Hermite-Hadamard Type Fuzzy Inequalities based on s-Convex Function in the Second Sense
Mathematics Letters
Volume 3, Issue 6, December 2017, Pages: 77-82
Received: Oct. 27, 2017; Accepted: Nov. 14, 2017; Published: Dec. 5, 2017
Views 1676      Downloads 141
Author
Lanping Li, School of Mathematics and Statistics, Hunan University of Finance and Economics, Changsha, China
Article Tools
Follow on us
Abstract
Integral inequalities have important applications in propability and engineering field. Sugeno integral is an important fuzzy integral in fuzzy theory, which has many applications in various fields. The object of this paper is to develop some new integral inequalities for Sugeno integral. Based on classical Hermite-Hadamard type inequality, this paper intends to extend it for the Sugeno integral. Some new Hermite-Hadamard type inequalities are derived for Sugeno integral based on s-convex function in the second sense. An example is used to illustrate the effectiveness of the new inequalities.
Keywords
Fuzzy Integral, Sugeno Integral, Herimite-Hadamard Inequality, s-Convex Function
To cite this article
Lanping Li, Hermite-Hadamard Type Fuzzy Inequalities based on s-Convex Function in the Second Sense, Mathematics Letters. Vol. 3, No. 6, 2017, pp. 77-82. doi: 10.11648/j.ml.20170306.14
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
Wu H C. Fuzzy Bayesian estimation on lifetime data [J]. Computational Statistics, 2004, 19(4): 613.
[2]
Dubois D, Prade H, Esteva F, et al. Fuzzy set modelling in case-based reasoning [J]. International Journal of Intelligent Systems, 2015, 13(4): 345-373.
[3]
Setz S, Semling M, Mülhaupt R. Fuzzy set approach for fitting a continuous response surface in adhesion formulation[J]. Journal of Chemometrics, 2015, 11(5): 403-418.
[4]
Dalman H, Güzel N, Sivri M. A fuzzy set-based approach to multi-objective multi-item solid transportation problem under uncertainty [J]. International Journal of Fuzzy Systems, 2016, 18(4): 716-729.
[5]
Wang W, Liu X. Fuzzy forecasting based on automatic clustering and axiomatic fuzzy set classification [J]. Information Sciences, 2015, 294(294): 78-94.
[6]
Liu C, Zuo X. A study on dynamic evaluation of urban integrated natural disaster risk based on vague set and information axiom [J]. Natural Hazards, 2015, 78(3): 1501-1516.
[7]
Wang L, Yu L, Qiao N, et al. Analysis and Simulation of Geomagnetic Map Suitability Based on Vague Set [J]. Journal of Navigation, 2016, 69(5): 1114-1124.
[8]
Chen T Y. The inclusion-based TOPSIS method with interval-valued intuitionistic fuzzy sets for multiple criteria group decision making [J]. Applied Soft Computing, 2015, 26: 57-73.
[9]
Dong J, Wan S. A new method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers [J]. Kybernetes, 2016, 45(1): 158-180.
[10]
Zhang X, Xu Z. Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making [J]. Applied Soft Computing, 2015, 26(26): 42-56.
[11]
Meng F, Chen X. Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures [J]. Cognitive Computation, 2015, 7(4): 445-463.
[12]
Meng F, Wang C, Chen X, et al. Correlation coefficients of interval-valued hesitant fuzzy sets and their application based on the Shapley function [J]. International Journal of Intelligent Systems, 2016, 31(1): 17-43.
[13]
Abbaszadeh S, Gordji M E, Pap E, et al. Jensen-type inequalities for Sugeno integral [J]. Information Sciences, 2016, 376: 148-157.
[14]
Zhang X, Zheng Y. Linguistic quantifiers modeled by interval-valued intuitionistic Sugeno integrals [J]. Journal of Intelligent & Fuzzy Systems, 2015, 29(2): 583-592.
[15]
Yager R R, Alajlan N. Sugeno integral with possibilistic inputs with application to multi-criteria decision making[J]. International Journal of Intelligent Systems, 2016, 31(8):813-826.
[16]
Pap E. Theory and applications of non-additive measures and corresponding integrals [J]. Lecture Notes in Computer Science, 2015, 8234: 1-10.
[17]
Wang J, Li X, Zhou Y. Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals via s-convex functions and applications to special means [J]. Filomat, 2016, 30(5): 1143-1150.
[18]
Sarikaya M Z, Kiris M E. Some new inequalities of hermite-hadamard type for s-convex functions [J]. Miskolc Mathematical Notes, 2015, 16(1): 491-501.
[19]
Latif M A. On Some new inequalities of Hermite–Hadamard type for functions whose derivatives are s-convex in the decond sense in the absolute value [J]. Ukrainian Mathematical Journal, 2015, 67(10): 1-20.
[20]
Hosseini M, Babakhani A, Agahi H, et al. On pseudo-fractional integral inequalities related to Hermite–Hadamard type [J]. Soft Computing, 2016, 20(7): 2521-2529.
[21]
Román-Flores H, Flores-Franulic A, Chalco-Cano Y. The fuzzy integral for monotone functions. Applied Mathematics & Computation, 2007, 185(1): 492-498.
[22]
Turhan S, Bekar N O, Akdemir H G. Hermite-Hadamard Type Inequality for Log-convex Functions via Sugeno Integrals[J]. Mathematics, 2015.
[23]
Caballero J, Sadarangani K. Hermite–Hadamard inequality for fuzzy integrals[J]. Applied Mathematics & Computation, 2009, 215(6): 2134-2138.
[24]
Li D Q, Song X Q, Yue T. Hermite–Hadamard type inequality for Sugeno integrals[J]. Applied Mathematics & Computation, 2014, 237(3): 632-638.
[25]
Abbaszadeh S, Eshaghi M. A Hadamard-type inequality for fuzzy integrals based on r-convex functions [J]. Soft Computing, 2016, 20(8), 3117-3124.
[26]
Latif M A, Irshad W, Mushtaq M. Hermite-Hadamardtypeinequalitiesfor m-convex and (a,m)-convex functions for fuzzy integrals [J]. Journal of Computational Analysis & Applications, 2018, 24(3): 497-506.
[27]
Hudzik H, Maligranda L. Some remarks on s -convex functions [J]. Aequationes Mathematicae, 1994, 48(1): 100-111.
[28]
Z. Wang, G. Klir, Fuzzy Measure Theory [M], Plenum, New York, 1992.
[29]
Ren H, Wang G, Luo L. Sandor type fuzzy inequality based on the (s,m)-convex function in the second sense [J]. Symmetry, 2017, 9(9): 181-190.
[30]
Guessab A, Schmeisser G. Sharp integral inequalities of the Hermite–Hadamard Type [J]. Journal of Approximation Theory, 2002, 115(2): 260-288.
[31]
Wang W, ˙Iscan I, Zhou H. Fractional integral inequalities of Hermite-Hadamard type for m-HH convex functions with applications [J]. Advanced Studies in Contemporary Mathematics, 2016, 26(3): 501-512.
[32]
Latif M A, Dragomir S S. New integral inequalities of hermite-hadamard type for n-times differentiable s-logarithmically convex functions with applications [J]. Miskolc Mathematical Notes, 2015, 16(1): 339-342.
[33]
Wang S H, Shi X T. Hermite-Hadamard type inequalities for n-time differentiable and GA-convex functions with applications to means [J]. 2016, 4(1): 15-22.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186