Document Type : Research Paper
Authors
Department of Mathematics, University of Maragheh, P. O. Box 55136-553, Maragheh, Iran.
Abstract
In this paper, we investigate Godunova type inequality for Sugeno integrals in two cases. At the first case, we suppose that the inner integral is the Riemann integral and the remaining two integrals are of Sugeno type. At the second case, all the integrals are assumed Sugeno integrals. We present several examples to illustrate validity of our results.
Keywords
[1] H. Agahia, R. Mesiar, Y. Ouyang, E. Pape and M. Strboja, Berwald type inequality for Sugeno integral, Appl. Math. Comput., 217 (2010), pp. 4100-4108.
[2] H. Agahia, R. Mesiar, Y. Ouyang, E. Pape and M. Strboja, On Stolarsky inequality for Sugeno and Choquet integrals, Inf. Sci., 266 (2014), pp. 134-139.
[3] B. Daraby and L. Arabi, Related Fritz Carlson type inequality for Sugeno integrals, Soft Comput., 17 (2013), pp. 1745-1750.
[4] B. Daraby, A. Shafiloo and A. Rahimi, Generalizations of the Feng Qi type inequality for pseudo-integral, Gazi Univ. J. Sci., 28(4) (2015), pp. 695-702.
[5] B. Daraby, H. Ghazanfary Asll and I. Sadeqi, General related inequalities to Carlson-type inequality for the Sugeno integral, Appl. Math. Comput., 305 (2017), pp. 323-329.
[6] I. Sadeqi, H. Ghazanfary Asll and B. Daraby, Gauss type inequality for Sugeno integral, J. Adv. Math. Stud., 10 (2) (2017), pp. 167-173.
[7] B. Daraby, General Related Jensen type Inequalities for fuzzy integrals, TWMS J. Pure Appl. Math., 8 (1) (2018), pp. 1-7.
[8] B. Daraby, A. Shafiloo and A. Rahimi, General Lyapunov type inequality for Sugeno integral, J. Adv. Math. Stud., 11 (1) (2018), pp. 37-46.
[9] B. Daraby, R. Mesiar, F. Rostampour and A. Rahimi, Related Thunsdorff type and Frank-Pick type inequalities for Sugeno integral, Appl. Math. Comput., 414 (2022), 126683.
[10] A. Flores-Franulic and H. Roman-Flores, A Chebyshev type inequality for fuzzy integrals, Appl. Math. Comput., 190 (2007), pp. 1178-1184.
[11] A. Flores-Franulic, H. Roman-Flores and Y. Chalco-Cano, Markov type inequalities for fuzzy integrals, Appl. Math. Comput., 207 (2009), pp. 242-247.
[12] M. Grabisch, Set functions, Games and Capacities in Decision Making, Springer, 2016.
[13] E.K. Godunova, Inequalities with convex functions, American Mathematical Society Translations: Series 2, 88 (1970), pp. 57-66.
[14] E. Pap, Null-additive Set Functions, Kluwer, Dordrecht, 1995.
[15] E. Pap, Pseudo-additive measures and their applications, Handbook of Neasure Theory (Editor E. Pap), Volume II, Elsevier, North-Holland, (2002), pp. 1403-1465.
[16] E. Pap, M.Strboja, Generalization of integral inegrals based on nonadditive measures, Topics in Intelligent Engineering and Informations, Intelligent Systems: Models and Applications (Ed. E. Pap), Springer, (2013), pp. 3-22.
[17] D. Ralescu and G. Adams , The fuzzy integral, J. Math. Anal. Appl., 75 (1980), pp. 562-570.
[18] H. Roman-Flores and Y. Chalco-Cano, H-continuity of fuzzy measures and set defuzzification, Fuzzy Sets Syst., 157 (2006), pp. 230-242.
[19] H. Roman-Flores, A. Flores-Franulic and Y. Chalco-Cano, A Jensen type inequality for fuzzy integrals, Inf. Sci., 177 (2007),. pp. 3192-3201.
[20] H. Roman-Flores, A. Flores-Franulic, R. Bassanezi and M. Rojas-Medar, On the level-continuity of fuzzy integrals, Fuzzy Sets Syst., 80 (1996), pp. 339-344.
[21] M. Sugeno, Theory of Fuzzy Integrals and its Applications, (Ph. D. dissertation), Tokyo Institute of Technology, 1974.
[22] Z. Wang and G.J. Klir, Fuzzy Measure Theory, Plenum Press, New York, 1992.
[23] L. Xiao and H. Yue, A Godunova-type inequality for fuzzy integrals, International Conference on Intelligent Computation Technology and Automation, 2010.
)
