JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 22-28.doi: 10.6040/j.issn.1671-9352.0.2015.634

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Inequalities of Hermite-Hadamard and Sandaor for fuzzy integral

LU Wei, SONG Xiao-qiu*, HUANG Lei-lei   

  1. College of Science, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
  • Received:2015-12-29 Online:2016-08-20 Published:2016-08-08

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Abstract: On the basis of the definitions of r-convex function and Orlicz-convex function, Sandors type inequality for fuzzy integrals upon r-convex function is proved. Hermite-Hadamard type inequality for fuzzy integrals based on Orlicz-convex function is investigated. Some examples are given to illustrate our theorems.

Key words: Orlicz-convex function, Sandors type inequality, r-convex function, Hermite-Hadamard type inequality

CLC Number: 

  • O159
[1] SUGENO M. Theory of fuzzy integrals and its applications[M]. Tokyo: Institute of Technology, 1974.
[2] WU Limin, SUN Jingbo, YE Xiqing. Hölder type inequality for Sugeno integrals [J]. Fuzzy Sets and Systems, 2010, 161(1):2337-2347.
[3] CABALLERO J, SADARANGANI K. Sandors inequality for Sugeno integrals[J]. Applied Mathematics and Computation, 2011, 218(5):1617-1622.
[4] CABALLERO J, SADARANGANI K. Hermite—Hadamard inequality for fuzzy integrals[J]. Applied Mathematics and Computation, 2009, 215(6):2134-2138.
[5] CABALLERO J, SADARANGANI K. A Cauchy-Schwarz type inequality for fuzzy integrals[J]. Non-Linear Analysis, 2010, 73(10):3329-3335.
[6] AGAHI H, MESIAR R, OUYANG Yao. General Minkowski type inequalities for Sugeno integrals[J]. Fuzzy Sets and Systems, 2010, 161(5):708-715.
[7] OUYANG Yao, FANG Jinxuan, WANG Lishe. Fuzzy Chebyshev type inequality[J]. International Journal of Approximate Reasoning, 2008, 48(3):829-835.
[8] SHILKRET N. Maxitive measure and integration[J]. Indagationes Mathematicae(Proceedings), 1971, 33:109-116.
[9] SONG Xiaoqiu, PAN Zhi. Fuzzy algebra in triangular norm system[J]. Fuzzy Sets and Systems, 1998, 93(3):331-335.
[10] LI Dongqing, SONG Xiaoqiu, YUE Tian, et al. Generalization of the Lyapunov type inequalities for pseudo-integrals[J]. Applied Mathematics and Computation, 2014, 241:64-69.
[11] LI Dongqing, SONG Xiaoqiu, YUE Tian. Hermite-Hadamard type inequality for Sugeno integrals[J]. Applied Mathematics and Computation, 2014, 237:632-638.
[12] 杨秀丽,宋晓秋, 卢威. 基于模糊积分的Sandors不等式[J]. 南京大学学报(数学半年刊), 2015, 32(2):144-156. YANG Xiuli, SONG Xiaoqiu, LU Wei. Sandors type inequality for fuzzy integrals[J]. Journal of Nanjing University(Mathematical Biquarterly), 2015, 32(2):144-156.
[13] SONG Yazhi, SONG Xiaoqiu, LI Dongqing, et al. Berwald type inequality for extremal universal integral based on(a,m)-concave functions[J]. Journal of Mathematical Inequalities, 2015, 9(1):1-15.
[14] RALESCU D, ADAMS G. The fuzzy integral[J]. Journal of Mathematical Analysis and Applications, 1980, 75(2):562-570.
[15] PAP E. Null-additive set functions[M]. Dordrecht: Kluwer Academic, 1995.
[16] WANG Zhenyuan, GEORGE J. KLIR. Generalized measure theory[M]. New York: Springer Verlag, 2008.
[17] PINHEIRO I M R. H-H inequality for s-convex functions[J]. International Journal of Pure and Applied Mathematics, 2008, 44(4):563-579
[18] SANDOR J. On the identric and logarithmic means[J]. Advances in Biochemical Engineering, 1990, 40(1):261-270.
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