Extended Rough Set Model And Fast Reduction Methods Based On Dominance Relations

In dominance relation-based rough set theory,an object x is called to dominate y only when all attribute values of x are superior to those of object y.This definition will lead to comparative small dominance classes especially when the number of attributes is large,and as a result,it will affect the extraction of decision rules and then the process of decision making.In addition,in order to obtain simple rules from complex information systems based on dominance relations,reducing the original attributes is often a necessary step to move the redundant information.Therefore,it is important to establish extended models of dominance relation rough set and develop the corresponding fast reduction methods.Our main work is as follows:On the one hand,the concept of dominance relation is extended by introducing a parameter.The implication underlying this extended concept is that,if “ the majority attribute values of an object x are superior to those of object y,x is called to dominate y ”.On this basis,the dominance set and approximation sets are correspondingly defined,and the VPRS model based on extended dominance relation is also developed.This model shows better classification accuracy than the traditional dominance relation-based rough set model because it can extract more useful information from the data sets.On the other hand,we consider information systems in which the condition attributes are preference-ordered while decision attributes symbolic class labels.To overcome the problem of low efficiency of attribute reduction based on above information systems,we introduce the idea of "positive approximation" into dominance relations and propose a new defined positive approximation,attribute importance measure,and then give the related theoretical results.Furthermore,the corresponding fast attribute reduction method is proposed for the positive region reduction,the compatible reduction,the distribution reduction and the maximum distribution reduction.In the method,the search space can be gradually reduced in the reduction process.Finally,the experimental results on UCI data show that the computational efficiency of the proposed method is obviously improved compared with its original version,while maintaining the same reduction set.