Further development of chebyshev type inequalities for sugeno integrals and t-(s-)evaluators

Kybernetika

Volumn 46, Issue 1, 2010, Pages 83-95

  Hamzeh, Agahi ^a   Radko, Mesiar ^b,c   Yao, Ouyang ^d  

^a SHAHID BAHONAR UNIVERSITY OF KERMAN   (Iran)

^b SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

^c INSTITUTE OF INFORMATION THEORY AND AUTOMATION   (Czech Republic)

^d HUZHOU UNIVERSITY   (China)

Author keywords

Chebyshev's inequality; Comonotone functions; Fuzzy measure; Sugeno integral; T (S )evaluators; T conorm; T norm

Indexed keywords

EID: 77953558735     PISSN: 00235954     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

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.
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.
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'.
5. S. Bodjanova and M. Kalina: T-evaluators and S-evaluators. Fuzzy Sets and Systems 160 (2009), 1965-1983.
6. A. Flores-Franulič and H. Román-Flores: A Chebyshev type inequality for fuzzy integrals. Appl. Math. Comput. 190 (2007), 1178-1184.
7. M. Grabisch, J.-L. Marichal, R. Mesiar, and E. Pap: Aggregation Functions. Cambridge University Press, Cambridge, 2009.
8. E. P. Klement, R. Mesiar, and E. Pap: Measure-based aggregation operators. Fuzzy Sets and Systems 142 (2004), 3-14.
9. E. P. Klement, R. Mesiar, and E. Pap: Triangular Norms, Trends in Logic. (Studia Logica Library, Vol. 8.) Kluwer Academic Publishers, Dodrecht 2000.
10. R. Mesiar and A. Mesiarová: Fuzzy integrals and linearity. Internat. J. Approx. Reason. 47(2008), 352-358.
11. R. Mesiar and Y. Ouyang: General Chebyshev type inequalities for Sugeno integrals. Fuzzy Sets and Systems 160 (2009), 58-64.
12. Y. Ouyang and J. Fang: Sugeno integral of monotone functions based on Lebesgue measure. Comput. Math. Appl. 56 (2008), 367-374.
13. Y. Ouyang, J. Fang, and L. Wang: Fuzzy Chebyshev type inequality. Internat. J. Approx. Reason. 48 (2008), 829-835.
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.
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.
17. Y. Ouyang, R. Mesiar, and J. Li: On the comonotonic-*-property for Sugeno integral. Appl. Math. Comput. 211 (2009), 450-458.
18. E. Pap: Null-additive Set Functions. Kluwer Academic Publishers, Dordrecht 1995.
19. D. Ralescu and G. Adams: The fuzzy integral. J. Math. Anal. Appl. 75 (1980), 562-570.
20. H. Román-Flores and Y. Chalco-Cano: H-continuity of fuzzy measures and set defuzzifincation. Fuzzy Sets and Systems 157 (2006), 230-242.
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.
22. H. Román-Flores, A. Flores-Franulič, and Y. Chalco-Cano: The fuzzy integral for monotone functions. Appl. Math. Comput. 185 (2007), 492-498.
23. H. Román-Flores, A. Flores-Franulič, and Y. Chalco-Cano: A Jensen type inequality for fuzzy integrals. Inform. Scie. 177(2007), 3192-3201.
24. P. Struk: Extremal fuzzy integrals. Soft Computing 10 (2006), 502-505.
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.