Study On The Sample Selection Based On Rough Sets

The rough set theory is a new mathematical tool to deal with uncertainty and vagueness of decision system and it has been applied successfully in many fields, such as artificial intelligence, data mining, pattern recognition and information processing fields so on. Rough set theory is used to identify the reduct set of all condition attributes of the decision system, namely attribute reduction which is one important and valuable topic of decision system in rough sets. Attribute reduction is used to delete the uncorrelated or unimportant conditional attribute as preserving the ability of classification of original decision table. The existing attribute reductions are designed to just keep confidence of every certain rule and cannot identify key conditional attributes explicitly for special decision rules. However, in many practical problems possible rules with greater confidence are always available; and key attributes for particular decision classes are more attractive, these two requirements motivate our idea to improve the existing attribute reduction in rough sets. In chapter three we develop the concept ofθ-local reduction in order to keep confidence of decision rules greater than or equal to a parameterθand offer a minimal description for these decision rules. The purpose ofθ-local reduction is used for possible rules with bigger confidence to identify key conditional attributes that have close relation with special decision classes. Approach of discernibility matrix is employed to investigate the structure ofθ-local reduction and compute allθ-local reductions. At last in this chapter an application to medical diagnosis is employed to illustrate our idea ofθ-local reduction. In the process of finding reducts, every sample is considered the same importance as other samples and they share the same problem of computing load when deal with large data sets. One natural idea is selecting fewer samples to find the same reducts as original decision table for reducing complexity of finding reducts, then we may reach the aim of compressing decision table. In chapter four sample selection with rough set is proposed in order to compress the discernibility matrix of a decision table so that only minimal elements in the discernibility matrix are employed to find reducts. In this chapter relative discernibility relation of conditional attribute is defined, indispensable and dispensable conditional attributes are characterized by their relative discernibility relations and key object pair set is defined for every conditional attribute. With the key object pair sets all the sample selections can be found. An example is employed in this paper to illustrate our idea of sample selection with rough set.