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中文摘要：
在粗糙集理论中存在一对近似算子：下近似算子和上近似算子．而在Dempser—Shafer证据理论中有一对对偶的不确定性测度：信任函数与似然函数．集合的下近似和上近似可以看成是对该集合所表示信息的定性描述，而同一集合的信任测度和似然测度可以看成是对该集合的不确定性的定量刻画．针对各种复杂系统中不确定性知识的表示问题，介绍了无限论域中经典和模糊环境下信任结构及其导出的信任函数与似然函数的概念，建立了Dempser—Sharer证据理论中信任函数与似然函数和粗糙集理论中下近似与上近似之间的关系．阐述了由近似空间导出的下近似和上近似的概率生成一对对偶的信任函数和似然函数；反之，对于任何一个信任结构及其生成的信任函数与似然函数，必可以找到一个概率近似空间，使得由近似空间导出的下近似和上近似的概率分别恰好就是所给的信任函数和似然函数．最后，指出了主要理论成果在智能信息系统的知识表示和知识获取方面的潜在应用．
英文摘要：
In rough set theory there exists a pair of approximation operators, the lower and upper approximations; whereas in Dempster-Shafer theory of evidence there exists a dual pair of uncertainty measures, the belief and plausibility functions. To represent uncertainty knowledge in various information systems in crisp and fuzzy environments, general types of belief structures and their inducing dual pairs of belief and plausibility functions in infinite universes of discourse are first introduced. Relationships between the belief and plausibility functions in the Dempser-Shafer theory of evidence and the lower and upper approximations in the rough set theory are then established. It is shown that the probabilities of lower and upper approximations induced from an approximation space yield a dual pair of belief and plausibility functions. And for any belief structure there must exist a probability approximation space such that the belief and plausibility functions defined by the given belief structure are, respectively, the lower and upper probabilities induced by the approximation space. The lower and upper approximations of a set characterize the non-numeric aspect of uncertainty of the available information and can be interpreted as the qualitative representation of the set, whereas the belief and plausibility measures of the set capture the numeric aspect of uncertainty of the available information and can be treated as the quantitative characterization of the set. Finally, the potential applications of the main results to knowledge discovery in intelligent information systems in various situations are explored.
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