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A Jensen type inequality for fuzzy integrals
Information Sciences, 2007The classical Jensen inequality for the Lebesgue integral is related to the convexity of discussed transforming functions, and it fails, in general, for the Sugeno integral. However, modifying the convexity by the boundedness by the identity as proposed in this paper, the authors show a version of Jensen's inequality for the Sugeno integral.
Heriberto Roman-Flores +1 more
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Hermite–Hadamard inequality for fuzzy integrals
Applied Mathematics and Computation, 20091 ...
Josefa Caballero, Kishin B. Sadarangani
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Robust stabilization of T-S fuzzy systems via improved integral inequality [PDF]
Soft Computing, 2021 Abstract This paper focuses on the state feedback control for uncertain nonlinear model, which can be denoted by Takagi - Sugeno (T-S) fuzzy model. We derive an improved integral inequality as a rearrangement of quadratic matrix-vector form combined with Jensen's inequality.
Dafik Dafik
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Steffensen type inequalities for fuzzy integrals
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marek Kaluszka, Michal Boczek
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A Chebyshev type inequality for fuzzy integrals
Applied Mathematics and Computation, 2007The classical Chebyshev's integral inequality \(\int_0^1 fg \,d\mu \geq(\int_0^1 f \,d\mu )(\int_0^1 g \,d\mu)\) for \(f, g: [0,1] \to [0, \infty )\) of the same monotonicity type is shown for the case, when the Lebesgue integral is replaced by the Sugeno integral. As a corollary an analogous result for finite number of fuctions is included.
A. Flores-Franulic +1 more
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A review on some fuzzy integral inequalities
2021Summary: In this paper, we introduce fuzzy measure and fuzzy integral concepts and express some of the fuzzy integral properties. The main purpose of this article is to reviewing of some important mathematical inequalities that have many applications in modeling mathematical problems.
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A Markov-type inequality for seminormed fuzzy integrals
Applied Mathematics and Computation, 20131 ...
Josefa Caballero, Kishin B. Sadarangani
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A Godunova-Type Inequality for Fuzzy Integrals
2010 International Conference on Intelligent Computation Technology and Automation, 2010In this paper, we prove a Godunova-type inequality for fuzzy Integrals. It yields important applications in the theory of fuzzy control.
Li Xiao, Hu Yue
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A Cauchy–Schwarz type inequality for fuzzy integrals
Nonlinear Analysis: Theory, Methods & Applications, 2010In this paper we prove a Cauchy-Schwarz type inequality for fuzzy integrals.
Caballero, J., Sadarangani, K.
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General Hardy type inequality for seminormed fuzzy integrals
Applied Mathematics and Computation, 2010The classical Hardy inequality \(\int_0^\infty (\frac Fx)^p\,dx< (\frac p{p-1})^p \int_0^\infty f^p(x) \,dx\) is generalized for seminormed fuzzy integrals. Hardy type inequalities based on an aggregation function for seminormed fuzzy integrals are shown.
Hamzeh Agahi, Mohammed Ali Yaghoobi
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