Construction of partially-known formal concepts based on operations of formal contexts

TIAN Xue; REN Ruisi

doi:10.16152/j.cnki.xdxbzr.2024-02-007

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Construction of partially-known formal concepts based on operations of formal contexts

更新时间：2024-04-19

- Construction of partially-known formal concepts based on operations of formal contexts
- Journal of Northwest University (Natural Science Edition) Vol. 54, Issue 2, Pages: 209-219(2024)
- 作者机构：
  
  1.西北大学　数学学院，陕西　西安　710127
  2.西北大学　概念、认知与智能研究中心，陕西　西安　710127
- 作者简介：
- 基金信息：
- DOI：10.16152/j.cnki.xdxbzr.2024-02-007
  CLC： O29; TP18
- Published：25 April 2024，
  
  Received：15 September 2023，
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TIAN Xue, REN Ruisi. Construction of partially-known formal concepts based on operations of formal contexts. [J]. Journal of Northwest University (Natural Science Edition) 54(2):209-219(2024)
DOI：

TIAN Xue, REN Ruisi. Construction of partially-known formal concepts based on operations of formal contexts. [J]. Journal of Northwest University (Natural Science Edition) 54(2):209-219(2024) DOI： 10.16152/j.cnki.xdxbzr.2024-02-007.

摘要

概念是利用形式概念分析进行知识获取的基础。在不完备形式背景中，为了表达“一定具有”以及“可能具有”的关系，概念的外延或内涵通常以区间集的形式表达，称这样的概念为部分已知概念。由部分已知概念的定义可知，其本质与不完备背景的最小和最大完备化有关，因而考虑对最小和最大完备化背景进行运算来寻找部分已知概念。通过将不完备形式背景的最小完备化与最大完备化分别进行并置和叠置构造两个新背景，其概念格分别同构于SE-ISI概念格和ISE-SI概念格，从而提出了构建SE-ISI概念格和ISE-SI概念格的新方法。对于ISE-ISI概念，使用不完备形式背景的最小与最大完备化的直和运算构造了新的形式背景，基于此背景提出了寻找ISE-ISI概念的方法。

Abstract

Concepts are the foundation for knowledge acquisition through formal concept analysis. In incomplete formal contexts

in order to express "jointly must possessing (possessed)" and "jointly might possessing (possessed)" relationships

the extent or intent of concepts is usually expressed in the form of interval set. We refer to such concepts as partially-known formal concepts. From the definition of partially-known formal concepts

it can be seen that their essence is related to the least and greatest completions of incomplete formal contexts. Therefore

we consider performing operations on the least and greatest completions of incomplete formal contexts to find partially-known formal concepts. We construct two new formal contexts based on the apposition and subposition of the least and greatest completions. Their concept lattices are isomorphic to the SE-ISI concept lattice and the ISE-SI concept lattice

respectively. Therefore

the new methods for constructing SE-ISI concept lattice and ISE-SI concept lattice are proposed. For the ISE-ISI concept

we use direct sum operation of the least and greatest completions to construct a new formal context

and propose a method to search for the ISE-ISI concepts.

关键词

不完备形式背景部分已知概念并置叠置直和

Keywords

incomplete formal contextpartially-known formal conceptappositionsubpositiondirect sum

references

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