# Rough Sets Analysis

Rough Sets Analysis (RSA) is the method to understand the phenomena roughly. It is also a method to find characteristics.

It is one of the methods of Data Mining .

The logic of "Rough sets" in mathematics and the method to find rough sets are not a pair. The method to find rough sets is studied in Sensitivity Engineering for design and planning. In this page, "Rough sets analysis" (RSA) is the method used in sensitivity engineering.

## Rough Sets

The Y of rough sets is category data, for example, "Go" and "No-Go". Here, X is also category data. But quantity data can be used.

• Lower Approximation : Sets of a level of each X contained Y certainly
• Upper Approximation : Sets of a level of each X contained Y almost

## Rough Sets Analysis

### Kinds of Data

The quantity data used in RSA is from 0 to 1. The variable expresses the pair idea like "Yes and No" and "Hot and Cold". SD method uses such data. So RSA is useful for the analysis questionnaire .

### To Find Lower Approximation

• 1. Divide samples into each category of Y : For example, "Go" and "No-Go".
• 2. Find the difference of each pair. The pairs are each sample and other sample of different category of Y : For example, looking for the difference between one of the samples of "Go" and one of the samples of "No-Go".
• 3. Get together of the output of 2 : For example, getting together the output of samples of "Go".
• 4. Delete the rare case. : The output of 3 contains the rare case and frequent case. Deleting rare case is to study the data roughly.
• 5. Put in order with logics : We can get compact output using logics. This is lower approximation.
• 6. Do from 2 to 5 for each category of Y : Lower approximations for all categories of Y

If the lower approximation of "Go" is "A=1 and B=2", it does not mean the lower approximation of "No-Go" is "A=2 and B=1". It is interesting.

## Similarity to Other Methods

There are similar methods of RSA. Relationship to the associations analysis is wrote in Associations Analysis .

### Decision Tree

We can also find the part of rough sets (lower and upper approximations) by Decision Tree .

We cannot find all part of rough sets because decision tree uses a tree model. But decision tree helps RSA because RSA is not good at big size data. Decision tree is expected to find main part of rough sets.

### Discriminant Analysis

Discriminant analysis also tells us the relationship between Y and X.

RSA is useful to analyze complicated interaction structure.