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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (2): 1-29.doi: 10.6040/j.issn.1671-9352.0.2018.698

• •    

大数据结构-逻辑特征与大数据规律

史开泉   

  1. 山东大学数学学院, 山东 济南 250100
  • 发布日期:2019-02-25
  • 作者简介:史开泉(1945— ), 男, 教授, 博士生导师, 研究方向为数据智能系统理论与应用. E-mail:shikq@sdu.edu.cn
  • 基金资助:
    山东省自然科学基金资助项目(zr2013aq019);福建省自然科学基金资助项目(2015J05010)

Big data structure-logic characteristics and big data law

SHI Kai-quan   

  1. School of Mathematics, Shandong University, Jinan 250100, Shandong, China
  • Published:2019-02-25

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摘要： P-集合、逆P-集合是把动态特征引入到有限普通元素集合X内,改进有限普通元素集合X得到的两个模型,利用P-集合、逆P-集合与它们的动态特征、逻辑特征分别给出具有属性合取扩展-收缩特征的∧型大数据结构与生成、具有属性析取扩展-收缩特征的∨型大数据结构与生成、∧型大数据与∨型大数据混合的∧-∨型大数据结构与生成;给出大数据融合与生成、大数据融合智能挖掘定理;给出大数据的颗粒特征与颗粒过滤定理;给出大数据遗传与生成、大数据遗传智能分离与分离定理;给出在P-增广矩阵推理条件下大数据隐藏-伪装与智能生成、大数据隐藏-伪装定理;给出大数据规律生成模型与方法以及大数据规律状态;利用大数据规律状态,给出投资-利润大数据的风险估计。

关键词: 大数据结构, 大数据融合, 大数据遗传, 大数据隐藏-伪装, 大数据规律, 风险估计

Abstract: P-sets, inverse P-sets are two models obtained by introducing dynamic features into a finite ordinary set X and improving the set X. By using P-sets, inverse P-sets and their dynamic and logical features, ∧-type big data structure and its generation with attribute conjunction extension-contraction feature, ∨-type big data structure and its generation with attribute disjunctive extension-contraction feature, and∧-∨type big data structure and its generation of the mixture of ∧-type big data and ∨-type big data are given respectively. The fusion and its generation of big data and the intelligent mining theorems of big data fusion are given. Granulation characteristics and granulation filtration theorems of big data are given. The heredity and its generation of big data, and heredity intelligence separation and separation theorem of big data are given. Big data hiding-camouflage and intelligent generation under the inference condition of P-augmented matrix, and big data hiding-camouflage theorems are given. The model and method of big data law generation, and the state of big data law are given. By using the state of big data law, the risk estimation of investment-profit big data is given.

Key words: big data structure, big data fusion, big data heredity, big data hiding-camouflage, big data law, risk estimation

中图分类号: 

