The Model Extension And Knowledge Reduction Based On Set-Valued Incomplete Information System

The classical rough set theory, first proposed by the Polish mathematician Paw- lak[1] in the early 1980s, is a mathematical tool to deal with uncertain concepts. The theory is characterized by being capable of effectively dealing with imprecise, incom -plete and inconsistent information and discovering latent knowledge and principles without any prior knowledge or additional information.The classical rough set theory is based on complete information systems. It classifies objects using upper-approximation and lower-approximation defined on an indiscernibility relation, which is a kind of equivalent relation. In order to process the incomplete information systems, the classical rough set theory, especially the indiscernibility relation, needs to be extended to some in equivalent relation. There are several extensions for the indiscernibility relation now, such as tolerance relation[2, 3], non-symmetric similarity relation[4], limited tolerance relation[5],and variable-precision tolerance relation[6-8]. Extending incomplete information systems to set-valued information systems provides a new approach to the study of incomplete information systems that extends it to set-valued information systems.Wang Hong and Song Xiao-Xue[10-14] proposed tolerance relation and dominance relation based on set-valued information system.The analysis of tolerance relation and limilarity relation, demonstrates that the conditions of tolerance relation based on set-valued information system are excessively free, and will put the objects which share no known property in common at all into the same tolerance class by mistake. Meanwhile, the dominance relation based on set-valued information system may put the objects which share a lot of properties in common into different dominance class.This paper proposes a new relation based on the analysis of the two relation. Through the performance analysis of the new relation and the original two relations, a more actual classification result is obtained.This paper also studies the knowledge reduction of the set-valued incomplete information systems based on the new relation. The judgement theories and the discernibility matrices of attribute reduction under set-valued incomplete information system are provided, and a specific approach to knowledge reduction is worked out.