区间数运算的一种新视角

A New Perspective of Interval Number Operation

文章将区间数看成在对应区间上满足均匀分布的随机变量,进而讨论2个、3个以至无穷多个区间数相加的规律性,以及其与正态分布的关联性。研究发现,两个区间数求和,左右端点分别相加,所得的结果还是一个区间,但是和所对应的区间的含义已经大大不同于原区间的含义,它不再是均匀分布,取在和区间中间点附近的槪率要高于取在区间端点的概率。随着区间个数的增加,相加的结果,其整个图形逐渐接近于正态分布的概率密度的图形。

This paper defines an interval number as a random variable satisfying a uniform distribution on the corresponding interval. Subsequently, the paper discusses the law of the addition of two, three or even infinite interval numbers and its correlation with the normal distribution. The study finds that the sum of the two interval numbers, the sum of the left and right endpoints, gives you still an interval number, but the meaning of the corresponding interval has become quite different from the meaning of the original interval. It is no longer uniformly distributed, as the probability of appearing in the middle of the sum of the intervals is larger than that of appearing at either end. With the increase of the number of intervals, the entire graph of the distribution function for the sum of the intervals gradually changes to probability density graph of the normal distribution functions.