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# System prepended metadata

title: 粗糙集(rough sets)RS約略集合

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# 粗糙集(rough sets)RS約略集合

* 定義: 可以處理基於單獨物件模型的質性資料
       一個在知識系統表達不確定性資料的方法。該理論已經被廣泛應用在制定決策中，特別是多準則中排序和分類的問題
      
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 * Rough Set terminology
   *  a data table is called an Information System( decision table )     
   * pair (U, A)
     *  U is a non-empty finite set of objects 
     *  A is  a non-empty finite set of attributes.The elements of A are called conditional attributes.Decision system is a pair of (U, A union {d})where d is decision attribute (instead of one we can consider more decision attributes).　
![](https://i.imgur.com/44H3zPZ.png =x300)
![](https://i.imgur.com/14gP5qf.png =x300)

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* reduce table size--->==Indiscernibility==

![](https://i.imgur.com/Elgt5uO.png =x300)

```
IND({p1}) = {{O1, O2}, {O3, O5, O7, O9, O10}, {O4, O6, O8}}

O1 and O2 are characterized by the same values of attribute p1 and the value is 1.
O3, O5, O7, O9, O10 are characterized by the same value of attribute p1 and the value is 2.
O4, O6, O8 are characterized by the same value of attribute p1 and the value is 0.

```
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* approximation 

![](https://i.imgur.com/kXsY5Ha.png)

```
 \cup \underline{P}X  represents the positive region which contains the objects definitely belonging to the target set X.
 U - \cup \bar{P}X  represents the negative region which contains the objects that can be definitely ruled out as a member of the target set X.
 \cup \bar{P}X - \cup \underline{P}X  represents the boundary region which contains the objects that may or may not belong to the target set X.

```
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![](https://i.imgur.com/U3x4Fdi.png)

![](https://i.imgur.com/9wiQDqv.png)

### 參考資料
[geeksforgeeks](https://www.geeksforgeeks.org/rough-set-theory-properties-and-important-terms-set-2/?ref=lbp)