摘要
文［１］提出了幂群的概念，给出了幂群中各元素是等势的基数定理，文［２］提出了Ｆｕｚｚｙ幂群的概念，但没研究其中各元素的基数问题，本文深入研究这一问题，得到了由Ｄ．Ｄｕｂｏｉｓ等在文［３］中提出的和由李洪兴等在文［４］中提出的两种Ｆｕｚｚｙ集基数形式下的Ｆｕｚｚｙ幂群的基数定理，并给出了Ｆｕｚｚｙ幂群中与基数有关的若干结果。
Paper [1] defined the concept of hypergroup and proved the cardinal number theorem that pointed out every element of a hypergroup has the same cardinal number. Paper [2] defined the concept of fuzzy group. However , the problem of cardinal number of element in a fuzzy hypergroup has not been studied. This paper gives some further description for this , we obtain a serious of cardinal number theorems of fuzzy hypergroup under the two forms of cardinal number of fuzzy set that raised by D. Dubois in Paper [3] and by Li Hongxing in Paper[4]. And we prove some results of fuzzy hypergroup about cardinal number.
出处
《模糊系统与数学》
CSCD
1998年第2期61-69,共9页
Fuzzy Systems and Mathematics
关键词
基数
同态
模糊幂群
幂群
Fuzzy hypergroup
Cardinal number
Homomrphism
