Research And Application Of Evidence Theory In The Reduction Of Knowledge

Since it does not need to know a priori probability,evidence theory can expresses "uncertainty" and "unknown" directly, which is a good reference for the expression and combination of uncertain information. The D-S combination rule cannot be used or obtain the result which contradicts with the fact, when the evidences absolutely conflict or highly conflict. Evidence theory is gradually improved after years of research by the domestic and foreign scholars. At present,it has been widely used in the field of artificial intelligence.Reduction of knowledge is one of the key point of rough sets theory,which mainly used in dimensionality reduction and feature extraction takes an important part in intelligent information processing. Reduction of knowledge reduces the redundant attributes on condition that it is able to keep the classification ability. However, getting the minimum reduction of decision table s is a NP-hard problem. Therefore,we usually use some heuristic method to reduce the redundant attributes. Among all the heuristic methods,we go deep into the research of reduction of knowledge based on attribute importance. While,there are not unified standards to measure the attribute importance and each method aims to find a local minimum reduction quickly. Therefore, the study of reduction of knowledge based on attribute importance is necessary.This paper applies evidence theory into rough sets theory,which aims to provide a kind of heuristic algorithm for reduction of knowledge based on evidence theory. First, it puts forward a new method of evidence combination,overcoming the disadvantages of D-S combination rules. Secondly, it gives the attribute information entropy based on the concept of equivalent partition of rough sets theory,after that it defines the entropy importance of each attribute. Then, it obtains the basic probability assignments of each attribute based on the entropy importance of each attribute,and establish an evidence function for each attribute by the concept of dichotomous mass functions. Then,it gets the evidence importance of each attribute by using the new method of evidence combination and Pignistic probability conversion. Finally,the core attributes are obtained by the entropy importance of each attribute,and set the core attributes as the start of the algorithm. Sort the other attributes by size of the evidence importance of each attribute,and put them into the core attributes one by one until it satisfies the condition of attribute reduction. The core attributes and the relative reduction of knowledge can be received through the above steps.Examples show that the extract of attribute importance based on the evidence theory has a better effect on the classification,and it is ideal in solving the core attributes and the reduction of knowledge. This heuristic algorithm is easy to understand and achieve,which can get the core attributes and the reduction of knowledge of decision tables quickly. However, this algorithm can only find a relative reduction of knowledge, and whether the reduction is a minimum reduction remaining to be proved.