不协调决策形式背景的属性约简  

Attribute Reduction in Inconsistent Decision Formal Contexts

作　　者：李仲玲[1] 米据生[2,3] 解滨 LI Zhong-ling;MI Ju-sheng;XIE Bin(HuiHua College,Hebei Normal University,Shijiazhuang 050091,China;College of Mathematics and Information Science,Hebei Normal University,Shijiazhuang 050024,China;Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang 050024,China;Key Laboratory of Data Science and Intelligence Application,Fujian Province University,Zhangzhou,Fujian 363000,China)

机构地区：[1]河北师范大学汇华学院,石家庄050091 [2]河北师范大学数学与信息科学学院,石家庄050024 [3]河北省计算数学与应用重点实验室,石家庄050024 [4]数据科学与智能应用福建省高校重点实验室,福建漳州363000

出　　处：《计算机科学》2019年第12期257-260,共4页Computer Science

基　　金：国家自然科学基金(61573127);河北省自然科学基金项目(F2018205196);河北省高等学校自然科学基金项目(QN2016133)资助

摘　　要：形式概念分析由德国数学家Wille于1982年提出,是刻画概念和概念之间层次化结构的数据分析工具,主要用于概念的发现、排序和显示。作为知识发现的有效工具,该理论已被成功地运用到信息检索、数据挖掘、模式识别等领域。而在实际问题中呈现出的形式背景往往具有冗余的属性,使得所生成的概念格结构非常复杂。为了提取更加简洁有效的概念格,需要对形式背景中的属性进行约简。因此,寻找更高效的属性约简方法成为了形式概念分析中的一个重要研究问题。文中把基于粗糙集理论的属性约简思想引入到形式背景中,进一步研究不协调决策形式背景的属性约简问题。一些学者在不协调信息系统中基于等价类提出了分布约简、最大分布约简、分配约简、近似约简,并且讨论了4个约简之间的关系。而形式背景是一种特殊的信息系统,文中用粒集代替信息系统中的等价类,提出了4种基于包含度的属性约简,即分布约简、最大分布约简、分配约简与上近似和约简,并证明了分布协调集必为最大分布协调集,分布协调集必为分配协调集,分配协调集与上近似和协调集等价等结论。最后以分配约简为例,给出了分配协调集的判定定理,构建了不同粒集之间的可辨识属性集合,得到了求解分配约简的布尔计算方法。Formal concept analysis was proposed by Wille R.in 1982.It is a model for the study of formal concepts and conceptual hierarchies.As an effective tool in knowledge discovery,it has been applied in various research areas such as information retrieval,data mining and pattern recognition.In practical applications,there may be a lot of redundant attributes in the formal context.Therefore,it is necessary to study the attribute reduction in formal concept analysis,and finding more concise approaches of attribute reduction is an important aspect in formal contexts.In this paper,inspired by the idea of rough set theory,attribute reduction in inconsistent decision formal contexts was studied.Some scholars proposed four definitions of distribution reduction,maximum distribution reduction,assignment reduction,and approximation reduction based on equivalency class in inconsistent information systems.As a formal context is a special information system,in this paper,substituting the equivalency class by the granular set,four new definitions of distribution reduction,maximum distribution reduction,assignment reduction,and upper approximation reduction based on inclusion degree were proposed.It is proved that the distribution reduction must be the maximum distribution reduction,the distribution reduction must be the assignment reduction,and the assignment reduction is equivalent to the upper approximation reduction.As an example,the judgement theorem for assignment consistent set was proved,and Boolean method for assignment reduction were given.

关 键 词：辨识矩阵 协调集 属性约简 决策形式背景 

分 类 号：O29[理学—应用数学]