决策形式背景基于OE-协调性的属性约简  

Attribute reduction in formal decision contextsbased on OE-consistency

作　　者：常丽娜[1,2] 魏玲 彭超林[4] CHANG Lina;WEI Ling;PENG Chaolin(Department of Mathematics,Changzhi University,Changzhi 046011,China;Institute of Concepts,Cognition and Intelligence,Northwest University,Xi’an 710127,China;School of Mathematics,Northwest University,Xi’an 710127,China;Adam Smith Business School,University of Glasgow,Glasgow G128QQ,Scotland)

机构地区：[1]长治学院数学系,山西长治046011 [2]西北大学概念、认知与智能研究中心,陕西西安710127 [3]西北大学数学学院,陕西西安710127 [4]格拉斯哥大学亚当斯密商学院,苏格兰格拉斯哥G128QQ

出　　处：《西北大学学报（自然科学版）》2024年第2期188-196,共9页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金(12171392);长治学院科研项目(XJZZ2021013)。

摘　　要：属性约简作为形式概念分析中非常重要的一个研究分支,在三支概念分析中也同样重要。基于对象导出三支概念格,提出了保持决策形式背景OE-协调性的属性约简理论,丰富了三支概念分析的约简理论。首先,定义了决策形式背景的OE-协调集和OE-约简,并将属性按其特征分为3类。其次,指出OE-约简的本质就是极小OE-协调集,给出了OE-协调集的几个判定定理,通过研究OE-协调集的充要条件,获取OE-约简的判定定理。最后,给出OE-差别矩阵和OE-差别函数的定义,并给出了利用OE-差别矩阵和OE-差别函数计算OE-约简的方法。Attribute reduction,as a very important branch of formal concept analysis,is equally important in the three-way concept analysis.Based on object-induced concept lattices,attribute reduction theory which preserve OE-consistency of formal decision contexts is proposed,which enriches the reduction theory of three-way concept analysis.Firstly,OE-consistent set and OE-reduct of formal decision contexts are defined,and the attributes are classified into three categories according to their characteristics.Then,it is pointed out the essence of OE-reduct is minimal OE-consistent set,and several judgement theorems of OE-consistent set are given.By studying the necessary and sufficient conditions of OE-consistent set,judgement theorem of OE-reduct is obtained.Finally,the definition of OE-discernibility matrix and OE-discernibility function are given,and the method of calculating OE-reduct by using OE-discernibility matrix and OE-discernibility function is given.

关 键 词：三支概念分析 属性约简 OE-协调性 决策形式背景 对象导出三支概念格 

分 类 号：O29[理学—应用数学] TP18[理学—数学]