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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.

NEXT Analysis of Similarity of Samples