Class-specific Attribute Reduction In Incomplete Decision Systems

As an important theoretical tool of data mining,rough set theory can discover the underlying laws by analyzing observable data.Attribute reduction is one of the important research contents of the rough set theory.By deleting the duplicate or unnecessary attributes,the optimal attribute subset can be selected from the original condition attributes,which can maintain certain classification characteristics of the original decision system,so as to reduce the computational cost.At the same time,the minimal attribute reduction can remove redundant attributes to the greatest extent,so finding the minimal reducts has been one of the hot topics in rough set theory.The classical rough set model describes the equivalence relation in the decision system,which requires the data integrity of the decision system.However,in some practical applications,incomplete decision systems often appears,that is,system data is missing.The existing attribute reduction methods of incomplete decision systems mainly focus on all decision classes,but there is no research on attribute reduction and minimal attribute reduction based on a specific decision class in an incomplete decision system.In addition,due to the different needs of researches or personal preferences,decision-makers are more inclined to pay attention to attribute reduction based on a specific decision class in some practical applications compared with all decision classes.Therefore,the attribute researches based on a specific decision class are more purposeful,concise and efficient.In view of the above considerations,the main researches on attribute reduction based on a specific decision class in incomplete systems are as follows:(1)Firstly,the basic definitions and related theorems of class-specific distribution reduction in incomplete decision systems and a reduction algorithm based on the discernibility matrix were proposed.Then,this paper compared the proposed algorithm with the distribution reduction algorithm of incomplete decision systems based on all decision classes.The experimental results showed that when a specific class is selected for distribution reduction,the average length of reducts is relatively short and the efficiency of reduction is also improved remarkably.(2)The minimal attribute reduction algorithm of positive region preserving based on a specific decision class in incomplete decision systems was proposed.By studying the corresponding relationship between each minimal disjunctive item of the main disjunctive normal form of the discernibility function and the positive region preservation reduction based on the specific class,the range of finding minimal reducts was reduced,and the minimal reducts of positive region preservation reduction based on the specific decision class was obtained by combining with the extension law.Finally,the proposed algorithm was compared with the algorithm based on all decision classes.The experimental results showed that when the decision class is a specific class,the reduction efficiency is significantly improved.