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The Sugeno fuzzy integral of concave functions | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 16، دوره 16، شماره 2، خرداد و تیر 2019، صفحه 197-204 اصل مقاله (213.88 K) | ||
نوع مقاله: Original Manuscript | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2019.4552 | ||
نویسندگان | ||
Madjid Eshaghi1؛ Sadegh Abbaszadeh2؛ Choonkil Park ![]() ![]() | ||
1Faculty of Mathematics, Statistics and Computer Sciences, Semnan University | ||
2Department of Computer Science, Paderborn University, Paderborn, Germany | ||
3Hanyang University | ||
چکیده | ||
The fuzzy integrals are a kind of fuzzy measures acting on fuzzy sets. They can be viewed as an average membership value of fuzzy sets. The value of the fuzzy integral in a decision making environment where uncertainty is present has been well established. Most of the integral inequalities studied in the fuzzy integration context normally consider conditions such as monotonicity or comonotonicity. In this paper, we are trying to extend the fuzzy integrals to the concept of concavity. It is shown that the Hermite-Hadamard integral inequality for concave functions is not satisfied in the case of fuzzy integrals. We propose upper and lower bounds on the fuzzy integral of concave functions. We present a geometric interpretation and some examples in the framework of the Lebesgue measure to illustrate the results. | ||
کلیدواژهها | ||
Sugeno fuzzy integral؛ Hermite-Hadamard inequality؛ Concave function؛ Supergradient | ||
مراجع | ||
[1] S. Abbaszadeh, A. Ebadian, Nonlinear integrals and Hadamard-type inequalities, Soft Computing, 22 (2018), 2843- 2849. [2] S. Abbaszade, M. Eshaghi Gordji, A Hadamard type inequality for fuzzy integrals based on r-convex functions, Soft Computing, 20 (2016), 3117-3124. [3] S. Abbaszadeh, M. Eshaghi Gordji, M. de la Sen, The Sugeno fuzzy integral of log-convex functions, Journal of Inequalities and Applications, 2015 (2015), 362. [4] S. Abbaszadeh, M. Eshaghi Gordji, E. Pap, A. Szak´al, Jensen-type inequalities for Sugeno integral, Information Sciences, 376 (2017), 148-157. [5] H. Agahi, R. Mesiar, Y. Ouyang, General Minkowski type inequalities for Sugeno integrals, Fuzzy Sets and Systems, 161 (2010), 708-715. [6] H. Agahi, R. Mesiar, Y. Ouyang, E. Pap, M. Strboja, General Chebyshev type inequalities for universal integral, Information Sciences, 187 (2012), 171-178. [7] H. Agahi, H. Rom´an-Flores, A. Flores-Franuliˇc, General Barnes-Godunova-Levin type inequalities for Sugeno integral, Information Sciences, 181 (2011), 1072-1079. [8] J. Caballero, K. Sadarangani, Hermite-Hadamard inequality for fuzzy integrals, Applied Mathematics and Computation, 215 (2009), 2134-2138. [9] J. Caballero, K. Sadarangani, A Cauchy-Schwarz type inequality for fuzzy integrals, Nonlinear Analysis, 73 (2010), 3329-3335. [10] J. Caballero, K. Sadarangani, Chebyshev inequality for Sugeno integrals, Fuzzy Sets and Systems, 161 (2010), 1480-1487. [11] J. Caballero, K. Sadarangani, Fritz Carlson’s inequality for fuzzy integrals, Computers & Mathematics with Applications, 59 (2010), 2763-2767. [12] J. Caballero, K. Sadarangani, Sandor’s inequality for Sugeno integrals, Applied Mathematics and Computation, 218 (2011), 1617-1622. [13] X. Chen, Z. Jing, G. Xiao, Nonlinear fusion for face recognition using fuzzy integral, Communications in Nonlinear Science and Numerical Simulation, 12 (2007), 823-831. [14] A. Croitoru, Fuzzy integral of measurable