Mi\u015b K (2017) QL-operations and QL-implication functions constructed from tuples (O, G, N) and the generation of fuzzy subsethood and entropy measures. Int J Approx Reason 82:170\u2013192","journal-title":"Int J Approx Reason"},{"key":"3402_CR16","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1016\/j.ins.2011.10.026","volume":"180","author":"F Durante","year":"2012","unstructured":"Durante F, Fern\u00e1ndez-S\u00e1nchez J, Quesada-Molina JJ (2012) On the $$\\alpha $$-migrativity of multivariate semi-copulas. Inf Sci 180:216\u2013223","journal-title":"Inf Sci"},{"key":"3402_CR17","unstructured":"Feng Q,(2019) Aggregation Functions and Their Applications. Science Press"},{"key":"3402_CR18","doi-asserted-by":"publisher","first-page":"1692","DOI":"10.1016\/j.fss.2007.02.020","volume":"158","author":"J Fodor","year":"2007","unstructured":"Fodor J, Rudas IJ (2007) On continuous triangular norms that are migrative. Fuzzy Sets Syst 158:1692\u20131697","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR19","doi-asserted-by":"publisher","first-page":"4860","DOI":"10.1016\/j.ins.2011.05.014","volume":"181","author":"J Fodor","year":"2011","unstructured":"Fodor J, Rudas IJ (2011) Migrative t-norms with respect to continuous ordinal sums. Inf Sci 181:4860\u20134866","journal-title":"Inf Sci"},{"key":"3402_CR20","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.fss.2010.09.020","volume":"168","author":"J Fodor","year":"2011","unstructured":"Fodor J, Rudas IJ (2011) An extension of the migrative property for triangular norms. Fuzzy Sets Syst 168:70\u201380","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR21","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1002\/int.21526","volume":"27","author":"J Fodor","year":"2012","unstructured":"Fodor J, Klement EP, Mesiar R (2012) Cross-migrative triangular norms. Int J Intell Syst 27:411\u2013428","journal-title":"Int J Intell Syst"},{"key":"3402_CR22","volume-title":"A Treatise on Many-Valued Logic","author":"S Gottwald","year":"2001","unstructured":"Gottwald S (2001) A Treatise on Many-Valued Logic. Research Studies Press, Baldock"},{"key":"3402_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1847-5","volume-title":"Fuzzy Techniques in Image Processing","author":"E Kerre","year":"2000","unstructured":"Kerre E, Nachtegael M (2000) Fuzzy Techniques in Image Processing. Springer-Verlag, New York"},{"key":"3402_CR24","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-9540-7","volume-title":"Triangular Norms","author":"EP Klement","year":"2000","unstructured":"Klement EP, Mesiar R, Pap E (2000) Triangular Norms. Kluwer Academic Publisher, Dordrecht"},{"key":"3402_CR25","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1002\/int.21708","volume":"30","author":"S Li","year":"2015","unstructured":"Li S, Qin F, Fodor J (2015) On the cross-migrativity with respect to continuous t-norms. Int J Intell Syst 30:550\u2013562","journal-title":"Int J Intell Syst"},{"issue":"6","key":"3402_CR26","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.1109\/TFUZZ.2007.896304","volume":"15","author":"M Mas","year":"2007","unstructured":"Mas M, Monserrat M, Torrens J, Trillas E (2007) A survey on fuzzy implication functions. IEEE Trans Fuzzy Syst 15(6):1107\u20131121","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"3402_CR27","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1016\/j.ins.2013.05.024","volume":"246","author":"M Mas","year":"2013","unstructured":"Mas M, Monserrat M, Ruiz-Aguilera D, Torrens J (2013) An extension of the migrative property for uninorms. Inf Sci 246:191\u2013198","journal-title":"Inf Sci"},{"key":"3402_CR28","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1016\/j.fss.2014.05.012","volume":"261","author":"M Mas","year":"2015","unstructured":"Mas M, Monserrat M, Ruiz-Aguilera D, Torrens J (2015) Migrative uninorms and nullnorms over t-norms and t-conorms. Fuzzy Sets Syst 261:20\u201332","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR29","doi-asserted-by":"publisher","first-page":"1967","DOI":"10.1016\/j.ins.2010.01.024","volume":"180","author":"R Mesiar","year":"2010","unstructured":"Mesiar R, Bustince H, Fernandez J (2010) On the $$\\alpha $$-migrativity of semicopulas, quasi-copulas, and copulas. Inf Sci 180:1967\u20131976","journal-title":"Inf Sci"},{"key":"3402_CR30","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1007\/978-3-540-71258-9_16","volume-title":"Fuzzy Logic: A Spectrum of Applied and Theoretical Issues","author":"J Montero","year":"2007","unstructured":"Montero J, L\u00f3pez V, G\u00f3mez D (2007) The role of fuzziness in decision making. In: Ruan D et al (eds) Fuzzy Logic: A Spectrum of Applied and Theoretical Issues. Springer, pp 337\u2013349"},{"key":"3402_CR31","unstructured":"Montero J, G\u00f3mez D, Mu\u00f1oz S,(2008) Fuzzy information representation for decision aiding. in: Proc. IPMU Conf., M\u00e1laga, Spain pp. 1425-1430"},{"key":"3402_CR32","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.fss.2012.03.008","volume":"211","author":"Y Ouyang","year":"2013","unstructured":"Ouyang Y (2013) Generalizing the migrativity of continuous t-norms. Fuzzy Sets Syst 211:73\u201383","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR33","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/j.fss.2022.04.006","volume":"456","author":"D Pan","year":"2023","unstructured":"Pan D, Zhou H, Yan X (2023) Characterizations for the migrativity of continuous t-conorms over fuzzy implications. Fuzzy Sets Syst 456:173\u2013196","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR34","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.fss.2017.11.012","volume":"346","author":"J Qiao","year":"2018","unstructured":"Qiao J, Hu BQ (2018) On the migrativity of uninorms and nullnorms over overlap and grouping functions. Fuzzy