[1]包研科,汪培庄,郭嗣琮.因素空间的结构与对偶回旋定理[J].智能系统学报,2018,13(4):656-664.[doi:10.11992/tis.201706057]
BAO Yanke,WANG Peizhuang,GUO Sicong.Structure of factor space and the dual convolution theorem[J].CAAI Transactions on Intelligent Systems,2018,13(4):656-664.[doi:10.11992/tis.201706057]
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BAO Yanke,WANG Peizhuang,GUO Sicong.Structure of factor space and the dual convolution theorem[J].CAAI Transactions on Intelligent Systems,2018,13(4):656-664.[doi:10.11992/tis.201706057]
因素空间的结构与对偶回旋定理
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
13
期数:
2018年第4期
页码:
656-664
栏目:
学术论文—人工智能基础
出版日期:
2018-07-05
- Title:
- Structure of factor space and the dual convolution theorem
- Keywords:
- factor space; structure; staggered automorphism transform; convolution lattice; dual convolution theorem
- 分类号:
- TP18;O29
- 摘要:
- 基于概念的内涵与外延的对合性与反变关系，以及概念形成过程中概括与解析的辩证统一性，深入讨论了因素空间的数学结构问题。系统梳理了由认知本体论原理构造出的因素空间的基本概念与核心命题，为基于因素空间的知识发现理论与技术的研究提供了一种新的思想框架。首次提出了格上的交错自同构变换与回旋格的概念，证明了因素空间上的对偶回旋定理，揭示出因素空间数学结构的几何表象是一个麦乌比斯环，为阐释人类思维与概念形成过程的动力学机制提供了一个新的数学模型。
- Abstract:
- Based on two expressions consistency and the reverse-change relation of conceptual connotation and extension, as well as the dialectical unity of summary and parsing in the concept formation process, in this paper, we present a detailed discussion of the mathematical structure of factor space. We systematically identify the basic concepts and core propositions of factor space, as constructed by the principle of cognitive ontology, and provide a new ideological framework for both the theoretical and technological research of knowledge discovery based on factor space. We propose novel concepts related to the staggered automorphism transform and the convolution lattice, prove the dual entanglement theorem of factor space, and introduce a geometrical representation of the mathematical structure of factor space as a Mobius strip, thereby establishing a new mathematical model for illustrating the dynamics mechanism of the formation of human thinking and conceptualization.
- 参考文献/References:
-
[1] 汪培庄, SUGENO M. 因素场与模糊集的背景结构[J]. 模糊数学, 1982(2):45-54. WANG Peizhuang, SUGENO M.. The factors field and background structure for fuzzy set[J]. Fuzzy math, 1982(2):45-54.
[2] 李仲来. 模糊数学与优化-汪培庄文集(北京师范大学数学家文库)[M]. 北京:北京师范大学出版社, 2013.
[3] 汪培庄, 李洪兴. 知识表示的数学理论[M]. 天津:天津科学技术出版社, 1994.
[4] 汪培庄, 李洪兴. 模糊系统理论与模糊计算机[M]. 北京:科学出版社, 1995.
[5] 李洪兴. 因素空间理论与知识表示的数学框架(Ⅰ)——因素空间的公理化定义与描述架[J]. 北京师范大学学报:自然科学版, 1996, 32(4):470-475. LI Hongxing. Factor spaces and mathematical frame of knowledge representation (Ⅰ)——axiomatic definition of factor spaces and description frame[J]. Journal of Beijing normal university:natural science, 1996, 34(4):470-475.
[6] 袁学海, 汪培庄. 因素空间中的一些数学结构[J]. 模糊系统与数学, 1993, 7(1):45-54. YUAN Xuehai, WANG Peizhuang. Some mathematical structures in factor spaces[J]. Fuzzy Systems and Mathematics, 1993, 7(1):45-54.
[7] 袁学海, 汪培庄. 因素空间和范畴[J]. 模糊系统与数学, 1995, 9(2):25-33. YUAN Xuehai, WANG Peizhuang. Factor spaces and categories[J]. Fuzzy systems and mathematics, 1995, 9(2):25-33.
