一种描述模糊不确定性问题的新方法

A new method of describing fuzzy uncertainty problems

文中将实测数据看作模糊数,其模糊幅度不会超出一定的范围,而观测值的不确定性因素所产生的误差一般不会大于极限误差,在对观测值进行模糊化处理时,按经典最小二乘法求得的中误差的3倍作为其模糊幅度的阈值。每个梯形模糊数的4个参数由软件自动生成的4个随机数(小于3)分别与中误差及对应观测值的乘积来确定。结合数值模拟和水准网平差实例均表明该方法能合理描述观测值中的不确定性因素。

In the paper, the measured data was considered as the fuzzy number and the fuzzy amplitude did not ex-ceed a certain range, and the error produced by the uncertainty factor of the observed value was generally not greater than the limit error. When the observed values were fuzzified, three times median errors obtained by the classical least squares method were the threshold of its fuzzy amplitude. The four parameters of each trapezoidal fuzzy number were determined by the product of the four random numbers （less than three） automatically generated by the software and the error and the corresponding observations. Examples combining with the numerical simulation and the leveling network adjustment showed that the method could reasonably describe the uncertainties in the observed values.