Knowledge Reducts to Incomplete Information System under the Similarity Relation

Certain rules and possible rules exist in incomplete information system, So membership function and generalized decision function under the similarity relation are proposed and some properties of them are proved. Based on the concepts, several types of knowledge reducts to object and system are defined under similarity relation, and mutual relationship among them is established. Several kinds of decision rules are defined according to the new definition of knowledge reducts. An example shows how to generate optimal certain rule and optimal generalized rule by using discernibility function, and the result shows that different knowledge reducts lead to different decision rules. The research on types of knowledge reducts is the theory foundation of knowledge acquisition algorithms to incomplete information system.