[8] 赵宝江, 张型岱, 袁学海, 等. 集合套范畴的研究[J]. 模糊系统与数学, 2002, 16(1):29-35. ZHAO Baojiang, ZHANG Xingdai, YUAN Xuehai, et al. Study on the category of nested sets[J]. Fuzzy Systems and Mathematics, 2002, 16(1):29-35.
[9] 刘增良, 刘有才. 因素神经网络理论及其应用[M]. 北京:北京师范大学, 1994.
[10] 郭春霞, 刘增良, 陶源, 等. 虚拟网络攻防分析模型[J]. 计算机工程与应用, 2008, 44(25):100-103. GUO Chunxia, LIU Zengliang, TAO Yuan, et al. Virtual internet offensive and defensive analysis model[J]. Computer engineering and applications, 2008, 44(25):100-103.
[11] 郭春霞, 刘增良, 张智南, 等. 网络攻击知识因素空间模型[J]. 电讯技术, 2009, 49(10):11-14. GUO Chunxia, LIU Zengliang, ZHANG Zhinan, et al. Network attack knowledge model based on factor space theory[J]. Telecommunication Engineering, 2009, 49(10):11-14.
[12] 郭春霞, 刘增良, 苗青. 网络攻击规划模型及其生成算法[J]. 计算机工程与应用, 2010, 46(31):121-123. GUO Chunxia, LIU Zengliang, MIAO Qing. Network attack planning model and its generating algorithm[J]. Computer engineering and applications, 2010, 46(31):121-123.
[13] 张友春, 魏强, 刘增良, 等. 信息系统漏洞挖掘技术体系研究[J]. 通信学报, 2011, 32(2):42-47. ZHANG Youchun, WEI Qiang, LIU Zengliang, et al. Architecture of Vulnerability Discovery Technique for Information Systems[J]. Journal on communications, 2011, 32(2):42-47.
[14] 王靳辉. 因素空间与诊断型专家系统[J]. 解放军测绘学院学报, 1993(1):71-74. WANG Jinhui. Facts space and a expert system of diagnose[J]. Journal of the PLA surveying and mapping, 1993(1):71-74.
[15] 于福生. 反向推理型诊断问题专家系统通用构建模型[J]. 系统工程理论与实践, 1998, 18(5):72-77. YU Fusheng. A general model for building diagnostic expert systems based on backwards reasoning[J]. Systems engineering-theory & practice, 1998, 18(5):72-77.
[16] 石岩, 马宝华, 谭惠民. 基于因素空间的多传感器决策融合方法[J]. 北京理工大学学报, 2000, 20(1):85-89. SHI Yan, MA Baohua, TAN Huimin. Multitarget decision fusion method based on fuzzy factor spaces[J]. Journal of Beijing institute of technology, 2000, 20(1):85-89.
[17] 吉君, 江青茵, 曹志凯. 啤酒发酵过程的多变量开关控制仿真研究[J]. 厦门大学学报:自然科学版, 2005, 44(2):246-249. JI Jun, JIANG Qingyin, CAO Zhikai. Simulation of multivariable on-off temperature control system in beel fermentation process[J]. Journal of Xiamen university:natural science, 2005, 44(2):246-249.
[18] 岳磊, 孙永刚, 史海波, 等. 基于因素空间的规则调度决策模型[J]. 信息与控制, 2010, 39(3):302-307. YUE Lei, SUN Yonggang, SHI Haibo, et al. Rule-based scheduling decision-making model based on factor spaces[J]. Information and control, 2010, 39(3):302-307.
[19] 张敏, 宋衍博, 江青茵, 等. 基于因素空间变权理论的开关控制仿真研究[J]. 厦门大学学报:自然科学版, 2012, 51(4):671-675. ZHANG Min, SONG Yanbo, JIANG Qingyin, et al. Simulation of on-off control based on the factor space and variable weight theory[J]. Journal of Xiamen university:natural science, 2012, 51(4):671-675.
