Sandor Type Inequalities for Sugeno Integral Based on s-Convex Function in the Second Sense
Mathematics Letters
Volume 4, Issue 1, March 2018, Pages: 14-19
Received: Mar. 1, 2018; Accepted: Mar. 27, 2018; Published: May 4, 2018
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Author
Lanping Li, School of Mathematics and Statistics, Hunan University of Finance and Economics, Changsha, China
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Abstract
Integral inequalities play important roles in the fields of measure theory, probability theory and control theory. The aim of this paper is to develop some fuzzy integral inequalities. Sugeno integral is one of the most important fuzzy integrals, which has many applications in various fields. This paper constructs some new Sandor type inequalities for the Sugeno integral based on s-convex function in the second sense. Numerical examples are used to illustrate the effectiveness and practicality of the new inequalities.
Keywords
Fuzzy Integral, Sugeno Integral, Sandor Inequality, s-Convex Function
To cite this article
Lanping Li, Sandor Type Inequalities for Sugeno Integral Based on s-Convex Function in the Second Sense, Mathematics Letters. Vol. 4, No. 1, 2018, pp. 14-19. doi: 10.11648/j.ml.20180401.13
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Copyright © 2018 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]
Fan B, Tsang E C C, Xu W, et al. Double-quantitative rough fuzzy set based decisions [J]. Information Sciences, 2017, 378 (C):264-281.
[4]
Ezghari S, Zahi A, Zenkouar K. A new nearest neighbor classification method based on fuzzy set theory and aggregation operators [J]. Expert Systems with Applications, 2017, 80:58-74.
[5]
Chen S M, Cheng S H, Chiou C H. Fuzzy multiattribute group decision making based on intuitionistic fuzzy sets and evidential reasoning methodology [J]. Information Fusion, 2016, 27:215-227.
[6]
Ye Y, Liang L, Cao Y, et al. Optimization and sorting method of the engineering layout scheme for interconnected river system network based on vague set and cloud model [J]. System Engineering Theory & Practice, 2017, 37 (7):1926-1936.
[7]
Zhu B, Xu Z, Xu J. Deriving a ranking from hesitant fuzzy preference relations under group decision making [J]. IEEE Transactions on Cybernetics, 2017, 44 (8):1328-1337.
[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]
Saito K, Notomi K, Hashimoto H and Saito M. Application of the Sugeno integral with λ-fuzzy measures to endoscopic diagnosis. Biomedical Fuzzy & Human Sciences the Official Journal of the Biomedical Fuzzy Systems Association, 2017, 9 (1): 11-16.
[11]
Melin P, Mendoza O, Castillo O. Face recognition with an improved interval type-2 fuzzy logic Sugeno integral and modular neural networks [J]. IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 2011, 41 (5):1001-1012.
[12]
Daraby B, Asll H G, Sadeqi I. General related inequalities to Carlson-type inequality for the Sugeno integral [J]. Applied Mathematics & Computation, 2017, 305:323-329.
[13]
Agahi H, Mesiar R, Ouyang Y, et al. Berwald type inequality for Sugeno integral [J]. Applied Mathematics & Computation, 2010, 217 (8):4100-4108.
[14]
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.
[15]
Caballero J, Sadarangani K. Hermite–Hadamard inequality for fuzzy integrals [J]. Applied Mathematics & Computation, 2009, 215 (6):2134-2138.
[16]
Abbaszadeh S, Gordji M E, Pap E, et al. Jensen-type inequalities for Sugeno integral [J]. Information Sciences, 2016, 376:148-157.
[17]
Abbaszadeh S, Eshaghi M. A Hadamard-type inequality for fuzzy integrals based on r -convex functions [J]. Soft Computing, 2016, 20 (8):3117-3124.
[18]
Agahi H, Babakhani A, Mesiar R. Pseudo-fractional integral inequality of Chebyshev type [J]. Information Sciences, 2015, 301 (C):161-168.
[19]
Alzer H, Man K K. A Hardy–Littlewood integral inequality on finite intervals with a concave weight [J]. Periodica Mathematica Hungarica, 2015, 71 (2):184-192.
[20]
Abbaszadeh S, Eshaghi M. A Hadamard-type inequality for fuzzy integrals based on r-convex functions [J]. Soft Computing, 2016, 20 (8), 3117-3124.
[21]
Latif M A, Irshad W, Mushtaq M. Hermite-Hadamard type inequalities for m-convex and (a, m)-convex functions for fuzzy integrals [J]. Journal of Computational Analysis & Applications, 2018, 24 (3):497-506.
[22]
Sándor J. On the identric and logarithmic means. Aequationes Mathematicae, 1990, 40 (1):261-270.
[23]
Caballero J, Sadarangani K. Sandor's inequality for Sugeno integrals [J]. Applied Mathematics & Computation, 2011, 218 (5):1617-1622.
[24]
Li D Q, Cheng Y H, Wang X S. Sandor type inequalities for Sugeno integral with respect to general (α, m, r) -convex functions [J]. Journal of Function Spaces, 2015, 2015 (37):1-13.
[25]
Yang X L, Song X Q, Lu W. Sandor’s type inequality for fuzzy integrals [J]. Journal of Nanjing University, 2015, 32 (2):144-156
[26]
Hudzik H, Maligranda L. Some remarks on s-convex functions [J]. Aequationes Mathematicae, 1994, 48 (1):100-111.
[27]
Kunt M. On New İnequalities of Hermite-Hadamard-Fejér Type for Harmonically s-Convex Functions via Fractional İntegrals [J]. Applied Mathematics & Computation, 2016, 259 (1):875-881.
[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]
Lu W, Song X Q, Huang L L. Inequalities of Hermite-Hadamard and Sandaor for fuzzy integral [J]. Journal of Shandong University (Natural Science), 2016, 51 (8): 22-28.
[31]
Yang Y Y, Qian W M. Two optimal inequalities related to the Sandor-Yang type mean and one-parameter mean [J]. Communications in Mathematical Research, 2016, 32 (4):352-358.
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