multifunctions, Iranian Journal of Fuzzy Systems, 9 (2012), 133-140. [15] A. Flores-Franuliˇc, H. Rom´an-Flores, A Chebyshev type inequality for fuzzy integrals, Applied Mathematics and Computation, 190(2) (2007), 1178-1184. [16] M. Kaluszka, A. Okolewski, M. Boczek, On Chebyshev type inequalities for generalized Sugeno integrals, Fuzzy Sets and Systems, 244 (2014), 51-62. [17] W. Lee, Evaluating and ranking energy performance of office buildings using fuzzy measure and fuzzy integral, Energy Conversion and Management, 51 (2010), 1970-203. [18] H. Liu, X. Wang, A. Kadir, Color image encryption using Choquet fuzzy integral and hyper chaotic system, Optik 124 (2013), 3527-3533. [19] J.M. Merig´o, M. Casanovas, Decision-making with distance measures and induced aggregation operators, Computers & Industrial Engineering, 60 (2011), 66-76. [20] J.M. Merig´o, M. Casanovas, Induced aggregation operators in the Euclidean distance and its application in financial decision making, Expert Systems with Applications, 38 (2011), 7603-7608. [21] H. Nemmour, Y. Chibani, Fuzzy integral to speed up support vector machines training for pattern classification, International Journal of Knowledge-Based and Intelligent Engineering, 14 (2010), 127-138. [22] D. Ralescu, G. Adams, The fuzzy integral, Journal of Mathematical Analysis and Applications, 75 (1980), 562-570. [23] R. T. Rockafellar, Convex analysis. Princeton Mathematical Series, No. 28, Princeton University Press, Princeton, New Jersey, 1970. xviii+451 pp. [24] H. Rom´an-Flores, Y. Chalco-Cano, H-continuity of fuzzy measures and set defuzzifincation, Fuzzy Sets and Systems, 157 (2006), 230-242. [25] H. Rom´an-Flores, Y. Chalco-Cano, Sugeno integral and geometric inequalities, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 15 (2007), 1-11. [26] H. Rom´an-Flores, A. Flores-Franuliˇc, Y. Chalco-Cano, A Jensen type inequality for fuzzy integrals, Information Sciences, 177 (2007), 3192-3201. [27] H. Rom´an-Flores, A. Flores-Franuliˇc, Y. Chalco-Cano, The fuzzy integral for monotone functions, Applied Mathematics and Computation, 185 (2007), 492-498. [28] S.M. Seyedzadeh, B. Norouzi, S. Mirzakuchaki, RGB color image encryption based on Choquet fuzzy integral, Journal of Systems and Software, 97 (2014), 128-139. [29] P. Soda, G. Iannello, Aggregation of classifiers for staining pattern recognition in antinuclear autoantibodies analysis, IEEE Trans. Information Technology Biomedical, 13 (2009), 322-329. [30] A. Soria-Frisch, A new paradigm for fuzzy aggregation in multisensorial image processing, in Computational Intelligence. Theory and Applications, B. von Bernd Reusch (ed.), Lecture Notes in Computer Science 2206, Springer, Dortmund, 2001, pp. 59-67. [31] M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Dissertation, Tokyo Institute of Technology, 1974. [32] A. Szak´al, E. Pap, S. Abbaszadeh, M. Eshaghi Gordji, Jensen inequality with subdifferential for Sugeno integral, in Mexican International Conference on Artificial Intelligence, Springer, Cham, 2016, pp. 193-199. [33] Z. Wang, G. Klir, Fuzzy measure theory, Plenum Press, New York, 1992. x+354 pp. [34] L. Wu, J. Sun, X. Ye, L. Zhu, H¨older type inequality for Sugeno integral, Fuzzy Sets and Systems, 161 (2010), 2337-2347. [35] X. Zhang, Y. Zheng, Linguistic quantifiers modeled by interval-valued intuitionistic Sugeno integrals, Journal of Intelligent & Fuzzy Systems, 29 (2015), 583-592. | ||
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