Title:
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Further development of Chebyshev type inequalities for Sugeno integrals and T-(S-)evaluators (English) |
Author:
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Agahi, Hamzeh |
Author:
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Mesiar, Radko |
Author:
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Ouyang, Yao |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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46 |
Issue:
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1 |
Year:
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2010 |
Pages:
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83-95 |
Summary lang:
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English |
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Category:
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math |
. |
Summary:
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In this paper further development of Chebyshev type inequalities for Sugeno integrals based on an aggregation function $H$ and a scale transformation $\varphi $ is given. Consequences for T-(S-)evaluators are established. (English) |
Keyword:
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Sugeno integral |
Keyword:
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fuzzy measure |
Keyword:
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comonotone functions |
Keyword:
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Chebyshev's inequality |
Keyword:
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t-norm; t-conorm |
Keyword:
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T-(S-)evaluators |
MSC:
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03E72 |
MSC:
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06A99 |
MSC:
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28E10 |
idZBL:
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Zbl 1188.28014 |
idMR:
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MR2666896 |
. |
Date available:
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2010-06-02T19:46:59Z |
Last updated:
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2013-09-21 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/140053 |
. |
Reference:
|
[1] H. Agahi and M. A. Yaghoobi: A Minkowski type inequality for fuzzy integrals.J. Uncertain Systems, in press. |
Reference:
|
[2] H. Agahi, R. Mesiar, and Y. Ouyang: General Minkowski type inequalities for Sugeno integrals.Fuzzy Sets and Systems 161 (2010), 708-715. MR 2578627 |
Reference:
|
[3] H. Agahi, R. Mesiar, and Y. Ouyang: New general extensions of Chebyshev type inequalities for Sugeno integrals.International Journal of Approximate Reasoning 51 (2009), 135-140. MR 2565211 |
Reference:
|
[4] P. Benvenuti, R. Mesiar, and D. Vivona: Monotone set functions-based integrals.In: Handbook of Measure Theory (E. Pap, ed.), Vol II, Elsevier, 2002, pp. 1329–1379. MR 1954643 |
Reference:
|
[5] S. Bodjanova and M. Kalina: T-evaluators and S-evaluators.Fuzzy Sets and Systems 160 (2009), 1965–1983. MR 2555004 |
Reference:
|
[6] A. Flores-Franulič and H. Román-Flores: A Chebyshev type inequality for fuzzy integrals.Appl. Math. Comput. 190 (2007), 1178–1184. MR 2339711 |
Reference:
|
[7] M. Grabisch, J.-L. Marichal, R. Mesiar, and E. Pap: Aggregation Functions.Cambridge University Press, Cambridge, 2009. MR 2538324 |
Reference:
|
[8] E. P. Klement, R. Mesiar, and E. Pap: Measure-based aggregation operators.Fuzzy Sets and Systems 142 (2004), 3–14. MR 2045339 |
Reference:
|
[9] E. P. Klement, R. Mesiar, and E. Pap: Triangular Norms, Trends in Logic.(Studia Logica Library, Vol. 8.) Kluwer Academic Publishers, Dodrecht 2000. MR 1790096 |
Reference:
|
[10] R. Mesiar and A. Mesiarová: Fuzzy integrals and linearity.Internat. J. Approx. Reason. 47 (2008), 352–358. MR 2410433 |
Reference:
|
[11] R. Mesiar and Y. Ouyang: General Chebyshev type inequalities for Sugeno integrals.Fuzzy Sets and Systems 160 (2009), 58–64. MR 2469431 |
Reference:
|
[12] Y. Ouyang and J. Fang: Sugeno integral of monotone functions based on Lebesgue measure.Comput. Math. Appl. 56 (2008), 367–374. MR 2442659 |
Reference:
|
[13] Y. Ouyang, J. Fang, and L. Wang: Fuzzy Chebyshev type inequality.Internat. J. Approx. Reason. 48 (2008), 829–835. MR 2437953 |
Reference:
|
[14] Y. Ouyang, R. Mesiar, and H. Agahi: An inequality related to Minkowski type for Sugeno integrals.Information Sciences, in press. |
Reference:
|
[15] Y. Ouyang and R. Mesiar: On the Chebyshev type inequality for seminormed fuzzy integral.Appl. Math. Lett. 22 (2009), 1810–1815. MR 2558545 |
Reference:
|
[16] Y. Ouyang and R. Mesiar: Sugeno integral and the comonotone commuting property.Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 17 (2009), 465–480. MR 2591398 |
Reference:
|
[17] Y. Ouyang, R. Mesiar, and J. Li: On the comonotonic-$\star $-property for Sugeno integral.Appl. Math. Comput. 211 (2009), 450–458. MR 2526043 |
Reference:
|
[18] E. Pap: Null-additive Set Functions.Kluwer Academic Publishers, Dordrecht 1995. Zbl 1003.28012, MR 1368630 |
Reference:
|
[19] D. Ralescu and G. Adams: The fuzzy integral.J. Math. Anal. Appl. 75 (1980), 562-570. MR 0581840 |
Reference:
|
[20] H. Román-Flores and Y. Chalco-Cano: H-continuity of fuzzy measures and set defuzzifincation.Fuzzy Sets and Systems 157(2006), 230–242. MR 2186225 |
Reference:
|
[21] H. Román-Flores and Y. Chalco-Cano: Sugeno integral and geometric inequalities.Internat. J. Uncertainty, Fuzziness and Knowledge-Based Systems 15 (2007), 1–11. MR 2298130 |
Reference:
|
[22] H. Román-Flores, A. Flores-Franulič, and Y. Chalco-Cano: The fuzzy integral for monotone functions.Appl. Math. Comput. 185 (2007), 492–498. MR 2297820 |
Reference:
|
[23] H. Román-Flores, A. Flores-Franulič, and Y. Chalco-Cano: A Jensen type inequality for fuzzy integrals.Inform. Scie. 177 (2007), 3192–3201. MR 2340853 |
Reference:
|
[24] P. Struk: Extremal fuzzy integrals.Soft Computing 10 (2006), 502–505. Zbl 1097.28013 |
Reference:
|
[25] M. Sugeno: Theory of Fuzzy Integrals and its Applications.Ph.D. Thesis. Tokyo Institute of Technology, 1974. |
Reference:
|
[26] Z. Wang and G. Klir: Fuzzy Measure Theory.Plenum Press, New York 1992. MR 1212086 |
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