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              形式背景上近似推理生成決策蘊涵研究

              張家錄 吳霞

              張家錄, 吳霞. 形式背景上近似推理生成決策蘊涵研究. 自動化學報, xxxx, xx(x): x?xx doi: 10.16383/j.aas.c220705
              引用本文: 張家錄, 吳霞. 形式背景上近似推理生成決策蘊涵研究. 自動化學報, 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決策蘊涵研究

              doi: 10.16383/j.aas.c220705
              基金項目: 湖南省自然科學基金 (2020JJ4561, 2020JJ4381), 湖南省“信息和計算科學專業校企合作創新創業教育基地”資助
              詳細信息
                作者簡介:

                張家錄:湘南學院數學與信息科學學院教授. 主要研究方向為智能信息處理, 知識發現, 非經典數理邏輯與近似推理. E-mail: zjl0735@163.com

                吳霞:湘南學院數學與信息科學學院教授. 主要研究方向為智能信息處理, 非經典數理邏輯與近似推理. 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: 決策蘊涵分析是形式概念分析研究的重要方面, 基于形式背景獲取決策蘊涵、概念規則等知識是數據分析、機器學習的重要研究內容之一. 首先, 利用屬性邏輯語義對決策蘊涵的特性進行刻畫. 其次, 在經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, 數值實驗說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
                下載: 導出CSV

                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$1111101
                $u_2$0010010
                $u_3$1000011
                $u_4$0110100
                下載: 導出CSV

                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$110011101
                $u_2$001111110
                $u_3$101001001
                $u_4$010101100
                $u_5$010111110
                $u_6$101011011
                $u_7$011100111
                下載: 導出CSV

                表  4  生成的擬決策蘊涵個數

                Table  4  The number of generated quasi-decision implications

                數據組別生成的擬決策蘊涵個數
                數據組162
                數據組258
                數據組374
                數據組471
                下載: 導出CSV

                表  5  生成的擬決策蘊涵后件與后件合取式的偽距離

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

                數據組別最大偽距離最小偽距離
                數據組10.1950.147
                數據組20.1890.160
                數據組30.1970.152
                數據組40.1940.161
                下載: 導出CSV

                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數最小偽距離
                數據組130.0082
                數據組250.0157
                數據組380.0256
                數據組4120.0324
                數據組5160.0418
                數據組6210.0527
                數據組7250.0619
                數據組8290.0718
                數據組9340.0821
                數據組10390.0913
                下載: 導出CSV

                表  7  后件集對結論的支持度及獲取決策蘊涵時間消耗對比

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

                數據組別$L$的后件集對結論支持度$\tau_{\varDelta}$方式一消耗時間(s)方式二總消耗時間 (s)增量獲取所消耗時間(s)
                數據組10.9330.2040.2230.103
                數據組20.9230.2830.3040.147
                數據組30.9140.3610.3890.198
                數據組40.9030.4500.4840.258
                數據組50.8930.5390.2580.326
                下載: 導出CSV
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                        • 收稿日期:  2022-09-06
                        • 錄用日期:  2023-01-14
                        • 網絡出版日期:  2023-10-07

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