Bases and intersection generation groups of polytomous knowledge structures

SUN Wen; LI Jinjin; LIN Yidong; HUANG Xiaoli

doi:10.16152/j.cnki.xdxbzr.2026-03-014

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Bases and intersection generation groups of polytomous knowledge structures

更新时间：2026-07-07

- Bases and intersection generation groups of polytomous knowledge structures
- Journal of Northwest University (Natural Science Edition) Vol. 56, Issue 3, Pages: 618-626(2026)
- 作者机构：
  
  1.闽南师范大学　数学与统计学院，福建　漳州　363000
  2.福建省粒计算及其应用重点实验室，福建　漳州　363000
- 作者简介：
- 基金信息：
- DOI：10.16152/j.cnki.xdxbzr.2026-03-014
  CLC： TP182
- Received：30 January 2026，
  
  Revised：2026-02-17，
  
  Published：25 June 2026
- 稿件说明：
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SUN Wen, LI Jinjin, LIN Yidong, et al. Bases and intersection generation groups of polytomous knowledge structures[J]. Journal of Northwest University (Natural Science Edition), 2026, 56(3): 618-626.
DOI：

SUN Wen, LI Jinjin, LIN Yidong, et al. Bases and intersection generation groups of polytomous knowledge structures[J]. Journal of Northwest University (Natural Science Edition), 2026, 56(3): 618-626. DOI： 10.16152/j.cnki.xdxbzr.2026-03-014.

摘要

在多分知识结构理论中，每个问题可以有不同的响应值，个体对问题的回答反映了个体对知识的理解水平。多分知识空间可由它的基来刻画，多分闭包空间可由其极小交式生成组来表示。问题不同响应值的多分知识空间的基由它的原子组成，而多分闭包空间的极小交式生成组由其所有交式生成子构成。基于问题不同响应值的多分知识结构对个体进行知识评价，可以通过测试部分问题评价出个体的多分知识状态，从而对个体进行学习指导。

Abstract

In polytomous KST

each item can be assigned a different response scale

and the individual’s answer to items reflects the individual’s understanding level of knowledge. The polytomous knowledge space can be described by its basis

and the polytomous closure space can be represented by its minimal intersection generation group. The basis of a polytomous knowledge space based on different response scales is composed of its atoms

while the minimal intersection generation group of a polytomous closure space is composed of all intersection generators. Based on polytomous knowledge structures of different response scales of items

the polytomous knowledge state of an individual can be evaluated in the finite steps of item tests. Based on polytomous knowledge structures of different response scales of items

the polytomous knowledge state of an individual can be evaluated by testing some items so as to guide learning of individuals.

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Keywords

references

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