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中文摘要：
粗糙集的不确定性度量方法，目前主要包括粗糙集的粗糙度、粗糙熵、模糊度和模糊熵。在不同知识粒度下，从属性的角度，给出了分层递阶的知识空间链，发现在分层递阶的知识粒度下部分文献中定义的粗糙集的粗糙熵和模糊度随知识粒度的变化规律不一定符合人们的认识规律。从信息熵的角度提出了一种粗糙集不确定性的模糊度度量方法，证明了这种模糊度随知识粒度的减小而单调递减，弥补了现有粗糙熵和模糊度度量粗糙集不确定性的不足。最后，分析了在不同知识粒度下粗糙度和模糊度的变化关系。
英文摘要：
Rougness, rough entropy, fuzziness, and fuzzy entropy are major methods for measuring the uncertainty of rough sets. In different knowledge granularity levels, a hierarchical knowledge space chain is proposed based on the attributes in information systems. Some regularities of the changing of rough entropy and fuzziness of a rough set with the knowledge granularity are found to be inconsistent with human cognition. A new method for measuring the fuzziness of rough sets is proposed based on information entropy. The fuzziness measured by the new method is monotonously decreasing with the refining of knowledge granularity in apporiximation spaces. It overcomes the problem of roughness and rough entropy. Finally, the relations of the changing of roughness and fuzziness are analyzed in different knowledge granularities.
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