论正态云模型的普适性

分布函数是分析随机现象的重要工具，正态分布是最重要的概率分布，在自然科学和社会科学中应用广泛；隶属函数是模糊集合的基石，正态隶属函数也有广泛的应用。但是，精确确定一个模糊概念的隶属函数已经成为模糊学应用的瓶颈。云模型把随机性和模糊性结合起来，用数字特征熵，揭示随机性与模糊性的关联性，并用来表示一个定性概念的粒度。正态云模型通过期望、熵和超熵构成的特定结构发生器，生成定性概念的定量转换值，体现概念的不确定性。这种特定结构不但放宽了形成正态分布的前提条件，而且把精确确定隶属函数放宽到构造正态隶属度分布的期望函数，因而更具有普遍适用性，更简单、直接地完成了定性与定量之间的相互转换过程。

Study on the Universality of the Normal Cloud Model

The distribution function is an important tool for the study of the stochastic variances. The normal distribution is very popular in the nature and human society. The idea of membership functions is the foundation of the fuzzy sets theory. While the fuzzy theory is widely used, the completely certain membership function which has no any fuzziness at all has been the bottleneck of the applications of this theory. Cloud models are effective tools in transforming between qualitative concepts and their quantitative expressions. It can represent the fuzziness and randomness and their relations of uncertain concepts. Also cloud models can show the concept granularity in multi-scale spaces by the digital characteristic Entropy (E n). The normal cloud models not only broaden the formation conditions of the normal distribution but also make the normal membership function be the expectation of the random membership degree. In this paper, the universality of the normal cloud model is proved,which is more superior and easier, and can fit the fuzziness and gentleness in human cognizing process. It would be more applicable and universal in the representation of uncertain notions.