  • O144
[1] WANG F Y, CARLEY K M, ZENG D, et al. Social computing: from social informatics to social intelligence[J]. IEEE Intelligent Systems, 2007, 22(2):79-83.
[2] ZHANG N, WANG F Y, ZHU F, et al. DynaCAS: computational experiments and decision support for ITS[J]. IEEE Intelligent Systems, 2008, 23(6):19-23.
[3] WANG F Y. Parallel control and management for intelligent transportation systems: concepts, architectures, and applications[J]. IEEE Transactions on Intelligent Transportation Systems, 2010, 11(3):630-638.
[4] WANG F Y. Scanning the issue and beyond: parallel driving with software vehicular robots for safety and smartness[J]. IEEE Transactions on Intelligent Transportation Systems, 2014, 15(4):1381-1387.
[5] LV Y, DUAN Y, KANG W, et al. Traffic flow prediction with big data: a deep learning approach[J]. IEEE Transactions Intelligent Transportation Systems, 2015, 16(2):865-873.
[6] LV Y, ZHANG X, KANG W, et al. Managing emergency traffic evacuation with a partially random destination allocation strategy: a computational-experiment-based optimization approach[J]. IEEE Transactions Intelligent Transportation Systems, 2015, 16(4):2182-2191.
[7] YUAN Y, WANG F Y, ZENG D. Developing a cooperative bidding framework for sponsored search markets: an evolutionary perspective[J]. Information Sciences, 2016, 369:674-689.
[8] WANG F Y. The emergence of intelligent enterprises: from CPS to CPSS[J]. IEEE Intelligent Systems, 2010, 25(4):85-88.
[9] GOODHOPE K, KOSHY J, KREPS J, et al. Building linkedin's real-time activity data pipeline[J]. IEEE Data Eng Bull, 2012, 35(2):33-45.
[10] MCKUSICK K, QUINLAN S. GFS: evolution on fast-forward[J]. Communications of the ACM, 2010, 53(3):42-49.
[11] COOPER B F, RAMAKRISHNAN R, SRIVASTAVA U, et al. PNUTS: Yahoo!'s hosted data serving platform[J]. Proceedings of the VLDB Endowment, 2008, 1(2):1277-1288.
[12] MELNIK S, GUBAREV A, LONG J J, et al. Dremel: interactive analysis of web-scale datasets[J]. Proceedings of the VLDB Endowment, 2010, 3(1/2):330-339.
[13] BU Y, HOWE B, BALAZINSKA M, et al. HaLoop: efficient iterative data processing on large clusters[J]. Proceedings of the VLDB Endowment, 2010, 3(1/2):285-296.
[14] LAM W, LIU L, PRASAD S T S, et al. Muppet: MapReduce-style processing of fast data[J]. Proceedings of the VLDB Endowment, 2012, 5(12):1814-1825.
[15] DITTRICH J, QUIANÉ-RUIZ J A, JINDAL A, et al. Hadoop++: making a yellow elephant run like a cheetah(without it even noticing)[J]. Proceedings of the VLDB Endowment, 2010, 3(1/2):515-529.
[16] CHEN S. CHEETAH: a high performance, custom data warehouse on top of MapReduce[J]. Proceedings of the VLDB Endowment, 2010, 3(1/2):1459-1468.
[17] CANIM M, MIHAILA G A, BHATTACHARJEE B, et al. SSD bufferpool extensions for database systems[J]. Proceedings of the VLDB Endowment, 2010, 3(1/2):1435-1446.
[18] LUO T, LEE R, MESNIER M, et al. hStorage-DB: heterogeneity-aware data management to exploit the full capability of hybrid storage systems[J]. Proceedings of the VLDB Endowment, 2012, 5(10):1076-1087.
[19] WONG P C, SHEN H W, JOHNSON C R, et al. The top 10 challenges in extreme-scale visual analytics[J]. IEEE Computer Graphics and Applications, 2012, 32(4):63-67.
