| In practical applications,many information systems contain both symbolic and ordinal attributes.For example,we can use Iris data in UCI database to identify the types of flowers based on the length and width of the bract and petals.The stock company could classify stocks of stockholders according to the stockholder's gender,age and investment amount.Usually,the ordinal attributes can be called as "standards," and the above classification problem is called multiple criteria classification.For this type of problems,the information systems containing hybrid data cannot be handled based on only equivalence relations or dominance relations individually,and that will also reduce the interpretability of the extracted rules.In this thesis,we introduce equivalence relations to symbolic attributes and dominance relations on ordinal attributes,respectively.Thus the hybrid data can be effectively handled and the corresponding attribute reduction method is also developed.Our main contributions are as follows:1.For information systems with ordinal conditional attributes and symbolic decision attributes,we introduce the definition of dominance-equivalence relations,and develop a matrix reduction algorithm based on sample pair selection.Different from the traditional method based on identification matrix,this algorithm can find attributes that are useful for reduction by selecting sample pairs without computing the identification matrix.Therefore,the proposed algorithm can significantly improve the computational performance of the process of attribute reduction.Furthermore,in order to deal with large-scale data,we propose an approximate reduction algorithm.This algorithm adds attributes to the reduction according to the importance of attributes,which further improves the efficiency.Finally,the experimental results on UCI data sets demonstrate the feasibility and effectiveness of the proposed algorithms.2.The proposed approximate reduction algorithm is applied to dynamic information systems.When adding or deleting multiple samples,the method only updates the dominance set to obtain the attribute reduction quickly.At the same time,the update principle is given with proof.Experiments on UCI datasets show that our method takes less time to obtain the same or more simplified attribute reduction than the traditional method and the condensed dominance matrix method.3.For multiple criteria classification problems with both non-ordinal/ordinal conditional attributes,the definition of hybrid information system is introduced.Correspondingly,the concepts of dominance/dominated set and the upper and lower approximate to decision classes are defined.An overlapping rule extraction method is then introduced.Finally,test examples could be classified by the extracted rules.The results show that the proposed method not only extracts more rules than the monotonic rules method but also can reduce the running time significantly with slight improvement of the classification precision. |
