形式背景上近似推理生成決策蘊涵研究
doi: 10.16383/j.aas.c220705 cstr: 32138.14.j.aas.c220705
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湘南學(xué)院數學(xué)與信息科學(xué)學(xué)院 郴州 423000
基金項目: 湖南省自然科學(xué)基金(2020JJ4561, 2020JJ4381), 湖南省信息和計算科學(xué)專(zhuān)業(yè)校企合作創(chuàng )新創(chuàng )業(yè)教育基地(2020-301)資助
Study on the Approximate Reasoning Models of Decision Implication in Formal Decision Context
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College of Mathematics and Information Science, Xiangnan University, Chenzhou 423000
Funds: Supported by Natural Science Foundation of Hunan Province (2020JJ4561, 2020JJ4381) and Information and Computing Science University-enterprise Cooperation Innovation and Entrepreneurship Education Base of Hunan Province (2020-301)
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摘要: 基于形式背景獲取決策蘊涵、概念規則等知識是數據分析、機器學(xué)習的重要研究?jì)热葜? 首先, 利用屬性邏輯語(yǔ)義對決策蘊涵的特性進(jìn)行刻畫(huà). 其次, 在經(jīng)典二值邏輯框架下分析決策蘊涵、概念規則的基于全蘊涵三I推理思想及分離規則(Modus ponens, MP)和逆分離規則(Modus tonens, MT)的近似推理模式的特征, 證明決策蘊涵的MP、MT近似推理結論是決策蘊涵, 概念規則的MP、MT近似推理結論是概念規則等結論. 引進(jìn)屬性邏輯公式的偽距離, 在屬性邏輯偽距離空間中分析推理對象范圍參數變化對決策蘊涵MP、MT近似推理結論的影響. 最后, 提出若干通過(guò)MP、MT近似推理生成決策蘊涵、概念規則及擬決策蘊涵的模式和方法, 數值實(shí)驗驗證了所提方法的有效性.Abstract: It is one of the contents of data analysis and machine learning to obtain the knowledge of decision implication and conceptual rule from formal decision context. Firstly, attribute logic semantics is used to analyze the characteristics of decision implication. Secondly, in the classical binary logic framework, the characteristics of modus ponens (MP) and modus tonens (MT) approximate reasoning models based on the all implication three-I inference idea is analyzed. It is proved that the MP and MT approximate reasoning conclusions of decision implications are decisions implications, the MP and MT approximate reasoning conclusions of concept rules are concept rules. The pseudo-metric of attribute logic formula is introduced, and the influence of MP and MT approximate reasoning conclusions of decision implication as the reasoning object range parameter changes in attribute logic pseudo-metric space is analyzed. Finally, some models and methods of generating decision implication, concept rules and quasi-decision implication through MP and MT approximate reasoning based on existing decision implication, concept rules and quasi-decision implication are proposed, numerical experiments show that the proposed methods are effective.
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表 1 形式背景$K=(G,M,I)$
Table 1 A formal context $K=(G,M,I)$
$G$ $a_1$ $a_2$ $a_3$ $a_4$ $a_5$ $u_1$ 1 1 0 0 1 $u_2$ 0 0 1 1 0 $u_3$ 1 0 1 0 0 $u_4$ 0 1 0 1 0 $u_5$ 0 1 0 1 1 $u_6$ 1 0 1 0 1 
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表 2 決策形式背景$K=(G,C,D,I,J)$
Table 2 A formal decision context $K=(G,C,D,I,J)$
$G$ $a_1$ $a_2$ $a_3$ $a_4$ $d_1$ $d_2$ $d_3$ $u_1$ 1 1 1 1 1 0 1 $u_2$ 0 0 1 0 0 1 0 $u_3$ 1 0 0 0 0 1 1 $u_4$ 0 1 1 0 1 0 0
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表 3 決策形式背景$K=(G,C,D,I,J)$
Table 3 A formal decision context $K=(G,C,D,I,J)$
$G$ $a_1$ $a_2$ $a_3$ $a_4$ $a_5$ $a_6$ $d_1$ $d_2$ $d_3$ $u_1$ 1 1 0 0 1 1 1 0 1 $u_2$ 0 0 1 1 1 1 1 1 0 $u_3$ 1 0 1 0 0 1 0 0 1 $u_4$ 0 1 0 1 0 1 1 0 0 $u_5$ 0 1 0 1 1 1 1 1 0 $u_6$ 1 0 1 0 1 1 0 1 1 $u_7$ 0 1 1 1 0 0 1 1 1
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表 4 生成的擬決策蘊涵個(gè)數
Table 4 The number of generated quasi-decision implications
數據組別 生成的擬決策蘊涵個(gè)數 數據組1 62 數據組2 58 數據組3 74 數據組4 71
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表 5 生成的擬決策蘊涵后件與后件合取公式的偽距離
Table 5 The pseudo-metric between the consequent of generated quasi-decision implications and the consequent conjunctive
數據組別 最大偽距離 最小偽距離 數據組1 0.195 0.147 數據組2 0.189 0.160 數據組3 0.197 0.152 數據組4 0.194 0.161
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表 6 測試數據變化生成的擬決策蘊涵表
Table 6 A table of generated quasi-decision implication as test data changes
數據組別 擬決策蘊涵個(gè)數 最小偽距離 數據組1 3 0.0082 數據組2 5 0.0157 數據組3 8 0.0256 數據組4 12 0.0324 數據組5 16 0.0418 數據組6 21 0.0527 數據組7 25 0.0619 數據組8 29 0.0718 數據組9 34 0.0821 數據組10 39 0.0913
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表 7 后件集對結論的支持度和獲取擬決策蘊涵時(shí)間成本對比
Table 7 Comparison of the support degree of consequent set to the conclusion and time consumption of obtaining quasi-decision implications
數據組別 $L$的后件集對結論支持度$\tau_{\Delta}$ 方式1)總時(shí)間成本(s) 方式2)總時(shí)間成本 (s) 增量獲取所用時(shí)間成本(s) 數據組1 0.933 0.204 0.223 0.103 數據組2 0.923 0.283 0.304 0.147 數據組3 0.914 0.361 0.389 0.198 數據組4 0.903 0.450 0.484 0.258 數據組5 0.893 0.539 0.258 0.326
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