[20] PIKE R, DORWARD S, GRIESEMER R, et al. Interpreting the data: parallel analysis with Sawzall[J]. Scientific Programming, 2005, 13(4):277-298.
[21] 史开泉. P-集合[J]. 山东大学学报(理学版), 2008, 43(11):77-84. SHI Kaiquan. P-sets [J]. Journal of Shandong University(Natural Science), 2008, 43(11):77-84.
[22] SHI Kaiquan. P-sets and its applications[J]. Advances in Systems Science and Applications, 2009, 9(2):209-219.
[23] 史开泉. P-集合与它的应用特性[J]. 计算机科学, 2010, 37(8):1-8. SHI Kaiquan. P-sets and its applied characteristics[J]. Computer Science, 2010, 37(8):1-8.
[24] 史开泉. P-推理与信息的P-推理发现-辨识[J]. 计算机科学, 2011, 38(7):1-9. SHI Kaiquan. P-reasoning and P-reasoning discovery-identification of information[J]. Computer Science, 2011, 38(7):1-9.
[25] 史开泉. P-集合,逆P-集合与信息智能融合-过滤辨识[J]. 计算机科学, 2012, 39(4):1-13. SHI Kaiquan. P-sets, inverse P-sets and the intelligent fusion—filter identification of information[J]. Computer Science, 2012, 39(4):1-13.
[26] FAN Chengxian, LIN Hongkang. P-sets and the reasoning-identification of disaster information[J]. International Journal of Convergence Information Technology, 2012, 7(1):337-345.
[27] LIN Hongkang, FAN Chengxian. The dual form of P-reasoning and identification of unknown attribute[J]. International Journal of Digital Content Technology and its Applications, 2012, 6(1):121-131.
[28] 张丽, 崔玉泉, 史开泉. 外P-集合与数据内-恢复[J]. 系统工程与电子技术, 2010, 32(6):1233-1238. ZHANG LI, CUI Yuquan, SHI Kaiquan. Outer P-sets and data internal recovery[J]. Systems Engineering and Electronics. 2010, 32(6):1233-1238.
[29] 汪洋, 耿红琴, 史开泉. P-集合与动态信息依赖-发现[J]. 系统工程与电子技术, 2011, 33(9):2035-2038. WANG Yang, GENG Hongqin, SHI Kaiquan. P-sets and dependence-discovery of dynamic information[J]. Systems Engineering and Electronics, 2011, 33(9):2035-2038.
[30] 李豫颖, 林宏康, 史开泉. 数据离散区间特征与数据发现-应用[J]. 系统工程与电子技术, 2011, 33(10):2258-2262. LI Yuying, LIN Hongkang, SHI Kaiquan. Characteristics of data discrete interval and data discovery-application[J]. Systems Engineering and Electronics, 2011, 33(10):2258-2262.
[31] 张凌, 汤积华, 史开泉. 内P-信息融合与它的属性合取特征[J]. 山东大学学报(理学版), 2014, 49(2):93-97. ZHANG Ling, TANG Jihua, SHI Kaiquan. The fusion of internal packet information and its feature of attribute conjunction[J]. Journal of Shandong University(Natural Science), 2014, 49(2):93-97.
[32] 史开泉, 张丽. 内P-集合与数据外-恢复[J]. 山东大学学报(理学版), 2009, 44(4):8-14. SHI Kaiquan, ZHANG Li. Internal P-set and data outer-recovery[J]. Journal of Shandong University(Natural Science), 2009, 44(4):8-14.
[33] 张冠宇, 周厚勇, 史开泉. P-集合与双P-数据恢复-辨识[J]. 系统工程与电子技术, 2010, 32(9):1919-1924. ZHANG Guanyu, ZHOU Houyong, SHI Kaiquan. P-sets and the recovery-identification double[J]. Systems Engineering and Electronics, 2010, 32(9):1919-1924.
[34] ZHANG Ling, REN Xuefang. P-sets and (f,( -)/f )-heredity[J]. Quantitative Logic and Soft Computing, 2010, 2(1):735-743.
[35] ZHANG Ling, XIU Ming, SHI Kaiquan. P-sets and application of internal-outer data circle[J]. Quantitative Logic and Soft Computing, 2010, 2(1):581-591.
[36] QIU Yufeng, CHEN Baohui. f-model generated by P-sets[J]. Quantitative Logic and Soft Computing, 2010, 2(1):613-620.
