机械故障诊断中存在着许多不确定性和知识冗余性，而粗糙集理论是一种新型的处理不确定性信息的数学工具，粗糙集理论提供了对机械故障进行诊断全新的有效途径。
There exists a lot of uncertainty and redundant knowledge in machinery fault diagnosis, while rough set theory is a new mathematical tool to deal with uncertain information.
约简与核是粗糙集理论的两个重要概念，而直接由定义来计算约简与核是一个典型的NP难题。
Reduction and core are two important concepts in rough set theory, while computing reductions and core according to the definitions directly is a typical NP problem.
而可变精度粗糙集作为对经典粗糙集理论的扩展，体现了等价类与集合的重叠度程度上的差别。
As the extension of rough set, variable precision rough set reflects the difference of degrees of overlap of kinds and sets.
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