保持决策蕴涵不变的决策背景属性约简  

Decision Implication Preserving Attribute Reduction in Decision Context

作　　者：毕盛 翟岩慧[1,2] 李德玉[1,2] BI Sheng;ZHAI Yanhui;LI Deyu(School of Computer and Information Technology,Shanxi University,Taiyuan 030006,China;Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学计算机与信息技术学院,太原030006 [2]山西大学计算智能与中文信息处理教育部重点实验室,太原030006

出　　处：《计算机科学》2024年第7期89-95,共7页Computer Science

基　　金：国家自然科学基金(61972238,62072294)。

摘　　要：形式概念分析是一种利用概念格进行数据分析的理论,属性约简是概念格约简的主要方式之一。决策蕴涵是形式概念分析在决策情形下的一种知识表示与推理模型。在已有保持决策背景知识信息不变的属性约简研究中,通常以保持概念规则或粒规则来保持决策背景的知识信息。而相比于概念规则与粒规则,决策蕴涵具备更强的知识表示能力。为了进一步缩小数据在属性约简前后对知识信息表示的差异,对保持决策蕴涵不变的属性约简进行了研究。首先,结合决策蕴涵的语义给出了保持决策蕴涵不变的协调集和约简定义,提出了判定协调集和约简的充要条件;接着,通过实例分析了该约简存在的问题,并结合蕴涵理论给出解决方法,从而给出了弱协调集和弱约简的定义;然后,从知识包含的角度分析了弱约简相比于约简的合理性;最后,提出了判定弱协调集和弱约简的充要条件,并结合决策蕴涵规范基给出了能够找到弱约简的方法,丰富了保持知识信息的属性约简研究内容。Formal concept analysis is a theory of data analysis using concept lattice,and attribute reduction is one of the main ways of concept lattice reduction.Decision implication is a knowledge representation and reasoning model of formal concept analysis in decision situations.In the existing research on attribute reduction that preserves decision context knowledge information,concept rules or granular rules are usually used to preserve decision context knowledge information.Compared with concept rules and granular rules,decision implication has a stronger ability of knowledge representation.To further reduce the difference between the representation of knowledge information before and after attribute reduction,a study is conducted on attribute reduction which preserves decision implication.Firstly,based on the semantics of decision implication,the definitions of consistent set and reduction that preserve decision implication aregiven,and the necessary and sufficient conditions for determining consistent set and reduction are provided.Examples show the problems of the reduction,and by combining implication theory,the definitions of weak consistent set and weak reduction are introduced.Then,the rationality of weak reduction compared with reduction is analyzed from the perspective of knowledge inclusion.Finally,the necessary and sufficient conditions for judging weak consistent set and weak reduction are provided,and the method that can find weak reduction is given by combining decision implication canonical basis,which enriches the research of attribute reduction that preserves knowledge information.

关 键 词：形式概念分析 属性约简 决策蕴涵 知识表示模型 决策蕴涵规范基 

分 类 号：TP182[自动化与计算机技术—控制理论与控制工程]