Research of Fuzzy-Norm Method and its Application in Uncertainty Metric with Poor Information

AbstractIt is difficult to get large numbers of data in the process of measurement and performance analysis for material and structure, while many situations in complex systems require quantitative estimates of the lack of information in one probability distribution. Considering unknown probability distribution and very small sample data, based on the original fuzzy norm method, two improved methods are presented. Using membership function and theory of minimization of maximum module norm, the probability distribution function and the interval evaluation under the given confidence level can be obtained for the data series with poor information by solving the optimization problem. Finally, all the given methods and the traditional statistical method are compared and analyzed