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).
References
[1] S. Bera, P. K. Giri, D. K. Jana, K. Basu and M. Maiti, Fixed charge 4D-TP for a breakable item under hybrid random type-2 uncertain environments, Inform. Sci. 527 (2020), 128–158. 10.1016/j.ins.2020.03.050Suche in Google Scholar
[2] X. Chen, Uncertain calculus with finite variation processes, Soft Comput. 19 (2015), no. 10, 2905–2912. 10.1007/s00500-014-1452-0Suche in Google Scholar
[3] X. Chen and B. Liu, Existence and uniqueness theorem for uncertain differential equations, Fuzzy Optim. Decis. Mak. 9 (2010), no. 1, 69–81. 10.1007/s10700-010-9073-2Suche in Google Scholar
[4] X. Chen and D. A. Ralescu, Liu process and uncertain calculus, J. Uncertain. Anal. Appl. 1 (2013), Article ID 3. 10.1186/2195-5468-1-3Suche in Google Scholar
[5] H. Dalman, Uncertain programming model for multi-item solid transportation problem, Int. J. Mach. Learn. Cyber. 9 (2018), no. 4, 559–567. 10.1007/s13042-016-0538-7Suche in Google Scholar
[6] M. Farrokh, A. Azar, G. Jandaghi and E. Ahmadi, A novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty, Fuzzy Sets and Systems 341 (2018), 69–91. 10.1016/j.fss.2017.03.019Suche in Google Scholar
[7] H. Gaspars-Wieloch, Project net present value estimation under uncertainty, CEJOR Cent. Eur. J. Oper. Res. 27 (2019), no. 1, 179–197. 10.1007/s10100-017-0500-0Suche in Google Scholar
[8] X. Huang and T. Yang, How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk, J. Bank. Finance 111 (2020), Article ID 105726. 10.1016/j.jbankfin.2019.105726Suche in Google Scholar
[9] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math. Stud. 204, Elsevier Science, Amsterdam, 2006. Suche in Google Scholar
[10] X. Li and B. Liu, Hybrid logic and uncertain logic, J. Uncertain Syst. 3 (2009), no. 2, 83–94. Suche in Google Scholar
[11] B. Li, Y. Zhu, Y. Sun, G. Aw and K. L. Teo, Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint, Appl. Math. Model. 56 (2018), 539–550. 10.1016/j.apm.2017.12.016Suche in Google Scholar
[12] B. Liu, Uncertainty Theory, 2nd ed., Stud. Fuzziness Soft Comput. 154, Springer, Berlin, 2007. Suche in Google Scholar
[13] B. Liu, Fuzzy process, hybrid process and uncertain process, J. Uncertain Syst. 2 (2008), 3–16. Suche in Google Scholar
[14] B. Liu, Some research problems in uncertainty theory, J. Uncertain Syst. 3 (2009), no. 1, 3–10. Suche in Google Scholar
[15] B. Liu, Uncertainty distribution and independence of uncertain processes, Fuzzy Optim. Decis. Mak. 13 (2014), no. 3, 259–271. 10.1007/s10700-014-9181-5Suche in Google Scholar
[16] S. Majumder, P. Kundu, S. Kar and T. Pal, Uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint, Soft Comput. 23 (2019), no. 10, 3279–3301. 10.1007/s00500-017-2987-7Suche in Google Scholar
[17] F. J. Santos-Arteaga, M. Tavana and D. Di Caprio, A new model for evaluating subjective online ratings with uncertain intervals, Expert Syst. Appl. 139 (2020), Article ID 112850. 10.1016/j.eswa.2019.112850Suche in Google Scholar
[18] S. Xie, Z. Hu, D. Zhou, Y. Li, S. Kong, W. Lin and Y. Zheng, Multi-objective active distribution networks expansion planning by scenario-based stochastic programming considering uncertain and random weight of network, Appl. Energy 219 (2018), 207–225. 10.1016/j.apenergy.2018.03.023Suche in Google Scholar
[19] X. Yang and B. Liu, Uncertain time series analysis with imprecise observations, Fuzzy Optim. Decis. Mak. 18 (2019), no. 3, 263–278. 10.1007/s10700-018-9298-zSuche in Google Scholar
[20] K. Yao and B. Liu, Parameter estimation in uncertain differential equations, Fuzzy Optim. Decis. Mak. 19 (2020), no. 1, 1–12. 10.1007/s10700-019-09310-ySuche in Google Scholar
[21] C. You and N. Xiang, Some properties of uncertain integral, Iran. J. Fuzzy Syst. 15 (2018), no. 2, 133–142. Suche in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- 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
Artikel in diesem Heft
- 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
