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形式背景上近似推理生成决策蕴涵研究

张家录 吴霞

张家录, 吴霞. 形式背景上近似推理生成决策蕴涵研究. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c220705
引用本文: 张家录, 吴霞. 形式背景上近似推理生成决策蕴涵研究. 自动化学报, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c220705
Zhang Jia-Lu, Wu Xia. Study on the approximate reasoning models of decision implication in formal decision context and its application. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c220705
Citation: Zhang Jia-Lu, Wu Xia. Study on the approximate reasoning models of decision implication in formal decision context and its application. Acta Automatica Sinica, xxxx, xx(x): x−xx doi: 10.16383/j.aas.c220705

形式背景上近似推理生成决策蕴涵研究

doi: 10.16383/j.aas.c220705
基金项目: 湖南省自然科学基金 (2020JJ4561, 2020JJ4381), 湖南省“信息和计算科学专业校企合作创新创业教育基地”资助
详细信息
    作者简介:

    张家录:湘南学院数学与信息科学学院教授. 主要研究方向为智能信息处理, 知识发现, 非经典数理逻辑与近似推理. E-mail: zjl0735@163.com

    吴霞:湘南学院数学与信息科学学院教授. 主要研究方向为智能信息处理, 非经典数理逻辑与近似推理. 本文通信作者. E-mail: wuxia351@163.com

Study on the Approximate Reasoning Models of Decision Implication in Formal Decision Context and Its Application

Funds: Supported by Natural Science Foundation of Hunan Province under Grant (2020JJ4561, 2020JJ4381), “Information and Computing Science University-enterprise Cooperation Innovation and Entrepreneurship Education Base” of Hunan Province
More Information
    Author Bio:

    ZHANG Jia-Lu Professor at College of Mathematics and Information Science, Xiangnan University. His research interest covers intelligent information processing, knowledge discovery, nonclassical mathematical logic and approximate reasoning

    WU Xia Professor at College of Mathematics and Information Science, Xiangnan University. His research interest covers intelligent information processing, nonclassical mathematical logic and approximate reasoning. Corresponding author of this paper

  • 摘要: 决策蕴涵分析是形式概念分析研究的重要方面, 基于形式背景获取决策蕴涵、概念规则等知识是数据分析、机器学习的重要研究内容之一. 首先, 利用属性逻辑语义对决策蕴涵的特性进行刻画. 其次, 在经典二值逻辑框架下分析决策蕴涵、概念规则的基于全蕴涵三I推理思想及分离规则 (Modus Ponens, MP) 和逆分离规则 (Modus Tonens, MT) 的近似推理模式的特征, 证明决策蕴涵的MP、MT近似推理结论是决策蕴涵, 概念规则的MP、MT近似推理结论是概念规则等结论. 引进属性逻辑公式的伪距离, 在属性逻辑伪距离空间中分析推理对象范围参数变化对决策蕴涵MP、MT近似推理结论的影响. 最后, 提出若干通过MP、MT近似推理生成决策蕴涵、概念规则及拟决策蕴涵的模式和方法, 数值实验说明所提出的方法是有效的.
  • 表  1  形式背景$K=(G,M,I)$

    Table  1  A formal context $K=(G,M,I)$

    $G$$a_1$$a_2$$a_3$$a_4$$a_5$
    $u_1$11001
    $u_2$00110
    $u_3$10100
    $u_4$01010
    $u_5$01011
    $u_6$10101
    下载: 导出CSV

    表  2  决策形式背景$K=(G,C,D,I,J)$

    Table  2  A formal decision context $K=(G,C,D,I,J)$

    $G$$a_1$$a_2$$a_3$$a_4$$d_1$$d_2$$d_3$
    $u_1$1111101
    $u_2$0010010
    $u_3$1000011
    $u_4$0110100
    下载: 导出CSV

    表  3  决策形式背景$K=(G,C,D,I,J)$

    Table  3  A formal decision context $K=(G,C,D,I,J)$

    $G$$a_1$$a_2$$a_3$$a_4$$a_5$$a_6$$d_1$$d_2$$d_3$
    $u_1$110011101
    $u_2$001111110
    $u_3$101001001
    $u_4$010101100
    $u_5$010111110
    $u_6$101011011
    $u_7$011100111
    下载: 导出CSV

    表  4  生成的拟决策蕴涵个数

    Table  4  The number of generated quasi-decision implications

    数据组别生成的拟决策蕴涵个数
    数据组162
    数据组258
    数据组374
    数据组471
    下载: 导出CSV

    表  5  生成的拟决策蕴涵后件与后件合取式的伪距离

    Table  5  The metric between the consequent of generated quasi-decision implication and the consequent conjunctive

    数据组别最大伪距离最小伪距离
    数据组10.1950.147
    数据组20.1890.160
    数据组30.1970.152
    数据组40.1940.161
    下载: 导出CSV

    表  6  测试数据变化生成的拟决策蕴涵表

    Table  6  A table of generated quasi-decision implication as test data changes

    数据组别拟决策蕴涵数最小伪距离
    数据组130.0082
    数据组250.0157
    数据组380.0256
    数据组4120.0324
    数据组5160.0418
    数据组6210.0527
    数据组7250.0619
    数据组8290.0718
    数据组9340.0821
    数据组10390.0913
    下载: 导出CSV

    表  7  后件集对结论的支持度及获取决策蕴涵时间消耗对比

    Table  7  The comparison of the support degree of consequent set to the conclusion an d time consumption of obtaining decision implications

    数据组别$L$的后件集对结论支持度$\tau_{\varDelta}$方式一消耗时间(s)方式二总消耗时间 (s)增量获取所消耗时间(s)
    数据组10.9330.2040.2230.103
    数据组20.9230.2830.3040.147
    数据组30.9140.3610.3890.198
    数据组40.9030.4500.4840.258
    数据组50.8930.5390.2580.326
    下载: 导出CSV
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  • 收稿日期:  2022-09-06
  • 录用日期:  2023-01-14
  • 网络出版日期:  2023-10-07

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