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Keywords:
Sugeno integral; fuzzy measure; comonotone functions; Chebyshev's inequality; t-norm; t-conorm; T-(S-)evaluators
Sugeno integral; fuzzy measure; comonotone functions; Chebyshev's inequality; t-norm; t-conorm; T-(S-)evaluators
Summary:
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.
References:
[1] H. Agahi and M. A. Yaghoobi: A Minkowski type inequality for fuzzy integrals. J. Uncertain Systems, in press.
[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
[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
[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
[5] S. Bodjanova and M. Kalina: T-evaluators and S-evaluators. Fuzzy Sets and Systems 160 (2009), 1965–1983. MR 2555004
[6] A. Flores-Franulič and H. Román-Flores: A Chebyshev type inequality for fuzzy integrals. Appl. Math. Comput. 190 (2007), 1178–1184. MR 2339711
[7] M. Grabisch, J.-L. Marichal, R. Mesiar, and E. Pap: Aggregation Functions. Cambridge University Press, Cambridge, 2009. MR 2538324
[8] E. P. Klement, R. Mesiar, and E. Pap: Measure-based aggregation operators. Fuzzy Sets and Systems 142 (2004), 3–14. MR 2045339
[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
[10] R. Mesiar and A. Mesiarová: Fuzzy integrals and linearity. Internat. J. Approx. Reason. 47 (2008), 352–358. MR 2410433
[11] R. Mesiar and Y. Ouyang: General Chebyshev type inequalities for Sugeno integrals. Fuzzy Sets and Systems 160 (2009), 58–64. MR 2469431
[12] Y. Ouyang and J. Fang: Sugeno integral of monotone functions based on Lebesgue measure. Comput. Math. Appl. 56 (2008), 367–374. MR 2442659
[13] Y. Ouyang, J. Fang, and L. Wang: Fuzzy Chebyshev type inequality. Internat. J. Approx. Reason. 48 (2008), 829–835. MR 2437953
[14] Y. Ouyang, R. Mesiar, and H. Agahi: An inequality related to Minkowski type for Sugeno integrals. Information Sciences, in press.
[15] Y. Ouyang and R. Mesiar: On the Chebyshev type inequality for seminormed fuzzy integral. Appl. Math. Lett. 22 (2009), 1810–1815. MR 2558545
[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
[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
[18] E. Pap: Null-additive Set Functions. Kluwer Academic Publishers, Dordrecht 1995. MR 1368630 | Zbl 1003.28012
[19] D. Ralescu and G. Adams: The fuzzy integral. J. Math. Anal. Appl. 75 (1980), 562-570. MR 0581840
[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
[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
[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
[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
[24] P. Struk: Extremal fuzzy integrals. Soft Computing 10 (2006), 502–505. Zbl 1097.28013
[25] M. Sugeno: Theory of Fuzzy Integrals and its Applications. Ph.D. Thesis. Tokyo Institute of Technology, 1974.
[26] Z. Wang and G. Klir: Fuzzy Measure Theory. Plenum Press, New York 1992. MR 1212086
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