New results of uncertain integrals and applications
-
Zehui Shao
,
Milad Yadollahzadeh
Abstract
Based on the uncertainty theory, Liu [B. Liu, Some research problems in uncertainty theory, J. Uncertain Syst. 3 2009, 1, 3–10] introduced an uncertain integral for applying uncertain differential equation, finance, control, filtering and dynamical systems. Since uncertain integrals are the important content of uncertainty theory, this paper explores an approach of the relationship between uncertain integrals by the well-known Chebyshev-type inequality. Also, we propose the concept of an uncertain fractional integral which is generalized version of an uncertain integral. The definition of a strong comonotonic uncertain process and some new properties of the uncertain integral were presented in [C. You and N. Xiang, Some properties of uncertain integral, Iran. J. Fuzzy Syst. 15 2018, 2, 133–142]. Based on the strong comonotonic uncertain process, as an application, we provide Chebyshev’s inequality for a fractional uncertain integral and an uncertain integral.
Funding statement: This research was supported by Hubei Province Key Laboratory of Intelligent Information Processing and Real-time Industrial System (Wuhan University of Science and Technology) (under grant 622274).
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Articles in the same Issue
- Frontmatter
- On the numerical solvability of the initial problem with weight for ordinary linear differential systems with singularities
- Multiplicative Lie-type derivations on standard operator algebras
- Numerical radius inequalities and estimation of zeros of polynomials
- Convolution equations on the Lie group G = (-1,1)
- Positive solutions for a fourth-order p-Laplacian boundary value problem
- Existence and asymptotic behavior of strictly convex solutions for singular k-Hessian equations with nonlinear gradient terms
- Characterization of Jordan two-sided centralizers and related maps on triangular rings
- Convergence and integrability of rational and double rational trigonometric series with coefficients of bounded variation of higher order
- Weak and strong type inequalities criteria for fractional maximal functions and fractional integrals associated with Gegenbauer differential operator
- Generating sets of F/R' Leibniz algebras
- New results of uncertain integrals and applications
- Multilinear commutators of multilinear strongly singular integral operators with generalized kernels
Articles in the same Issue
- Frontmatter
- On the numerical solvability of the initial problem with weight for ordinary linear differential systems with singularities
- Multiplicative Lie-type derivations on standard operator algebras
- Numerical radius inequalities and estimation of zeros of polynomials
- Convolution equations on the Lie group G = (-1,1)
- Positive solutions for a fourth-order p-Laplacian boundary value problem
- Existence and asymptotic behavior of strictly convex solutions for singular k-Hessian equations with nonlinear gradient terms
- Characterization of Jordan two-sided centralizers and related maps on triangular rings
- Convergence and integrability of rational and double rational trigonometric series with coefficients of bounded variation of higher order
- Weak and strong type inequalities criteria for fractional maximal functions and fractional integrals associated with Gegenbauer differential operator
- Generating sets of F/R' Leibniz algebras
- New results of uncertain integrals and applications
- Multilinear commutators of multilinear strongly singular integral operators with generalized kernels
