Barnes−Godunova−Levin Type Inequalities for Generalized Sugeno Integral

Document Type : Original Scientific Paper

Authors

Department of Mathematics, Payame Noor Universtiy, PO BOX 19395-3697 Tehran, Iran

Abstract

‎This article will prove the Barnes–Godunova–Levin (B-G-L) type inequalities for generalized Sugeno integrals‎. ‎Also‎, ‎we use some techniques and properties of concave functions to prove theorems and to obtain new results‎. ‎We will present a more robust version of the B-G-L type inequality for the operator $\star$‎.

Keywords

Main Subjects


[1] N. Shilkret, Maxitive measure and integration, Indag. Math. 74 (1971) 109 −
116.
[2] F. S. Garcĺa and P. G. Álvarez, Two families of fuzzy integrals, Fuzzy Sets
Syst. 18 (1) (1986) 67 − 81, https://doi.org/10.1016/0165-0114(86)90028-X.
[3] J. Borzová-Molnárová, L. Halčinová and O. Hutnĺk, The smallest semicopulabased universal integrals I: properties and characterizations, Fuzzy Sets Syst.
271 (15) (2015) 1 − 17, https://doi.org/10.1016/j.fss.2014.09.023.
[4] D. Dubois, H. Prade, A. Rico and B. Teheux, Generalized qualitative Sugeno integrals, Inf. Sci. 415-416 (2017) 429 − 445,
https://doi.org/10.1016/j.ins.2017.05.037.
[5] D. Dubois, H. Prade, A. Rico and B. Teheux, Generalized Sugeno Integrals,
16th International Conference on Information Processing and Management
of Uncertainty in Knowledge-Based Systems (2016) Eindhoven, Netherlands,
363 − 374.
[6] M. Sugeno, Theory of Fuzzy Integrals and its Applications, Ph.D. thesis, Tokyo
Institute of Technology, 1974.
[7] H. Agahi, H. Román-Flores and A. Flores-Franulič, General
Barnes–Godunova–Levin type inequalities for Sugeno integral, Inf. Sci.
181 (6) (2011) 1072 − 1079, https://doi.org/10.1016/j.ins.2010.11.029.
[8] S. Abbaszadeh, A. Ebadian and M. Jaddi, Hölder type integral inequalities
with different pseudo-operations, Asian-Eur. J. Math. 12 (2019) p. 1950032,
https://doi.org/10.1142/S1793557119500323.
[9] D. Ralescu and G. Adams, The fuzzy integral, J. Math. Anal. Appl. 75 (2)
(1980) 562 − 570, https://doi.org/10.1016/0022-247X(80)90101-8.
[10] Z. Wang and G. J. Klir, Generalized Measure Theory, Springer New York,
NY, 2009.
[11] E. Pap, Null-additive Set Functions, Springer Dordrecht, 1995.
[12] R. Mesiar and A. Mesiarová, Fuzzy integrals and linearity, Int. J. Approx.
Reason., 47 (3) (2008) 352 − 358, https://doi.org/10.1016/j.ijar.2007.05.013.
[13] Z. Wang and G. J. Klir, Fuzzy Measures Theory, Springer New York, NY,
1992.
[14] M. E. Cattaneo, Statistical Decisions Based Directly on the Likelihood
Function, Ph.D. thesis, ETH Zorich, 2007, https://doi.org/10.3929/ethz-a-005463829.
[15] R. Mesiar and Y. Ouyang, General Chebyshev type inequalities
for Sugeno integrals, Fuzzy Sets Syst. 160 (1) (2009) 58 − 64,
https://doi.org/10.1016/j.fss.2008.04.002.
[16] Y. Ouyang, R. Mesiar and J. Li, On the comonotonic-H-property
for Sugeno integral, Appl. Math. Comput. 211 (2) (2009) 450 − 458,
https://doi.org/10.1016/j.amc.2009.01.067.
[17] E. P. Klement, Construction of fuzzy σ-algebras using triangular norms, J.
Math. Anal. Appl. 85 (2) (1982) 543 − 565, https://doi.org/10.1016/0022-
247X(82)90015-4.
[18] E. P. Klement, R. Mesiar and E. Pap, Triangular norms, Springer Dordrecht
2000.
[19] J. Pečarić, F. Proschan and Y. L. Tong, Partial Orderings and Statistical
Applications; Academic Press, New York, NY, USA, 1992.
[20] T. K. Pogány, On an open problem of F. Qi, J. Inequal. Pure Appl. Math. 3
(4) (2002).