[20] 于福生, 罗承忠. 基于因素空间理论的故障诊断数学模型及其应用[J]. 模糊系统与数学, 1990, 13(1):47-53. YU Fusheng, LUO Chengzhong. A mathematical model of diagnostic problem based on factors space theory and it’s application[J]. Fuzzy system and mathematics, 1990, 13(1):47-53.
[21] 米洪海, 闫广霞, 于新凯, 等. 基于因素空间的多层诊断识别问题的数学模型[J]. 河北工业大学学报, 2003, 32(2):77-80. MI Honghai, YAN Guangxia, YU Xinkai, et al. The Mathematical Model of Multi-layer Diagnosis-type Recognition Problem[J]. Journal of Hebei university of technology, 2003, 32(2):77-80.
[22] 董学军, 陈英武. 基于补偿和不可替代因素合成的人因可靠性分析方法[J]. 系统工程理论与实践, 2012, 32(9):2087-2094. DONG Xuejun, CHEN Yingwu. Method of human reliability analysis based on CSICF[J]. Systems engineering-theory & practice, 2012, 32(9):2087-2094.
[23] 崔铁军, 马云东. 基于因素空间的煤矿安全情况区分方法的研究[J]. 系统工程理论与实践, 2015, 35(11):2891-2897. CUI Tiejun, MA Yundong. Research on the Classification Method about Coal Mine Safety Situation Based on the Factor Space[J]. Systems engineering-theory & practice, 2015, 35(11):2891-2897.
[24] 赵梦辉. 基于因素空间的油气SCADA系统信息安全评价方法研究[D]. 成都:西南石油大学, 2016. ZHAO Menghui. Research on information security evaluation of oil and gas SCADA system based on factor spaces[D]. Chengdu:Southwest Petroleum University, 2016.
[25] 何清, 童占梅. 基于因素空间和模糊聚类的概念形成方法[J]. 系统工程理论与实践, 1999, 19(8):99-104. HE Qing, TONG Zhanmei. The concept formation method based on factor spaces and fuzzy clustering[J]. Systems engineering-theory & practice, 1999, 19(8):99-104.
[26] 汪培庄. 因素空间与因素库[J]. 辽宁工程技术大学学报:自然科学版, 2013, 32(10):1297-1304. WANG Peizhuang. Factor spaces and factor data-bases[J]. Journal of Liaoning technical university:Natural Science, 2013, 32(10):1297-1304.
[27] 汪培庄. 因素空间与数据科学[J]. 辽宁工程技术大学学报:自然科学版, 2015, 34(2):273-280. WANG Peizhuang. Factor spaces and data science[J]. Journal of Liaoning technical university:natural science, 2015, 34(2):273-280.
[28] 汪培庄, 郭嗣琮, 包研科, 等. 因素空间中的因素分析法[J]. 辽宁工程技术大学学报:自然科学版, 2014, 33(7):865-870. WANG Peizhuang, GUO Sicong, BAO Yanke, et al. Causality analysis in factor spaces[J]. Journal of Liaoning technical university:natural science, 2014, 33(7):865-870.
[29] 包研科, 茹慧英, 金圣军. 因素空间中知识挖掘的一种新算法[J]. 辽宁工程技术大学学报:自然科学版, 2014, 33(8):1141-1144. BAO Yanke, RU Huiying, JIN Shengjun. A new algorithm of knowledge mining in factor space[J]. Journal of Liaoning Technical University:Natural Science, 2014, 33(8):1141-1144.
[30] 李兆钧. 因素空间理论在文本挖掘中的应用[D]. 广州: 广州大学, 2016. LI Zhaojun. The application of factor spaces theory in text mining[D]. Guangzhou:Guangzhou University, 2016.
[31] 刘影. 面向领域的隐性政策血缘关系挖掘方法研究[D]. 哈尔滨:哈尔滨工程大学, 2013. Liu Ying. Research on domain-oriented recessive policy lineage mining method[D]. Harbin:Harbin Engineering University, 2013.
