Uncertainty distribution and independence of uncertain processes
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Uncertain process is a sequence of uncertain variables indexed by time. This paper presents a concept of uncertainty distribution for describing uncertain process. Some sufficient and necessary conditions are also proved for uncertainty distribution and inverse uncertainty distribution of uncertain process. Finally, this paper proposes an independence definition of uncertain processes and shows some mathematical properties of it.
KeywordsUncertainty theory Uncertain process Uncertainty distribution
This work was supported by National Natural Science Foundation of China Grants No. 61273044 and No. 91224008.
- Chen, X. W., & Ralescu, D. A. (2013). Liu process and uncertain calculus. Journal of Uncertainty Analysis and Applications, 1, Article 3.Google Scholar
- Liu, B. (2008). Fuzzy process, hybrid process and uncertain process. Journal of Uncertain Systems, 2(1), 3–16.Google Scholar
- Liu, B. (2009). Some research problems in uncertainty theory. Journal of Uncertain Systems, 3(1), 3–10.Google Scholar
- Liu, B. (2012a). Why is there a need for uncertainty theory? Journal of Uncertain Systems, 6(1), 3–10.Google Scholar
- Liu, B. (2013a). Toward uncertain finance theory. Journal of Uncertainty Analysis and Applications, 1, Article 1.Google Scholar
- Liu, B. (2013c). Polyrectangular theorem and independence of uncertain vectors. Journal of Uncertainty, Analysis and Applications, 1.Google Scholar
- Liu, Y. H. (2012b). An analytic method for solving uncertain differential equations. Journal of Uncertain Systems, 6(4), 244–249.Google Scholar
- Liu, Y. H., & Ha, M. H. (2010). Expected value of function of uncertain variables. Journal of Uncertain Systems, 4(3), 181–186.Google Scholar
- Yao, K. (2013). Extreme values and integral of solution of uncertain differential equation. Journal of Uncertainty Analysis and Applications, 1, Article 2.Google Scholar