摘要
在Fuzzy集的研究中,罗承忠教授的集合套理论起了重要的作用,它刻划了Fuzzy集和集合套类之间的一一对应关系。本文用汪培庄教授的落影理论讨论集合套的落影,建立了集合套类的落影与Fuzzy集的一一对应关糸,并用实数空间上的概率分布函数表示了集合套的落影函数和任意Fuzzy集的隶属函数。最后还用集合套证明了集值统计对Fuzzy集隶属度估计的可行性。
In the paper [2], Professor Luo Cheng Zhong had used the set-embedding to express the fuzzy set and a main consequence was obtained: a fuzzy set and a equivalent classes of the set-embedding are one-to-one correspondence. In this paper, we have used the theory of the falling shadow of professor Wang Pei Zhuang to research the falling shadow of the setembedding and have obtained a result: a fuzzy set add a falling shadow of equivalent classes of the set-embedding are one-to-one correspondence. We have still expressed the function of falling shadow of the set-embedding and the function of membership of a fuzzy set by using of distribution functions of probability on the real number space. Lastly, we have used the setembedding to-prove feasibility estimated the grade of membership of a fuzzy set by set-valued statistics.
出处
《模糊系统与数学》
CSCD
1990年第2期38-45,共8页
Fuzzy Systems and Mathematics