The Research Of Attribute Reduction For Numerical Attribute Information Systems

Attribute reduction is one of the important applications and focuses of rough set theory. However, classical rough set theory based on equivalence relation only processes the discrete data, so it is restricted in practical applications because of widely existing numerical attribute information systems. Therefore, it is important to explore effective methods of attribute reduction in numerical attribute information systems and is necessary to develop related theory.In this dissertation, the overall research status of rough set theory, as well as the theory framework, concepts and knowledge reduction of classical rough set theory are presented firstly. Secondly, the attribute reduction theory of rough set and the existing attribute reduction methods, which consists of the algorithm based on discernibility matrix and logic operation, the algorithm based on information entropy and the algorithm based on information quantity are summarized. Thirdly, two different kind of algorithms for numerical attribute reduction are proposed.1. With respect to the numerical attribute information systems, an attribute reduction algorithm based on the discernibility matrix is proposed. This algorithm introduces the near neighborhood relation instead of equivalence relation. By defining similarity between objects about single attribute and constructing the discernibility matrices, and by means of the connection between set covering and attribute reduction, the minimum attribute reduction problem could be translated to the set covering problems, and then a method for minimum attribute reduction algorithm could be got. Furthermore, simulation experiments with UCI data sets show that this method can select a few attributes but keep, even improve classification ability.2. With respect to the numerical attribute decision systems, an attribute reduction algorithm based on the information quantity is proposed. This algorithm is the extension of the existing attribute reduction method based on information quantity. By constructing similar matrices between objects about single attribute, the information quantity, the joint information quantity, the conditional information quantity and the significance of an attribute are redefined. Using the greedy algorithm in the course of reduction. Experimental results show that this algorithm is feasible and effective.Finally, by combining the compatibility relation and the above two algorithms, new attribute reduction method for the numerical attribute information systems containing incomplete attribute values is proposed.