[37] LI Yuying, ZHANG Li, SHI Kaiquan. Generation and recovery of compressed data and redundant data[J]. Quantitative Logic and Soft Computing, 2010, 2(1):661-671.
[38] XIU Ming, SHI Kaiquan, ZHANG Li. P-sets and ( -)/f -data selection-discovery[J]. Quantitative Logic and Soft Computing, 2010, 2(1):791-799.
[39] 赵树理, 范成贤, 史开泉. 外P-信息生成与它的推理-搜索发现[J]. 山东大学学报(理学版), 2012, 47(11):99-104. ZHAO Shuli, FAN Chenxian, SHI Kaiquan. Outer P-information generation and its reasoning-searching discovery[J]. Journal of Shandong University(Natural Science), 2012, 47(1):99-104.
[40] 赵树理, 吴松丽, 史开泉. 内P-推理信息恢复与属性潜藏推理发现[J]. 计算机科学, 2013, 40(4):209-213. ZHAO Shuli, WU Songli, SHI Kaiquan. Internal P-reasoning information recovery and attribute hiding searching discovery[J]. Computer Science, 2013, 40(4):209-213.
[41] 史开泉. 函数P-集合[J]. 山东大学学报(理学版), 2011, 46(2):62-69. SHI Kaiquan. Function P-sets[J]. Journal of Shandong University(Natural Science), 2011, 46(2):62-69.
[42] SHI Kaiquan. Function P-sets[J]. International Journal of Machine Learning and Cybernetics, 2011, 2(4):281-288.
[43] 史开泉. P-信息规律智能融合与软信息图像智能生成[J]. 山东大学学报(理学版), 2014, 49(4):1-17. SHI Kaiquan. P-information law intelligent fusion and soft information image intelligent generation[J]. Journal of Shandong University(Natural Science), 2014, 49(4):1-17.
[44] 汤积华, 张凌, 史开泉. 信息规律智能融合与它的智能融合分离[J]. 计算机科学, 2015, 42(2):204-209. TANG Jihua, ZHANG Ling, SHI Kaiquan. Intelligent fusion of information law and its inner separation[J]. Computer Science, 2015, 42(2):204-209.
[45] 林蓉, 范成贤. 函数P-集合与信息规律动态特性[J]. 山东大学学报(理学版), 2012, 47(1):121-126. LIN Rong, FAN Chengxian. Function P-sets and dynamic characteristics of information law[J]. Journal of Shandong University(Natural Science), 2012, 47(1):121-126.
[46] 任雪芳, 张凌, 史开泉. 两类动态信息规律模型及其在信息伪装、风险识别中的应用[J]. 计算机科学,2018, 45(9):230-236. REN Xuefang, ZHANG Ling, SHI Kaiquan. Two types of dynamic information law models and their applications in information camouflage and risk identification[J]. Computer Science, 2018, 45(9):230-236.
[47] 陈保会, 张凌, 史开泉. P-信息智能动态融合与信息规律状态智能识别[J]. 山东大学学报(理学版), 2018, 53(2):83-87. CHEN Baohui, ZHANG Ling, SHI Kaiquan. Intelligent dynamic fusion of packet information and the intelligent state recognition of information law[J]. Journal of Shandong University(Natural Science), 2018, 53(2):83-87.
[48] TANG Jihua, ZHANG Ling, SHI Kaiquan, et al. Outer P-information law reasoning and its application in intelligent fusion and separating of information law[J]. Microsystem Technologies, 2018, 24(10):4389-4398.
[49] 史开泉. P-增广矩阵与信息的智能动态发现-辨识[J]. 山东大学学报(理学版), 2015, 50(10):1-12. SHI Kaiquan. P-augmented matrix and dynamic intelligent discovery-identification of information[J]. Journal of Shandong University(Natural Science), 2015, 50(10):1-12.
[50] 史开泉. 逆P-集合[J]. 山东大学学报(理学版), 2012, 47(1):98-109. SHI Kaiquan. Inverse P-sets[J]. Journal of Shandong University(Natural Science), 2012, 47(1):98-109.
[51] 史开泉, 汤积华, 张凌. 逆P-信息智能融合与信息智能隐藏的隐性传递[J]. 系统工程与电子技术, 2015, 37(3):599-605. SHI Kaiquan, TANG Jihua, ZHANG Ling. Intelligent fusion of inverse packet information and recessive transmission of informations intelligent hiding[J]. Systems Engineering and Electronics, 2015, 37(3):599-605.
