Analysis of order statistics of uncertain variables

Yuan Gao1, Rong Gao2, Lixing Yang1
1State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing, China
2Department of Mathematical Sciences, Tsinghua University, Beijing, China

Tóm tắt

In this paper, a concept of order uncertain variable is introduced as a main tool in analysis of k-out-of-n system with uncertain lifetimes. Then, by the operational law of uncertain variable, the uncertainty distribution of order uncertain variable is deduced. At last, the k-out-of-n system is studied, and the uncertainty distribution of k-out-of-n system lifetime is given.

Tài liệu tham khảo

Chen, X, Dai, W: Maximum entropy principle for uncertain variables. Int. J. Fuzzy Syst. 13(3), 232–236 (2011).

Gao, X: Some properties of continuous uncertain measure. Int. J. Uncertainty Fuzziness Knowledge-Based Syst. 17(3), 419–426 (2009).

Li, X, Liu, B: Hybrid logic and uncertain logic. J. Uncertain Syst. 3(2), 83–94 (2009).

Liu, B: Uncertainty Theory. 2nd ed. Springer-Verlag, Berlin (2007).

Liu, B: Theory and Practice of Uncertain Programming. 2nd ed. Springer-Verlag, Berlin (2009).

Liu, B: Polyrectangular theorem and independence of uncertain vectors. J. Uncertainty Anal. Appl. 1, 9 (2013). doi:10.1186/2195-5468-1-9.

Peng, Z, Iwamura, K: Some properties of product uncertain measure. J. Uncertain Syst. 6(4), 263–269 (2012).

Zhu, Y: Uncertain optimal control with application to a portfolio selection model. Cybernet. Syst. 41(7), 535–547 (2010).