不完备序信息系统的模型扩展及其属性约简  

Extension of rough set model and attribute reduction in incomplete ordered information system based on dominance relation

作　　者：莫京兰[1,2] 吕跃进[2] 李金海[3] 

机构地区：[1]广西科技大学鹿山学院基础教学部,柳州545616 [2]广西大学数学与信息科学学院,南宁530004 [3]昆明理工大学理学院,昆明650500

出　　处：《南京大学学报（自然科学版）》2015年第2期430-437,共8页Journal of Nanjing University（Natural Science）

基　　金：国家自然科学基金(61305057;71361002);广西高等学校立项科研项目(2013LX095;YB2014501)

摘　　要：粗糙集理论是一种处理不精确、不确定和不完备知识的有效数学工具.经典粗糙集是基于完备信息系统建立的,然而现实世界中不完备信息系统也是经常遇到的.因此,不完备序信息系统的粗糙集模型推广及其属性约简是基本的研究内容.对于有遗漏型的未知属性值的不完备序信息系统,广义扩展优势关系与限制扩展优势关系都不能合理比较论域中任意两个对象间的优势关系.针对这个缺点,基于属性值的概率分布原理,提出β优势关系及其粗糙集扩展模型;在此基础上,从矩阵角度给出基于β优势关系的近似约简的概念及约简方法.然后,通过实例分析表明β优势关系的有效性和优越性.最后,在UCI数据集上进行仿真实验,实验结果说明基于β优势关系的不完备序信息系统,可以获得更加合理的近似精度.Rough set theory is an effective mathematical tool to deal with inaccuracy,uncertainty,and incompleteness of knowledge.The classical rough set theory is based on complete information systems.However,incomplete information systems are frequently encountered in the real world.As a result,extension of rough set model and attribute reduction are basic issues for incomplete ordered information systems.For the incomplete ordered information systems with missing unknown attribute values,both the generalized extended dominance relation and limited extended dominance relation are not able to compare the dominance relationship of two objects.Motivated by this problem,β-dominance relation was proposed based on the probability distributions of attribute values.And then,we put forwardthe notion ofβ-dominance-relation-based relative reducts and their implementation method from the perspective of matrix.Furthermore,a real example was used to show the validity and advantages ofβ-dominance relation.Finally,we carry on the simulation experiments on UCI data sets,and simulation experiments were made to illustrate that more reasonable approximation accuracy can be obtained usingβ-dominance relation of the incomplete ordered information system.

关 键 词：粗糙集 不完备序信息系统 优势关系 概率分布 相对约简 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]