[52] 史开泉. 函数逆P-集合与信息规律融合[J]. 山东大学学报(理学版), 2012, 47(8):73-80. SHI Kaiquan. Function inverse P-sets and information law fusion[J]. Journal of Shandong University(Natural Science), 2012, 47(8):73-80.
[53] LIN Kongkang, FAN Chengxian. Embedding camouflage of inverse P-information and application[J]. International Journal of Convergence Information and Technology, 2012, 7(20):471-480
[54] FAN Chengxian, HUANG Shunliang. Inverse P-reasoning discovery identification of inverse P-information[J]. International Journal of Digital Content Technology and its Applications, 2012, 6(20):735-744.
[55] SHI Kaiquan. Function inverse P-sets and the hiding information generated by function inverse P-information law fusion[C] // Proc of the 13th IFIP WG 6.11 Conference on e-Business, e-Services, and e-Society, Sanya, China, 2014: Digital Services and Information Intelligence, 224-237.
[56] 汤积华, 陈保会, 张凌, 等. 函数逆P-集合与逆P-信息规律动态分离[J]. 山东大学学报(理学版), 2013, 48(8):104-110. TANG Jihua, CHEN Baohui, ZHANG Ling,et al. Function inverse P-sets and the dynamic separation of inverse P-information laws[J]. Journal of Shandong University(Natural Science), 2013, 48(8):104-110.
[57] 郭华龙, 任雪芳, 张凌. 数据的动态挖掘与P-增广矩阵关系[J]. 山东大学学报(理学版), 2016, 51(8):105-110. GUO Hualong, REN Xuefang, ZHANG Ling. Relationships between dynamic data mining and P-augmented matrix[J]. Journal of Shandong University(Natural Science), 2016, 51(8):105-110.
[58] 郭华龙, 陈保会, 汤积华. 逆P-集合与信息智能融合挖掘-发现[J]. 山东大学学报(理学版), 2013, 48(8):97-103,110. GUO Hualong, CHEN Baohui, TANG Jihua. Inverse P-sets and intelligent fusion mining-discovery of information[J]. Journal of Shandong University(Natural Science), 2013, 48(8):97-103,110.
[59] ZHANG Ling, REN Xuefang, SHI Kaiquan. The dynamic segmentation characteristics of P-augmented matrix and the dynamic intelligent acquisition of P-information[J]. International Journal of Applied Decision Sciences, 2016, 9(4):413-425.
[60] ZHANG Ling, REN Xuefang, SHI Kaiquan, et al. Inverse packet matrix reasoning model-based the intelligent dynamic separation and acquisition of educational information[J]. Microsystem Technologies, 2018, 24(10):4415-4421.
[61] REN Xuefang, ZHANG Ling, SHI Kaiquan, et al. Inverse P-augmented matrix method-based the dynamic findings of unknown information[J]. Microsystem Technologies, 2018, 24(10):4187-4192.
[62] ZHANG Ling, REN Xuefang, SHI Kaiquan. Inverse P-information law models and the reality-camouflage intelligent transformations of information image[C] // Proceedings of the 2016 International Conference on Network and Information Systems for Computers, Washington: IEEE, 2016:337-341.
[63] ZHANG Ling, REN Xuefang, SHI Kaiquan. Inverse P-data models and data intelligent separation[C] // Proceedings of the 2016 International Conference on Electronic Information Technology and Intellectualization, DOI: 10.12783/dtcse/iceiti2016/6107, 2016.
[64] 任雪芳, 张凌, 史开泉. 基数余-亏与逆P-增广矩阵[J] ,山东大学学报(理学版), 2015, 50(10):13-18, 26. REN Xuefang, ZHANG Ling, SHI Kaiquan. Surplus-deficiency of cardinal number and inverse P-augmented matrices[J]. Journal of Shandong University(Natural Science), 2015, 50(10):13-18, 26.
