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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (1): 68-74.doi: 10.6040/j.issn.1671-9352.4.2020.156

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基于依赖空间的F-C变精度概念格

张静(),马建敏*()   

  1. 长安大学理学院, 陕西 西安 710064
  • 收稿日期:2020-06-15 出版日期:2021-01-01 发布日期:2021-01-05
  • 通讯作者: 马建敏 E-mail:jiing_z@126.com;cjm-zm@126.com
  • 作者简介:张静(1996—)，女，硕士研究生，研究方向为粗糙集与概念格. E-mail: jiing_z@126.com
  • 基金资助:
    国家自然科学基金资助项目(61772019);国家自然科学基金资助项目(61603278);国家自然科学基金资助项目(71701021)

F-C variable threshold concept lattices based on dependence spaces

Jing ZHANG(),Jian-min MA*()   

  1. School of Science, Chang'an University, Xi'an 710064, Shaanxi, China
  • Received:2020-06-15 Online:2021-01-01 Published:2021-01-05
  • Contact: Jian-min MA E-mail:jiing_z@126.com;cjm-zm@126.com

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摘要：

在模糊形式背景中, 首先基于变精度算子定义属性幂集上的一致关系, 引入依赖空间; 根据一致关系构造闭包算子, 研究闭包算子与变精度概念之间的关系; 进一步通过研究闭包算子的不动点和变精度概念的内涵之间的关系, 给出变精度概念格的构造算法; 最后通过实验验证本文方法的可行性。

关键词: 模糊形式背景, 依赖空间, 一致关系, 闭包算子

Abstract:

For a fuzzy formal context, a congruence relation is defined based on a variable precision operator on the power set of attributes. A congruence relation is obtained. Based on it, a dependence space is shown. By constructing a closure operator according to the congruence relation, the relationships between the closure operator and the variable precision concepts are discussed. Furthermore, applying the properties of the closure operator, we get that any fixed point of the closure operator is exactly the intension of some variable precision concept. Based on these, an algorithm to construct all variable precision concepts is obtained. Experiments are used to verify the feasibility of the proposed method.

Key words: fuzzy formal context, dependence space, congruence relation, closure operator

中图分类号: 

  • TP18

表1

模糊形式背景"

U a b c d e
x1 0.6 1.0 0.6 0.7 1.0
x2 0.7 0.8 1.0 0.8 0.5
x3 1.0 0.7 1.0 0.6 0.3
x4 1.0 0.6 0.9 1.0 0.2

表2

δ=1的F-C变精度概念内涵"

B 1 2 3 4
abcde 0.6 0.5 0.3 0.2
ac 0.6 0.7 1.0 0.9
be 1.0 0.5 0.3 0.2
ad 0.6 0.7 0.6 1.0
c 0.6 1.0 1.0 0.9
a 0.6 0.7 1.0 1.0
Ø 1.0 1.0 1.0 1.0

图1

δ为1.0、0.8、0.7时F-C变精度概念格"

表3

对象集增加, 属性集不变的算法运行时间对比(|A|=5)"

|U| 5 10 15 20 25
Algorithm in this paper 0.253 1.091 8.875 46.752 117.323
Original algorithm 0.527 7.169 34.893 106.605 319.498

表4

属性集增加, 对象集不变的算法运行时间对比(|U|=5)"

|A| 5 10 15 20 25
Algorithm in this paper 0.467 0.951 0.998 1.115 1.214
Original algorithm 0.625 6.362 37.214 124.872 356.699

图2

运行时间 红色折线为本文算法的运行时间, 蓝色折线为原始构建概念的算法运行时间。"

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