基于概念约简的概念格还原

赵思雨; 魏玲

doi:10.16152/j.cnki.xdxbzr.2026-01-014

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基于概念约简的概念格还原

粗糙集与形式概念分析中的约简研究 | 更新时间：2026-02-24

- 基于概念约简的概念格还原
- Concept lattice restoration based on concept reducts
- 西北大学学报（自然科学版） 2026年56卷第1期页码：151-158
- 作者机构：
  
  1.西北大学　数学学院，陕西　西安　710127
  2.咸阳师范学院　数学与统计学院，陕西　咸阳　712000
- 作者简介：
  
  赵思雨，女，博士研究生，讲师，从事形式概念分析等研究，418589952@qq.com。
  魏玲，女，教授，博士生导师，从事形式概念分析、粒计算、三支决策理论研究，wl@nwu.edu.cn。
- 基金信息：
  
  国家自然科学基金(12171392);陕西数理基础科学研究项目(23JSZ008);陕西省教育厅专项科研计划项目(25JK0721)
- DOI：10.16152/j.cnki.xdxbzr.2026-01-014
  中图分类号： O29;TP18
- 收稿：2025-07-15，
  
  修回：2025-08-20，
  
  纸质出版：2026-02-25
- 稿件说明：
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赵思雨, 魏玲. 基于概念约简的概念格还原[J]. 西北大学学报（自然科学版）, 2026,56(1):151-158.

ZHAO Siyu, WEI Ling. Concept lattice restoration based on concept reducts[J]. Journal of Northwest University (Natural Science Edition), 2026, 56(1): 151-158.
赵思雨, 魏玲. 基于概念约简的概念格还原[J]. 西北大学学报（自然科学版）, 2026,56(1):151-158. DOI： 10.16152/j.cnki.xdxbzr.2026-01-014.

ZHAO Siyu, WEI Ling. Concept lattice restoration based on concept reducts[J]. Journal of Northwest University (Natural Science Edition), 2026, 56(1): 151-158. DOI： 10.16152/j.cnki.xdxbzr.2026-01-014.

摘要

探讨基于概念约简的概念格还原方法。首先，通过建立概念约简子集与概念格交不可约概念的联系，揭示概念约简与交不可约概念集的关系，进而提出对概念约简中形式概念先求上确界后求下确界来还原概念格的方法。对偶地，通过建立概念约简与并不可约概念集的关系，提出对概念约简中形式概念先求下确界后求上确界的概念格还原方法。研究表明，概念约简可用部分形式概念还原概念格，因此可有效压缩和储存概念格的基本信息，为概念约简提供实际意义和潜在应用价值。

Abstract

The concept lattice restoration methods are investigated through concept reducts. First

the relationship between subsets of concept reducts and meet-irreducible concepts is established

thereby revealing the connection between concept reducts and meet-irreducible concept sets. Based on this foundation

a concept lattice restoration method is proposed in which supremums are first computed

followed by infimums

for formal concepts in concept reducts. Dually

an alternative restoration approach is presented in which infimums are first computed

then supremums. It is demonstrated that concept lattices can be restored by concept reducts using partial formal concepts

thereby achieving effective compression and storage of lattice information. This provides practical significance and potential application value for concept reduction.

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references

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