The Study Of Attribute Reduction For Objects In The Decision Tables

The rough sets have been introduced by polish scientist Pawark in1982. It is a kind of soft computing tool for dealing with inexact, uncertain and vague knowledge. Its main idea is to get the decision and classification rules by knowledge reduction under the premise of the classification ability was unchanged. Reduction theory of information system is one of the core contents of rough sets. A variety of overall attributes reduction methods are proposed according to the background of the actual problems, such as attributes reductions based on rough positive domain, the theory of inclusion degree, the information entropy and so on. However, the research of the attributes reduction for the object in a decision table is relatively rare. In fact, the attribute reduction for objects in the decision tables can be used to get more concise knowledge. This paper is devoted to the discussion of five kinds of attribute reduction methods for the objects in the inconsistent decision tables. The basic properties, judgment theorems and calculation methods for these attribute reductions are presented. Concretely, the following achievements are obtained:1. The five kinds of attribute reduction concepts for the objects in inconsistent decision tables and their implication relationships are studied. Some of the implication relationships between these five types of reductions provided by Kryszkiewicz are proved not true by examples.2. The judgment theorems with respect to the five kinds of attribute reductions for the objects in inconsistent decision tables are obtained. The attribute reduction methods are provided based on the discernibility matrix and discernibility formulas.3. Taking the μ-decision reduction as example, the algorithm for the calculation method of this reduction is designed and the programming for the algorithm is provided by VC++. The validity and practicability of the algorithm is analyzed by examples.