[65] 张凌, 任雪芳. 基数余-亏定理与数据外-内挖掘-分离[J]. 山东大学学报(理学版), 2015, 50(8):90-94. ZHANG Ling, REN Xuefang. Surplus-deficient theorem of cardinal number and data internal-outer mining-separation[J]. Journal of Shandong University(Natural Science), 2015, 50(8):90-94.
[66] 郭华龙, 张凌. 数据分离与属性状态特征[J]. 山东大学学报(理学版), 2017, 52(12):89-94. GUO Hualong, ZHANG Ling. Data separation and its attribute state characteristics[J]. Journal of Shandong University(Natural Science), 2017, 52(12):89-94.
[67] 汤积华, 任雪芳, 张龙. 外逆 P-信息智能融合与属性析取收缩关系[J]. 山东大学学报(工学版), 2014, 49(4):46-51. TANG Jihua, REN Xuefang, ZHANG Long. The relationship between intelligent fusion of outer inverse packet information and attribute disjunction contraction[J]. Journal of Shandong University(Engineering Science), 2014, 49(4):46-51.
[68] 汤积华,陈保会. 内逆 P-信息智能融合与属性析取扩展关系[J]. 山东大学学报(理学版), 2014, 49(2):89-92, 97. TANG Jihua, CHEN Baohui. Intelligent fusion of internal inverse packet information and expansion relationship of attribute disjunction[J]. Journal of Shandong University(Natural Science), 2014, 49(2):89-92, 97.
[69] 张凌, 任雪芳, 史开泉. 信息规律智能变换-伪装与P-规律增广矩阵[J]. 山东大学学报(理学版), 2016, 51(8):90-97. ZHANG Ling, REN Xuefang, SHI Kaiquan. Intelligent switch-camouflage of information laws and P-law augmented matrices[J]. Journal of Shandong University(Natural Science), 2016, 51(8):90-97.
[70] 汤积华, 陈保会, 史开泉. P-增广矩阵推理与信息的智能分解挖掘[J]. 山东大学学报(理学版), 2016, 51(12):61-66. TANG Jihua, CHEN Baohui, SHI Kaiquan. P-augmented matrix reasoning and intelligent decomposition mining of information[J]. Journal of Shandong University(Natural Science), 2016, 51(12):61-66.
[71] 任雪芳, 张凌, 史开泉. 逆P-集合的边界特征与系统状态监测[J]. 计算机科学, 2016,43(10):211-213,255. REN Xuefang, ZHANG Ling, SHI Kaiquan. Boundary characteristics of inverse P-sets and system condition monitoring[J]. Computer Science, 2016, 43(10):211-213, 255.
[72] 任雪芳, 张凌. 逆P-集合的扰动定理与数据的扰动挖掘[J]. 山东大学学报(理学版), 2016, 51(12):54-60. REN Xuefang, ZHANG Ling. Perturbation theorems of inverse P-sets and perturbation-based data mining[J]. Journal of Shandong University(Natural Science), 2016, 51(12):54-60.
[73] 史开泉, 姚炳学. 函数S-粗集与规律辨识[J]. 中国科学(E 信息科学), 2008, 38(4):553-564. SHI Kaiquan, YAO Bingxue. Function S-rough sets and law identification[J]. Science in China(E Information Science), 2008, 38(4):553-564.
[74] 史开泉, 赵建立. 函数S-粗集与隐藏规律安全认证[J]. 中国科学(E 信息科学), 2008, 38(8):1234-1243. SHI Kaiquan, ZHAO Jianli. Function S-rough sets and security-authentication of hiding law[J]. Science in China(E Information Science), 2008, 38(8):1234-1243.
[75] SHI Kaiquan, YAO Bingxue. Function S-rough sets and law identification[J]. Science in China(F Information Science), 2008, 51(5):499-510.
[76] SHI Kaiquan, ZHAO Jianli. Function S-rough sets and security-authentication of hiding law[J]. Science in China(F information Sciences,)2008, 51(7):924-935.
[1] 陈保会,张凌,史开泉. P-信息智能动态融合与信息规律状态智能识别[J]. 山东大学学报（理学版）, 2018, 53(2): 83-87.
[2] 郭华龙,张凌. 数据分离与属性状态特征[J]. 山东大学学报（理学版）, 2017, 52(12): 89-94.
[3] 张秀全,李小朝. P-信息融合与它的P-矩阵推理智能生成[J]. 山东大学学报（理学版）, 2017, 52(4): 93-99.
[4] 徐凤生,于秀清,史开泉. 属性基数余-亏值定理与信息规律动态内-外分离[J]. 山东大学学报（理学版）, 2017, 52(4): 87-92.
[5] 任雪芳,张凌. 逆P-集合的扰动定理与数据的扰动挖掘[J]. 山东大学学报（理学版）, 2016, 51(12): 54-60.
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