Fuzzy Chebyshev type inequality

International Journal of Approximate Reasoning

Volumn 48, Issue 3, 2008, Pages 829-835

  Ouyang, Yao ^a,b   Fang, Jinxuan ^b   Wang, Lishe ^a  

^a HUZHOU UNIVERSITY   (China)

^b NANJING NORMAL UNIVERSITY   (China)

Author keywords

Chebyshev's inequality; Monotone function; Stolarsky's inequality; Sugeno integral

Indexed keywords

INTEGRAL EQUATIONS;

APPLIED MATHEMATICS; CHEBYSHEV; ELSEVIER (CO); FUZZY INTEGRALS; SUGENO INTEGRALS;

FUZZY LOGIC;

EID: 45049085664     PISSN: 0888613X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijar.2008.01.004     Document Type: Article

References (17)

1. Anastassiou G. Chebyshev-Grüss type inequalities via Euler type and Fink identities. Mathematical and Computer Modelling 45 (2007) 1189-1200
2. N over spherical shells and balls. Applied Mathematics Letters (2007) 10.1016/j.aml.2007.02.015
3. Flores-Franulič A., and Román-Flores H. A Chebyshev type inequality for fuzzy integrals. Applied Mathematics and Computation 190 (2007) 1178-1184
4. Flores-Franulič A., Román-Flores H., and Chalco-Cano Y. A note on fuzzy integral inequality of Stolarsky type. Applied Mathematics and Computation (2007) 10.1016/j.amc.2007.05.032
5. Li J., and Yasuda M. On Egoroff's theorems on finite monotone non-additive measure space. Fuzzy Sets and Systems 153 (2005) 71-78
6. Mesiar R., and Mesiarová A. Fuzzy integrals and linearity. International Journal of Approximate Reasoning (2007) 10.1016/j.ijar.2007.05.013
7. Mesiar R., Mesiarová-Zemánková A., and Valášková L. Basic generated universal fuzzy measures. International Journal of Approximate Reasoning (2006) 10.1016/j.ijar.2006.12.012
8. Murofushi T., and Sugeno M. A theory of fuzzy measures: representations, the Choquet integral, and null sets. Journal of Mathematical Analysis and Applications 159 (1991) 532-549
9. Y. Ouyang, J. Fang, Sugeno integral of monotone functions based on Lebesgue measure, submitted for publication.
10. Pap E. Null-additive Set Functions (1995), Kluwer, Dordrecht
11. Ralescu D., and Adams G. The fuzzy integral. Journal of Mathematics Analysis and Application 75 (1980) 562-570
12. Román-Flores H., Flores-Franulič A., and Chalco-Cano Y. The fuzzy integral for monotone functions. Applied Mathematics and Computation 185 (2007) 492-498
13. Román-Flores H., Flores-Franulič A., and Chalco-Cano Y. A Jensen type inequality for fuzzy integrals. Information Sciences 177 (2007) 3192-3201
14. M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Dissertation, Takyo Institute of Technology, 1974.
15. Wagener A. Chebyshev's Algebraic Inequality and comparative statics under uncertainty. Mathematical Social Sciences 52 (2006) 217-221
16. Wang Z., and Klir G.J. Fuzzy Measure Theory (1992), Plenum Press, New York
17. Wen J., and Wang W. Chebyshev type inequalities involving permanents and their applications. Linear Algebra and its Applications 422 (2007) 295-303