摘要
迄今,有关 Fuzzy 集基数的研究进展甚微,主要困难在于如何给它一个恰当的定义.D.Dubois 和 H.Prade 在[1]中曾对有限支集的 Fuzzy 集以及在极苛刻条件下的无限 Fuzzy 集给出过一种定义.然而,正如本文将要指出的那样,该定义是不太合理的.本文将给出 Fuzzy 集基数的一般性定义.基于这一定义,不但得到有关基数的大部分结论,而且有其自身的特有性质,特别对连续统假设这一世界难题可能会有新的启示.
Up to now,the study on the cardinal number of fuzzy sets has progressed slowly because it is very hard to give it an appropriate definition.Althrough D.Dubois and H.Prode has given a definition for it in [1],it is with some harsh terms and is not reasonable as we point out in this paper.In this paper,we give a general definition of fuzzy cardinal number.Based on this definition,we have not only obtained a large part of results with respect to cardinal number,but also given a few new properties of fuzzy cardinal num- ber.Especially,from fuzzy cardinal number we may have some new idea on the continuum hypothesis.
关键词
基数
连续统假设
广义
模糊集
Fuzzy cardinal number
Continuum hypothesis(CH)
General continuum hypothesis(GCH)
