{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T16:20:56Z","timestamp":1774023656244,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2015,10,28]],"date-time":"2015-10-28T00:00:00Z","timestamp":1445990400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2016,7]]},"DOI":"10.1007\/s00500-015-1909-9","type":"journal-article","created":{"date-parts":[[2015,10,28]],"date-time":"2015-10-28T04:01:22Z","timestamp":1446004882000},"page":"2513-2519","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Carlson\u2019s inequality for Sugeno and Choquet integrals"],"prefix":"10.1007","volume":"20","author":[{"given":"Micha\u0142","family":"Boczek","sequence":"first","affiliation":[]},{"given":"Marek","family":"Kaluszka","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,10,28]]},"reference":[{"key":"1909_CR1","doi-asserted-by":"crossref","first-page":"1972","DOI":"10.1016\/j.amc.2010.03.027","volume":"216","author":"H Agahi","year":"2010","unstructured":"Agahi H, Yaghoobi MA (2010) General Hardy type inequality for seminormed fuzzy integrals. Appl Math Comput 216:1972\u20131977","journal-title":"Appl Math Comput"},{"key":"1909_CR2","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ins.2011.10.021","volume":"190","author":"H Agahi","year":"2012","unstructured":"Agahi H, Mesiar R, Ouyang Y (2012) On some advanced type inequalities for Sugeno integral and T-(S-)evaluators. Inf Sci 190:64\u201375","journal-title":"Inf Sci"},{"key":"1909_CR3","doi-asserted-by":"crossref","unstructured":"Barza S, Peoari J, Persson L-E (1998) Carlson type inequalities. J Inequal Appl 2:121\u2013135","DOI":"10.1155\/S1025583498000071"},{"key":"1909_CR4","doi-asserted-by":"crossref","first-page":"2763","DOI":"10.1016\/j.camwa.2010.01.045","volume":"59","author":"J Caballero","year":"2010","unstructured":"Caballero J, Sadarangani K (2010) Fritz Carlson\u2019s inequality for fuzzy integrals. Comput Math Appl 59:2763\u20132767","journal-title":"Comput Math Appl"},{"key":"1909_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02384433","volume":"25","author":"F Carlson","year":"1934","unstructured":"Carlson F (1934) Une inegalit\u00e9. Arkiv f\u00f6r Matematik Astronomi och Fysik 25:1\u20135","journal-title":"Arkiv f\u00f6r Matematik Astronomi och Fysik"},{"key":"1909_CR6","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1007\/s13348-010-0031-7","volume":"62","author":"J Cerd\u00e0","year":"2011","unstructured":"Cerd\u00e0 J, Mart\u00edn J, Silvestre P (2011) Capacitary function spaces. Collect Math 62:95\u2013118","journal-title":"Collect Math"},{"key":"1909_CR7","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1007\/s00500-013-1024-8","volume":"17","author":"B Daraby","year":"2013","unstructured":"Daraby B, Arabi L (2013) Related Fritz Carlson type inequalities for Sugeno integrals. Soft Comput 17:1745\u20131750","journal-title":"Soft Comput"},{"key":"1909_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-017-2434-0","volume-title":"Non-additive measure and integral","author":"D Denneberg","year":"1994","unstructured":"Denneberg D (1994) Non-additive measure and integral. Kluwer Academic Publishers, Dordrecht"},{"key":"1909_CR9","first-page":"315","volume":"41","author":"F Durante","year":"2005","unstructured":"Durante F, Sempi C (2005) Semicopulae. Kybernetika 41:315\u2013328","journal-title":"Kybernetika"},{"key":"1909_CR10","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.1016\/j.amc.2007.02.143","volume":"190","author":"A Flores-Franuli\u010d","year":"2007","unstructured":"Flores-Franuli\u010d A, Rom\u00e1n-Flores H (2007) A Chebyshev type inequality for fuzzy integrals. Appl Math Comput 190:1178\u20131184","journal-title":"Appl Math Comput"},{"key":"1909_CR11","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1016\/j.ijar.2011.06.001","volume":"52","author":"B Girotto","year":"2011","unstructured":"Girotto B, Holzer S (2011) Chebyshev type inequality for Choquet integral and comonotonicity. Int J Approx Reason 52:1118\u20131123","journal-title":"Int J Approx Reason"},{"key":"1909_CR12","first-page":"267","volume":"23","author":"B Girotto","year":"2012","unstructured":"Girotto B, Holzer S (2012) Chebyshev and Jensen inequalities for Choquet integral. Math Pannonica 23:267\u2013275","journal-title":"Math