基于特定类的区间值决策系统的分布约简

Class-specific Distribution Preservation Reduction in Interval-valued Decision Systems

在粗糙集理论中,属性约简是重要的研究内容之一。通过属性约简可以去除冗余属性,求得保持决策系统某种分类能力不变的最小属性子集。分布约简保持决策系统中所有决策类的分布不变,但针对所有决策类的分布约简在实际问题中可能是不必要的。针对以上问题,文中给出了区间值决策系统中基于α-相容关系的特定类分布约简的概念,证明了特定类分布约简的相关定理,构造了特定类分布约简对应的差别矩阵,提出了基于差别矩阵的特定类的分布约简算法(CDRDM),并分析了特定类的分布约简算法和全局分布约简算法(DRDM)构造的差别矩阵中非空元素的集合之间的关系。实验中选取了6组UCI数据集,引入了区间参数,当区间参数为1.2、阈值为0.5时,比较了DRDM算法和3种不同决策类下的CDRDM算法的约简结果和平均约简长度,并且当区间参数分别为1.2和1.6、阈值分别为0.4和0.5时,给出了DRDM算法和两种不同决策类下的CDRDM算法的约简时间随着对象数目和属性数目的变化情况。实验结果表明,特定类分布约简算法针对不同决策类的约简结果可能不同,并且当决策系统中的决策类数量大于1时,特定类分布约简算法的平均约简长度小于或等于全局分布约简算法的平均约简长度,特定类分布约简算法针对不同的决策类在约简效率上有不同程度的改进。

Attribute reduction is one of the important areas in rough set theory.A minimal set of attributes which preserves a certain classification ability in decision tables is solved through a process of attribute reduction,and the process is to remove the redundant feature attributes and select the useful feature subset.A distribution reduct can preserve the distribution of all decision classes in decision tables,but the reducts of all decision classes may not be necessary in the practice.To solve the above problems,this paper proposed the concept of class-specific distribution preservation reduction based onα-tolerance relations in interval-valued decision systems.Some theorems of class-specific distribution preservation reduction were proved and the relevant discerni-bility matrix of class-specific distribution preservation reduction was constructed.And then this paper proposed class-specific distribution preservation reduction algorithm based on discernibility matrices(CDRDM),and analyzed the relationship between the set of non-empty elements in the discernibility matrices constructed by class-specific distribution preservation reduction algorithm and distribution preservation reduction algorithm(DRDM).In the experiment,six sets of UCI data sets were selected and the interval parameter was introduced.When the interval parameter is 1.2 and threshold is 0.5,the results and average length of reducts in DRDM algorithm and CDRDM algorithm were compared.When the interval parameter is 1.2 and 1.6 and threshold is 0.4 and 0.5 respectively,the changes of reduction time of DRDM algorithm and CDRDM algorithm with the number of objects and attributes were given.Moreover,the experiment indicates that CDRDM algorithm has different results for different decision classes.And when there are more than one decision class in decision tables,the average length of reducts of CDRDM algorithm is less than or equal to the average length of reducts of DRDM algorithm,the reduction efficiency based on different decision classes in CDRDM algorithm is improved in varying degrees.