[32] 崔铁军, 李莎莎, 王来贵. 基于因素逻辑的分类推理法重构[J]. 计算机应用研究, 2016, 33(12):3671-3675. CUI Tiejun, LI Shasha, WANG Laigui. Classification reasoning method reconstruction based on factors logic[J]. Application research of computers, 2016, 33(12):3671-3675.
[33] 刘思圆. 因素空间的扩展定义[J]. 教育教学论坛. 2016(10):194-195. LIU Siyuan. The extension definition of the factor space[J]. Education teaching forum, 2016(10):194-195.
[34] 包研科. 认知本体论视角下因素空间的性质与对偶空间[J]. 模糊系统与数学, 2016, 30(10):127-136. BAO Yanke. The property of the factor space and the dual space in perspective of the cognitive ontology[J]. Fuzzy systems and mathematics, 2016, 30(2):127-136.
[35] 冯嘉礼. 思维与智能科学中的性质论方法[M]. 北京:原子能出版社, 1990. FENG Jiali. A Theory of nature method of thinking and intelligence science[M]. Beijing:Atomic Energy Press, 1990.
[36] 刘海涛, 郭嗣琮, 戴宁, 等. 因素空间与形式概念分析及粗糙集的比较[J]. 辽宁工程技术大学学报:自然科学版, 2017, 36(3):324-330. LIU Haitao, GUO Sicong, DAI Ning, et al. Comparative study for factor space, formal concept analysis and rough sets[J]. Journal of Liaoning technical university:natural science, 2017, 36(3):324-330.
[37] 佩捷, 王兰新. 从麦比乌斯到陈省身——麦比乌斯变换与麦比乌斯带[M]. 哈尔滨:哈尔滨工业大学出版社, 2014.
[38] 周才军. M?bius交错偏序集[J]. 上海师范大学学报:自然科学版, 1995, 24(2):17-22. ZHOU Caijun. Alternate M?bius posets[J]. Journal of Shanghai teachers university:natural science, 1995, 24(2):17-22.
[39] 邱懿. M?bius交错偏序集[J]. 数学年刊A辑, 2002, 23(5):643-648. QIU Yi. Posets with M?bius function alternating in sign[J]. Chinese annals of mathematics, 2002, 23(5):643-648. (请核对英文刊名)
[40] 霍丽芳, 赵丽娟, 丁萌, 等. 有限偏序集上格的M?bius函数和特征多项式[J]. 数学的实践与认识, 2015, 45(18):303-306. HUO Lifang, ZHAO Lijuan, DING Meng, et al. M?bius functions and characteristic polynomial in the finite lattices[J]. Mathematics in practice and theory, 2015, 45(18):303-306.
[41] NIELSEN M A, CHUANG I L. 量子计算和量子信息(一):量子计算部分[M]. 北京:清华大学出版社, 2004.
[42] NIELSEN M A, CHUANG I L. 量子计算和量子信息(二):量子信息部分[M]. 北京:清华大学出版社, 2005.
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备注/Memo
收稿日期:2017-06-16。
基金项目:国家自然科学基金项目（71371091）；中国工程院2017年重点咨询项目（2017-XZ-23）.
作者简介:包研科,男,1962年生,副教授,主要研究方向为工程数据分析、统计预测与决策、统计机器学习以及基于因素空间的知识发现理论与应用。发表学术论文20余篇,出版著作3部;汪培庄,男,1936年生,教授,博士生导师,主要研究方向为模糊数学和人工智能的理论与应用,创立模糊落影表示、真值流推论和因素空间理论,近年主要关注因素空间在人工智能和数据科学中的应用。获国家级奖励多项和国际奖项1项。发表学术论文200余篇,出版著作多部;郭嗣琮,男,1951年生,教授,博士生导师,国家政府特殊津贴获得者,主要研究方向为模糊数学、模糊预测与决策技术以及模糊运筹学理论与应用,创立了基于模糊结构元方法的模糊值函数分析学理论。发表学术论文200余篇,出版著作3部。
通讯作者:包研科.E-mail:baoyanke_9257@163.com.
更新日期/Last Update:
2018-08-25