关于模糊数空间的上确界度量化问题

About the problem of the Supremum of Quantification on the Fuzzy Number Space

讨论了模糊数空间的上确界度量化问题,指出了已有上确界度量,即一致Hausdorff度量的不足。利用区间数和模糊数的关系,给出了模糊数空间上的一种新的上确界度量,即EW-型上确界度量,并通过实例验证了其有效性和合理性。讨论了EW-型上确界度量的相关性质,并证明了EW-型上确界度量同样使模糊数空间成为完备的度量空间。

In this paper, we discuss the supremum metric in the space of fuzzy numbers, and point out that the already had supremum metric which consistency Hausdorff metric is insufficient. And we give a new supremum metric in the space of fuzzy numbers by the relationship between interval numbers and fuzzy numbers which that is the EW-supremum metric, and prove its validity and rationality by actual examples. In addition, some properties about EW-supremum of quantification are discussesd, and we prove that the EW-supremum of quantification make fuzzy number space be a complete metric space.