中文摘要：

粒计算是一个新的研究领域,其思想被广泛地运用于各种理论和计算方法,比如粗糙集理论,模糊集理论和商空间理论.在以往的研究中,基于划分的粒计算模型得到了广泛地研究,即粒度空间中粒子间是两两不相交的.但是,在有些实际问题中,要将问题空间粒化为论域的划分在有些情况下是困难的,或者是没有必要的.因此,基于覆盖的粒计算模型是粒计算研究中的一个重要方向.本文对覆盖粒度空间的层次模型进行了研究,指出了当前两种层次模型中存在的问题,重新定义了一种新的层次模型,并对其重要性质进行了分析.阐述了覆盖粒度空间中知识不确定的原理,采用知识熵对覆盖粒度空间的知识量进行度量,并对知识熵和覆盖上偏序较细关系之间的联系进行了分析,从定量的角度给出了知识粒度的解释.

英文摘要：

Granular computing is a new field of research. Its ideas, principles and strategies have appeared in many branches of science and different fields of computer science, such as rough set theory, fuzzy set theory and quotient space theory, etc. In general, the granular space discussed in many theories is a partition of the given universe. In this case, we call it partition based granular computing. However, it is difficult or unnecessary to granulate the universe into a partition. So, it is necessary and significant to study covering-based granular computing. In order to apply granular computing in solving problems, one key issue needed to be addressed is to construct the hierarchical model of granular space. In the past few years, two hierarchical models have been proposed. One was proposed by Huang in 2004, the other was developed by Zhang in 2007. In this paper, we analyze these two models, and find that both of them have their own limitations, namely they are not keeping with our understanding with granularity. So, a new hierarchical model is defined in this paper. By analysis, we find that this definition can interpret knowledge granularity commendably. Moreover, the relationships of this definition with the other two models are discussed. In order to quantitatively analyze the knowledge of covering granular space, the knowledge entropy of covering granular space is developed. It gives the interpretation of knowledge granularity in quantity.