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International Journal for Uncertainty Quantification
IF: 0.967 5-Year IF: 1.301

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2018020455
pages 251-266

A METRIC ON UNCERTAIN VARIABLES

Tingqing Ye
School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
Yuanguo Zhu
School of Science, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

ABSTRACT

Metric is a vital concept on a space. In this paper, a new metric is proposed to study the space consisting of uncertain variables. Then, some formulas of calculating the metric in some cases are presented. Finally, the convergence of uncertain sequences in metric is defined and the relationships among convergence in metric, convergence in measure, convergence in mean, convergence in distribution and uniform convergence almost surely are studied.