基于期望值与宽度的区间数距离及其完备性

The Interval Number Distance and Completeness Based on the Expectation and Width

首先根据区间数的期望值及宽度给出了一种新的区间数距离,并讨论了它的一些相关性质;其次讨论了区间数序列的收敛性问题,并证明了在此距离之下区间数全体成为完备度量空间;最后通过实例与其它两种区间数距离公式进行比较,验证了本文所引进的区间数距离公式的合理性及有效性。

According to the expectation and width of the interval number, we firstly present a new interval number distance and of its discusses some related properties in this paper. Secondly we discuss the convergence of interval numbers sequence and prove that all the interval numbers become a complete metric space under this interval number distance. Finally, we compared the other two interval number distance formulas by an example and testified the rationality and validity of interval distance formula in this paper.