一个概念（或集合）的下近似（lower approximation）概念（或集合）指的是，其下近似中的元素肯定属于该概念；一个概念（或集合）的上近似（upper approximation）概念（或集合）指的...
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In the end , we compare the different definitions of the lower approximation operator on the approximation space, and point out the research directions.
最后是结束语，对模糊近似空间上的下近似算子进行了比较，并指出了以后的研究方向。
参考来源 - 模糊近似空间上模糊集的粗糙集及其粗糙度So we advance tolerance rough set theory (TRST) and the concept corresponding to it, for example, tolerance upper approximation, tolerance lower approximation, tolerance relation sets and so on.
基于此，我们提出了容错粗集理论的概念，用容错关系代替了严格的相等关系，并提出了与标准粗集理论相对应的基本概念，如容错上近似、容错下近似、容错关系集等。
参考来源 - 基于C/S模式数据挖掘的研究及其在AEFS中的应用·2,447,543篇论文数据，部分数据来源于NoteExpress
讨论了利用模糊集的下近似和上近似定义的模糊测度和概率模糊测度的关系。
We discuss the relation between fuzzy measure defined by lower approximation and upper approximation of fuzzy set and probability fuzzy measures.
用基于随机集的上粗相等、下粗相等来表示随机上近似算子、随机下近似算子。
The upper rough equal, the lower rough equal based on the random sets are used to express upper approximation operators and the lower approximation operators based on the random sets.
讨论随机模糊下近似、上近似集的模糊概率与模糊信任测度、模糊似然测度之间的关系。
The relationship between fuzzy probability defined by lower approximation and upper approximation of random fuzzy sets and fuzzy belief measures, fuzzy plausibility measures is discussed.
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