Pannonica"},{"issue":"1","key":"1909_CR13","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1007\/s10479-009-0655-8","volume":"175","author":"M Grabisch","year":"2010","unstructured":"Grabisch M, Labreuche C (2010) A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Ann Oper Res 175(1):247\u2013286","journal-title":"Ann Oper Res"},{"key":"1909_CR14","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/S0167-6687(03)00144-6","volume":"33","author":"S Heilpern","year":"2003","unstructured":"Heilpern S (2003) A rank-dependent generalization of zero utility principle. Insur Math Econ 33:67\u201373","journal-title":"Insur Math Econ"},{"key":"1909_CR15","doi-asserted-by":"crossref","first-page":"1673","DOI":"10.1016\/j.ins.2006.09.009","volume":"177","author":"Y Hu","year":"2007","unstructured":"Hu Y (2007) Fuzzy integral-based perceptron for two-class pattern classification problems. Inf Sci 177:1673\u20131686","journal-title":"Inf Sci"},{"key":"1909_CR16","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.insmatheco.2011.11.001","volume":"50","author":"M Kaluszka","year":"2012","unstructured":"Kaluszka M, Krzeszowiec M (2012) Pricing insurance contracts under cumulative prospect theory. Insur Math Econ 50:159\u2013166","journal-title":"Insur Math Econ"},{"key":"1909_CR17","doi-asserted-by":"crossref","unstructured":"Kaluszka M, Okolewski A, Boczek M (2014a) On Chebyshev type inequalities for generalized Sugeno integrals. Fuzzy Sets Syst 244:51\u201362","DOI":"10.1016\/j.fss.2013.10.015"},{"key":"1909_CR18","doi-asserted-by":"crossref","unstructured":"Kaluszka M, Okolewski A, Boczek M (2014b) On the Jensen type inequality for generalized Sugeno integral. Inf Sci 266:140\u2013147","DOI":"10.1016\/j.ins.2014.01.004"},{"key":"1909_CR19","doi-asserted-by":"crossref","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 Publishers, Dordrecht"},{"key":"1909_CR20","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1109\/TFUZZ.2009.2039367","volume":"18","author":"EP Klement","year":"2010","unstructured":"Klement EP, Mesiar R, Pap E (2010) A universal integral as common frame for Choquet and Sugeno integral. IEEE Trans Fuzzy Syst 18:178\u2013187","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"1909_CR21","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1016\/j.fss.2008.04.002","volume":"160","author":"R Mesiar","year":"2009","unstructured":"Mesiar R, Ouyang Y (2009) General Chebyshev type inequalities for Sugeno integrals. Fuzzy Sets Syst 160:58\u201364","journal-title":"Fuzzy Sets Syst"},{"key":"1909_CR22","first-page":"1098","volume":"46","author":"R Mesiar","year":"2010","unstructured":"Mesiar R, Li J, Pap E (2010) The Choquet integral as Lebesgue integral and related inequalities. Kybernetika 46:1098\u20131107","journal-title":"Kybernetika"},{"key":"1909_CR23","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-011-3562-7","volume-title":"Inequalities involving functions and their integrals and derivatives","author":"DS Mitrinovi\u0107","year":"1991","unstructured":"Mitrinovi\u0107 DS, Pe\u010dari\u0107 JE, Fink AM (1991) Inequalities involving functions and their integrals and derivatives. Kluwer, Dordrecht"},{"key":"1909_CR24","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1016\/0022-247X(91)90213-J","volume":"159","author":"T Murofushi","year":"1991","unstructured":"Murofushi T, Sugeno M (1991) A theory of fuzzy measures: representations, the Choquet integral and null sets. J Math Anal Appl 159:532\u2013549","journal-title":"J Math Anal Appl"},{"key":"1909_CR25","doi-asserted-by":"crossref","first-page":"4686","DOI":"10.1016\/j.ins.2007.05.010","volume":"177","author":"Y Narukawa","year":"2007","unstructured":"Narukawa Y, Torra V (2007) Fuzzy measures and integrals in evaluation of strategies. Inf Sci 177:4686\u20134695","journal-title":"Inf Sci"},{"key":"1909_CR26","doi-asserted-by":"crossref","DOI":"10.1007\/0-387-31077-0","volume-title":"Convex functions and their applications. A contemporary approach","author":"C Niculescu","year":"2006","unstructured":"Niculescu C, Persson L-E (2006) Convex functions and their applications. A contemporary approach. Springer, New York"},{"key":"1909_CR27","unstructured":"Ouyang Y (2015) On Carlson inequality for the Choquet integral (personal