知识空间与简单拟阵的关系  

Relationship between knowledge space and simple matroid

作　　者：杨桃丽 周银凤 YANG Taoli;ZHOU Yinfeng(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2021年第3期30-38,共9页Journal of Minnan Normal University：Natural Science

摘　　要：知识空间理论是数学心理学的重要组成部分.简单拟阵是组合优化中的一个重要分支,几何格是拟阵论中的一个重要概念.知识空间理论与简单拟阵之间存在着紧密的联系.首先基于技能映射中技能与问题之间的联系确定知识基,通过知识基来生成简单拟阵的一个闭集族.其次定义了问题与技能的伽罗瓦联络,讨论知识空间的伽罗瓦格与简单拟阵闭集族的几何格之间的关系.随后在伽罗瓦格与几何格同构的意义下,以构造的方式建立起知识空间与简单拟阵的关系.最后得出了知识空间与简单拟阵是一一对应的结论 .Knowledge space theory is an important part of mathematical psychology.Simple matroid is an important branch of combinatorial optimization and geometric lattice is an important concept in matroid theory.There is a close relationship between knowledge space theory and simple matroid.Firstly,this paper determines the knowledge base based on the connection between skills and problems in a skill map,and generates a closed set family of simple matroids through knowledge base.Secondly,the Galois connection of problem and skill is defined,and the relationship between the Galois lattice of knowledge space and the geometric lattice of closed set family of simple matroids is discussed.Thirdly,in the sense of isomorphism between Galois lattice and geometric lattice,the relationship between knowledge space and simple matroid is constructed.Finally,it is concluded that knowledge space and simple matroid are one-to-one correspondence.

关 键 词：知识空间理论 简单拟阵 技能映射 知识基 伽罗瓦格 几何格 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] O14[自动化与计算机技术—控制科学与工程]