Research On Attribute Reduction Based On Equivalence Class With Uncertain Decision Value

In this paper, we address the attributes reduction problem of real data. Attribute reduction is reducing condition attribute of decision table with the invariant classification capability in the decision table. Using the rough sets characteristic that only depends on original data and have no association with the information except original data, we make rough set theory as a tool to solve the problem of attribute reduction.This paper discusses the problems as follows:Firstly, rough set theory proposed by Z.Pawlak based on indiscernibility relation only can deal with discrete attribute value, so a novel method for discretization in rough set theory based on relative positive region of decision attribute is presented. The method which distinguishes from traditional discrete methods is based on the internal relations of the data. By getting the relative positive region of decision attribute, the universe partitioned into the set of equivalence class with uncertain decision values and the set of equivalence class with certain decision values. After sorting the equivalence classes by the values of condition attribute in ascending order, we combine equivalence class with the adjacent attribute values in the set of equivalence class with uncertain decision values and combine equivalence class with the adjacent attribute values in the set of equivalence class with certain decision values. Then we discrete continuous attributes in the way of making cut at the border of two equivalence classes with adjacent values.Secondly, we present a novel attribute reduction method based on equivalence class with uncertain decision values. The method is based on the equivalence class with uncertain decision values in a single condition attribute. After sorting condition attributes by the cardinality of equivalence class with certain decision value in ascending order, we use the result that the cardinality of uncertain equivalence class decrease after combining condition attributes and then we use greedy algorithm combining condition attributes. When the attribute subset combined by condition attributes satisfies the condition that the cardinality of uncertain equivalence class in the set combined by condition attributes is 0, the indiscernibility relation induced by the obtained attribute subset is the same as the indiscernibility relation in original information system and the attribute subset is independent, the subset is a attribute reduction of the information system.Finally, the two methods analyse and utilize the relation contained in the data set in rough set viewpoint and give a novel way to solve continuous attribute discretization problem and attribute reduction problem.