基于极小析取范式的属性约简算法  

The Algorithm of Attribute Reduction Based on Minimal Disjunctive Normal Form

作　　者：索中英[1] 程嗣怡[2] 苟新禹[2] 

机构地区：[1]空军工程大学理学院,陕西西安710051 [2]空军工程大学航空航天工程学院,陕西西安710038

出　　处：《空军工程大学学报（自然科学版）》2012年第6期66-70,共5页Journal of Air Force Engineering University(Natural Science Edition)

基　　金：陕西省自然科学基础研究计划资助项目(2012JQ8019);陕西省电子信息系统综合集成重点实验室基金资助项目(201113Y01)

摘　　要：属性约简是粗糙集理论的核心问题之一,针对求取决策表所有决策约简集的NP问题,化繁为简将问题转化为对象动态增加下的决策约简求取问题。在深入分析了可辨识矩阵中可辨识集的特点及相互关系的基础上,优化改进决策辨识矩阵:①两对象之间不作逆向比较;②将决策可辨识矩阵列简化为属性等价类;③正域等价类作为决策可辨识矩阵的行,分情况给出了新决策表求取所有决策约简集的极小析取范式属性约简方法。该方法统一解决了相容和不相容决策表所有决策约简集的求取问题,最后通过实例分析验证了算法的可行性与有效性,为决策表的属性约简提供了一条高效的途径。Attribute reduction is a key problem in theoretical research of rough set. Aiming at the NP-hard problem of acquiring all decision reduction in decision table, the paper simplifies the problem to decision reduction computation in incremental object, The arithmetic of attribute reduction based on minimal dis- junctive normal form is respectively offered on the basis of analyzing the characteristic and correlation of discernibility set in discernibility matrix, in which the decision discernibility matrix is optimized by （1） o- mitting repeated contrast between the objects; （2） transforming the row of the decision discernibility matrix to the equivalent set; （3） treating the equivalent set of the positive field as the other row of the decision dis- cernibility matrix. The method offers a tool to uniformly acquire all decision reduction of consistent and in- consistent decision table. The example analysis shows this algorithm＇s feasibility and validity, which offers an effective way for attribute reduction.

关 键 词：粗糙集 属性约简 决策约简集 可辨识矩阵 极小析取范式 

分 类 号：TK401[动力工程及工程热物理—动力机械及工程]