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Hölder type inequality for Sugeno integral. (English) Zbl 1194.28019

Summary: Two inequalities for the Sugeno integral on abstract spaces are studied in rather general forms, which generalize most of the results on the same topic obtained by other authors, thus closing the series of papers on this topic. As an application, a Hölder type inequality is obtained. Finally, some conclusions are drawn and some problems for further investigation are suggested.

MSC:

28E10 Fuzzy measure theory
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[1] H. Agahi, M.A. Yaghoobi, A Minkowski type inequality for fuzzy integrals, Journal of Uncertain Systems, in press. · Zbl 1200.26038
[2] Agahi, H.; Mesiar, R.; Ouyang, Y., General Minkowski type inequalities for sugeno integrals, Fuzzy sets and systems, 161, 708-715, (2010) · Zbl 1183.28027
[3] Agahi, H.; Mesiar, R.; Ouyang, Y., New general extensions of Chebyshev type inequalities for sugeno integrals, International journal of approximate reasoning, 51, 135-140, (2009) · Zbl 1196.28026
[4] Benvenuti, P.; Mesiar, R.; Vivona, D., Monotone set functions-based integrals, (), 1329-1379 · Zbl 1099.28007
[5] Flores-Franulič, A.; Román-Flores, H., A Chebyshev type inequality for fuzzy integrals, Applied mathematics and computation, 190, 1178-1184, (2007) · Zbl 1129.26021
[6] Hardy, G.H.; Littlewood, J.E.; Polya, G., Inequalities, (1952), Cambridge University Press Cambridge · Zbl 0047.05302
[7] Lu, J.; Wu, K.; Lin, J., Fast full search in motion estimation by hierarchical use of Minkowski’s inequality, Pattern recognition, 31, 945-952, (1998)
[8] Mesiar, R.; Mesiarová, A., Fuzzy integrals and linearity, International journal of approximate reasoning, 47, 352-358, (2008) · Zbl 1183.28034
[9] Mesiar, R.; Ouyang, Y., General Chebyshev type inequalities for sugeno integrals, Fuzzy sets and systems, 160, 58-64, (2009) · Zbl 1183.28035
[10] H. Minkowski, Geometrie der Zahlen, Teubner, Leipzig, 1910. · JFM 41.0239.03
[11] Narukawa, Y.; Torra, V., Fuzzy measures and integrals in evaluation of strategies, Information sciences, 177, 4686-4695, (2007) · Zbl 1284.91066
[12] Ouyang, Y.; Fang, J., Sugeno integral of monotone functions based on Lebesgue measure, Computers and mathematics with applications, 56, 367-374, (2008) · Zbl 1155.28305
[13] Ouyang, Y.; Fang, J.; Wang, L., Fuzzy Chebyshev type inequality, International journal of approximate reasoning, 48, 829-835, (2008) · Zbl 1185.28025
[14] Ouyang, Y.; Mesiar, R., On the Chebyshev type inequality for seminormed fuzzy integral, Applied mathematics letters, 22, 1810-1815, (2009) · Zbl 1185.28026
[15] Ouyang, Y.; Mesiar, R., Sugeno integral and the comonotone commuting property, International journal of uncertainty, fuzziness and knowledge based-systems, 17, 465-480, (2009) · Zbl 1178.28031
[16] Ouyang, Y.; Mesiar, R.; Agahi, H., An inequality related to Minkowski type for sugeno integrals, Information sciences, 180, 2793-2801, (2010) · Zbl 1193.28016
[17] Ouyang, Y.; Mesiar, R.; Li, J., On the comonotonic-\(☆\)-property for sugeno integral, Applied mathematics and computation, 211, 450-458, (2009) · Zbl 1175.28011
[18] Özkan, U.M.; Sarikaya, M.Z.; Yildirim, H., Extensions of certain integral inequalities on time scales, Applied mathematics letters, 21, 993-1000, (2008) · Zbl 1168.26316
[19] Pap, E., Null-additive set functions, (1995), Kluwer Dordrecht · Zbl 0856.28001
[20] Ralescu, D.; Adams, G., The fuzzy integral, Journal of mathematical analysis and applications, 75, 562-570, (1980) · Zbl 0438.28007
[21] Román-Flores, H.; Chalco-Cano, Y., H-continuity of fuzzy measures and set defuzzification, Fuzzy sets and systems, 157, 230-242, (2006) · Zbl 1084.28010
[22] Román-Flores, H.; Chalco-Cano, Y., Sugeno integral and geometric inequalities, International journal of uncertainty, fuzziness and knowledge-based systems, 15, 1-11, (2007) · Zbl 1118.28012
[23] Román-Flores, H.; Flores-Franulič, A.; Chalco-Cano, Y., The fuzzy integral for monotone functions, Applied mathematics and computation, 185, 492-498, (2007) · Zbl 1116.26024
[24] Román-Flores, H.; Flores-Franulič, A.; Chalco-Cano, Y., A Jensen type inequality for fuzzy integrals, Information sciences, 177, 3192-3201, (2007) · Zbl 1127.28013
[25] Rudin, W., Real and complex analysis, (1987), McGraw-Hill New York · Zbl 0925.00005
[26] Suárez García, F.; Gil Álvarez, P., Two families of fuzzy integrals, Fuzzy sets and systems, 18, 67-81, (1986) · Zbl 0595.28011
[27] M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology, 1974.
[28] Temko, A.; Macho, D.; Nadeu, C., Fuzzy integral based information fusion for classification of highly confusable non-speech sounds, Pattern recognition, 41, 1814-1823, (2008) · Zbl 1140.68482
[29] Wang, Z.; Klir, G., Generalized measure theory, (2008), Springer Verlag New York
[30] Wu, S., Generalization of a sharp Hölder’s inequality and its application, Journal of mathematical analysis and applications, 332, 741-750, (2007) · Zbl 1120.26024
[31] Ying, M., Linguistic quantifiers modeled by sugeno integrals, Artificial intelligence, 170, 581-606, (2006) · Zbl 1131.68551
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