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中文摘要：
对S-粗集给出改进,把函数这个分析工具引入到S-粗集中,提出函数S-粗集（function singularrough sets）。函数单向S-粗集（function one direction singular rough sets）是函数S-粗集的基本形式之一,它是以R-函数等价类[u]定义的;ui∈[u]是一个函数,函数是一个规律。函数单向S-粗集具有单向动态特性与规律特征：利用函数单向S-粗集的规律特征,给出F-规律推理与F-规律推理的规律挖掘概念,提出F-规律推理的规律挖掘定理,F-规律推理的规律挖掘原理与F-规律推理的规律挖掘应用。F-规律推理的规律挖掘是寻找系统中未知规律研究的一个新的研究方向。
英文摘要：
S-rough sets is improved, a function analysis tool is introduced into the S-rough sets, and the concept of function S-rough sets（function singular rough sets） is put forward. Function one direction S-rough sets is one of the basic forms of function S-rough sets, and it is defined by R-function equivalence classesui[u],∈[u]is a function, and the function is a law. Function one direction S-rough sets has one direction dynamic characteristics and law characteristics： using the law characteristic of function one direction S-rough sets, this paper gives the two concepts： the F-law inference and the law mining of F-law inference and puts forward the theorem of law mining of F-law inference, the law mining principle of the F-law inference and its application. The law mining of the F-law inference is a new research direction for the study of looking for unknown law in system.
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