Minimum Attribute Number in Decision Table Based on Maximum Entropy Principle

Decision tables are always extremely important objects in data mining. People often require the more simple decision table in order to reduce the scale of tables. But a decision table is not always the most simple, so we have to try reducting it to learn which condition attributes are essential. It is known that the reduct results are not usually unique and the cardinal numbers of condition attributes set in different deducted tables of the same tables are different. From research findings on reducted tables, however, we can find out a simplest condition attributes set and call it Minimum Attribute Set. According to information theory, in this paper, we have deduced a formula to calculate the cardinal number of the Minimum Attribute Set, which is called Minimum Attribute Number. Moreover, before reducted we can just know whether the table is the simplest one or not. Eventually, we give a simple test example.