Sets Syst 346:1\u201354","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR35","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.fss.2018.01.007","volume":"357","author":"J Qiao","year":"2019","unstructured":"Qiao J, Hu BQ (2019) On generalized migrativity property for overlap functions. Fuzzy Sets Syst 357:91\u2013116","journal-title":"Fuzzy Sets Syst"},{"issue":"2","key":"3402_CR36","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1109\/TFUZZ.2020.3040038","volume":"30","author":"J Qiao","year":"2022","unstructured":"Qiao J, Zhao B (2022) On $$\\alpha $$-cross-migrativity of overlap (0-overlap) functions. IEEE Trans Fuzzy Syst 30(2):448\u2013461","journal-title":"IEEE Trans Fuzzy Syst"},{"issue":"1","key":"3402_CR37","doi-asserted-by":"publisher","first-page":"104","DOI":"10.1007\/s40314-024-03028-3","volume":"44","author":"Y Song","year":"2025","unstructured":"Song Y, Qiao J (2025) $$\\alpha $$-cross-migrativity between fuzzy implications and grouping functions. Comput Appl Math 44(1):104","journal-title":"Comput Appl Math"},{"key":"3402_CR38","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2022.12.001","volume":"466","author":"HX Song","year":"2023","unstructured":"Song HX, Yu P, Liu H (2023) From pre-(quasi-)grouping functions to directional monotonic fuzzy implications. Fuzzy Sets Syst 466:108445","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR39","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/j.ins.2015.07.030","volume":"325","author":"Y Su","year":"2015","unstructured":"Su Y, Zong W, Liu HW, Xue P (2015) Migrativity property for uninorms and semi t-operators. Inf Sci 325:455\u2013465","journal-title":"Inf Sci"},{"key":"3402_CR40","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.ins.2014.12.027","volume":"300","author":"Y Su","year":"2015","unstructured":"Su Y, Zong W, Liu HW, Wang F (2015) On migrativity property for uninorms. Inf Sci 300:114\u2013123","journal-title":"Inf Sci"},{"key":"3402_CR41","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1016\/j.fss.2015.05.018","volume":"287","author":"Y Su","year":"2016","unstructured":"Su Y, Zong W, Liu HW (2016) Migrativity property for uninorms. Fuzzy Sets Syst 287:213\u2013226","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR42","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.ins.2019.02.029","volume":"486","author":"Y Su","year":"2019","unstructured":"Su Y, Zong W, Qin F, Zhao B (2019) The cross-migrativity with respect to continuous traingular norms revisited. Inf Sci 486:114\u2013118","journal-title":"Inf Sci"},{"key":"3402_CR43","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.fss.2018.09.015","volume":"372","author":"YM Wang","year":"2019","unstructured":"Wang YM, Liu HW (2019) The modularity condition for overlap and grouping functions. Fuzzy Sets Syst 372:97\u2013110","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR44","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1016\/j.fss.2012.12.013","volume":"226","author":"L Wu","year":"2013","unstructured":"Wu L, Ouyang Y (2013) On the migrativity of triangular subnorms. Fuzzy Sets Syst 226:89\u201398","journal-title":"Fuzzy Sets Syst"},{"key":"3402_CR45","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/j.ins.2005.03.003","volume":"173","author":"P Yan","year":"2005","unstructured":"Yan P, Chen G (2005) Discovering a cover set of Arsi with hierarchy from quantitative databases. Inf Sci 173:319\u2013336","journal-title":"Inf Sci"},{"issue":"1","key":"3402_CR46","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1049\/cje.2020.11.011","volume":"30","author":"P Yu","year":"2021","unstructured":"Yu P (2021) Quantitative Method Based on Cotangent Similarity Degree in Three-Valued \u0141ukasiewicz Logic. Chin J Electron 30(1):134\u2013144","journal-title":"Chin J Electron"},{"key":"3402_CR47","doi-asserted-by":"publisher","first-page":"1219","DOI":"10.1007\/s00010-016-0437-8","volume":"90","author":"H Zhan","year":"2016","unstructured":"Zhan H, Liu H (2016) The cross-migrative property for uninorms. Aequ Math 90:1219\u20131239","journal-title":"Aequ Math"},{"key":"3402_CR48","first-page":"1877","volume":"32","author":"H Zhan","year":"2017","unstructured":"Zhan H, Liu H (2017) Cross-migrative uninorms with different neutral elements. Int J Intell Syst 32:1877\u20131889","journal-title":"Int J Intell Syst"},{"key":"3402_CR49","doi-asserted-by":"crossref","unstructured":"Zhang X, Zhang F, Zhang M, Qin M, (2025)The migrativity of grouping functions over fuzzy implications from generator functions. In, 4th International Symposium on Computer Applications and Information Technology (ISCAIT). IEEE 2025:1597\u20131600","DOI":"10.1109\/ISCAIT64916.2025.11010486"},{"key":"3402_CR50","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.fss.2019.11.011","volume":"403","author":"H Zhou","year":"2021","unstructured":"Zhou H, Yan X (2021) Migrativity properties of overlap functions over uninorms. Fuzzy Sets Syst 403:10\u201337","journal-title":"Fuzzy Sets Syst"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03402-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03402-9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03402-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T06:02:20Z","timestamp":1769839340000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03402-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,15]]},"references-count":50,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,3]]}},"alternative-id":["3402"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03402-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,15]]},"assertion":[{"value":"9 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 July 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 August 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"54"}}