communication)"},{"key":"1909_CR28","doi-asserted-by":"crossref","first-page":"1810","DOI":"10.1016\/j.aml.2009.06.024","volume":"22","author":"Y Ouyang","year":"2009","unstructured":"Ouyang Y, Mesiar R (2009) On the Chebyshev type inequality for seminormed fuzzy integral. Appl Math Lett 22:1810\u20131815","journal-title":"Appl Math Lett"},{"key":"1909_CR29","volume-title":"Null-additive set functions","author":"E Pap","year":"1995","unstructured":"Pap E (1995) Null-additive set functions. Kluwer, Dordrecht"},{"key":"1909_CR30","doi-asserted-by":"crossref","first-page":"3192","DOI":"10.1016\/j.ins.2007.02.006","volume":"177","author":"H Rom\u00e1n-Flores","year":"2007","unstructured":"Rom\u00e1n-Flores H, Flores-Franuli\u010d A, Chalco-Cano Y (2007) A Jensen type inequality for fuzzy integrals. Inf Sci 177:3192\u20133201","journal-title":"Inf Sci"},{"key":"1909_CR31","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S1385-7258(71)80017-3","volume":"33","author":"N Shilkret","year":"1971","unstructured":"Shilkret N (1971) Maxitive measure and integration. Indag Math 33:109\u2013116","journal-title":"Indag Math"},{"key":"1909_CR32","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s11587-008-0025-x","volume":"57","author":"S Shirali","year":"2008","unstructured":"Shirali S (2008) Analog of $$L^p$$ L p with a subadditive measure. Ric di Mat 57:43\u201354","journal-title":"Ric di Mat"},{"key":"1909_CR33","doi-asserted-by":"crossref","unstructured":"Su\u00e1rez Garc\u00eda F, Gil \u00c1lvarez P (1986) Two families of fuzzy integrals. Fuzzy Sets Syst 18:67\u201381","DOI":"10.1016\/0165-0114(86)90028-X"},{"key":"1909_CR34","unstructured":"Sugeno M (1974) Theory of fuzzy integrals and its applications. Ph.D. dissertation, Tokyo Institute of Technology"},{"key":"1909_CR35","unstructured":"Tang YL, Ouyang Y (2012) On the Carlson inequality for the Choquet integral. J Huzhou Teach Coll 2:21\u201325 (in Chinese)"},{"key":"1909_CR36","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s12190-009-0358-y","volume":"35","author":"R-S Wang","year":"2011","unstructured":"Wang R-S (2011) Some inequalities and convergence theorems for Choquet integrals. J Appl Math Comput 35:305\u2013321","journal-title":"J Appl Math Comput"},{"key":"1909_CR37","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-76852-6","volume-title":"Generalized measure theory","author":"Z Wang","year":"2009","unstructured":"Wang Z, Klir G (2009) Generalized measure theory. Springer, New York"},{"key":"1909_CR38","doi-asserted-by":"crossref","unstructured":"Wang X, Bai C (2011) General Fritz Carlson\u2019s type inequality for Sugeno integrals. Hindawi Publ Corp J Inequal Appl Article ID 761430, 9 pages","DOI":"10.1155\/2011\/761430"},{"key":"1909_CR39","doi-asserted-by":"crossref","first-page":"2337","DOI":"10.1016\/j.fss.2010.04.017","volume":"161","author":"L Wu","year":"2010","unstructured":"Wu L, Sun J, Ye X, Zhu L (2010) H\u00f6lder type inequality for Sugeno integral. Fuzzy Sets Syst 161:2337\u20132347","journal-title":"Fuzzy Sets Syst"},{"key":"1909_CR40","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.aml.2011.09.072","volume":"25","author":"Q Xu","year":"2012","unstructured":"Xu Q, Ouyang Y (2012) A note on a Carlson-type inequality for the Sugeno integral. Appl Math Lett 25:619\u2013623","journal-title":"Appl Math Lett"},{"key":"1909_CR41","doi-asserted-by":"crossref","unstructured":"Zhao X, Zhang Q (2011) H\u00f6lder type inequality and Jensen type inequality for Choquet integral. In: Wang Y, Li T (eds) Knowledge engineering and management. AISC 123, pp 219\u2013224","DOI":"10.1007\/978-3-642-25661-5_29"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1909-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00500-015-1909-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-015-1909-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,31]],"date-time":"2019-08-31T21:49:14Z","timestamp":1567288154000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00500-015-1909-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,28]]},"references-count":41,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2016,7]]}},"alternative-id":["1909"],"URL":"https:\/\/doi.org\/10.1007\/s00500-015-1909-9","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,10,28]]}}}