动态信息与动态信息规律特征研究
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摘要
康拓集合论的创立,奠定了现代数学理论与应用研究的基础,推动了产生于上个世纪的新型学科：信息科学、系统科学、计算机科学研究的进步,促进了产生于上世纪末出现的生物信息科学的基础研究。有限普通康拓集合具有三个特征：Ⅰ.精确性,Ⅱ.边界确定性,Ⅲ.静态性。特性Ⅰ～Ⅲ潜藏在有限普通集合X内多年,没有引起人们对它们的注意。在1965年之前,没有人利用特性Ⅰ～Ⅲ对有限普通集合给出新的认识。或许人们认为：有限普通集合仅是一个定义或者一个数学概念,事实并非如此。
1965年,L.A.Zadeh用“边界不确定性”代替“边界确定性”,改进了有限普通集合,提出模糊集合,模糊集合已成为研究信息科学、系统科学、计算机科学中的一个新兴的研究分支之一。1982年,Z.Pawlak用“近似性”代替“精确性”,改进有限普通集合,提出粗集合,粗集合已被成功的应用到数据挖掘-知识发现研究中。数据挖掘-知识发现是信息科学、系统科学、计算机科学中一个新的研究分支之一。2008年,史开泉教授用“动态性”代替“静态性”,改进有限普通集合X提出P-集合与它的结构。2011年,史开泉教授将函数概念引入到P-集合内并改进它,提出函数P-集合与它的结构。P-集合、函数P-集合在一类动态信息、一类动态信息规律系统中得到了多个应用。2012年,史开泉教授用“动态特性”代替“静态特性”,改进有限普通集合X提出逆P-集合与它的结构。2012年,史开泉将函数概念引入到逆P-集合内并改进它,提出函数逆P-集合与它的结构。逆P-集合、函数逆P-集合在另一类动态信息、另一类动态信息规律系统中得到了多个应用。
在信息科学、系统科学与计算机科学中的诸多工程问题中遇到的信息、信息规律都具有动态特性,动态特性是信息的真实面貌。抽掉信息系统(如电力信息系统)中的名称,把信息系统进行数学抽象,利用P-集合模型,逆P-集合模型、函数P-集合模型与函数逆P-集合模型与它的一般理论,居高临下的认识信息系统中包含的一些理论问题,给人们研究动态信息、动态信息规律提供了一个新的研究工具与新的理论支持。
本文利用P-集合、函数P-集合、逆P-集合、函数逆P-集合,给出了P-信息、P-信息规律、逆P-信息、逆P-信息规律定义以及对它们的动态特性理论研究,并给出这些理论在信息系统(如电力信息系统)中的应用。主要研究内容如下：
(1)本文利用P-集合与P-信息的动态特性,给出P-信息(如电力信息)的P-推理及其结构,提出了P-推理的存在性定理,P-推理发现定理,P-推理的属性删除-补充定理,P-推理与普通推理的关系定理；给出了P-推理信息圆以及信息圆的动态特征,提出了内-同心圆定理,外-同心圆定理,P-信息环定理,P-推理信息环的动态特性定理。根据P-推理的结构,提出了P-信息的倒向P-推理及其结构,给出倒向P-推理生成的属性剩余发现,倒向P-推理的属性补充-删除定理,倒向P-推理与普通推理的关系定理。根据P-信息的P-推理及其定理,给出了未知动态信息的P-推理挖掘-发现在电力企业优秀职工评选中的应用。
(2)利用函数P-集合与它生成的信息规律及其特征,给出P-信息规律(如电力信息规律)的区间稳定定理、属性控制定理与恢复-辨识定理；给出P-信息规律的属性依赖与依赖定理,提出属性单依赖传递性定理,属性单依赖的单位离散区间内点定理,属性单依赖-属性双依赖定理,内P-信息规律与属性单依赖定理,外P-信息规律与属性单依赖定理,P-信息规律与属性单依赖定理。利用P-信息规律的动态特性,给出P-信息规律推理与未知信息规律内-外发现定理,提出P-信息迭代规律存在性定理,P-信息迭代规律属性补充-删除定理。利用P-信息规律推理,给出P-信息规律推理在电力经济信息规律中的应用。
(3)利用逆P-信息的动态特性,给出逆P-信息(如电力信息)的逆P-推理及其结构,提出逆P-信息的逆P-推理发现-辨识定理；给出逆P-信息的嵌入-伪装定理,逆P-信息的逆P-伪装属性定理,逆P-信息的逆P-伪装还原定理,逆P-信息的逆P-伪装辨识定理与不可辨识定理。利用逆P-信息的嵌入-伪装与还原定理,给出逆P-信息的嵌入-伪装与还原在电力故障信息安全传递中的应用。
(4)利用函数逆P-集合与它生成逆P-信息规律及其特征,给出了逆P-信息规律(如电力信息规律)还原定理,逆P-信息规律属性定理,逆P-信息规律的动态分离与发现定理；给出了逆P-信息规律推理及其推理结构,提出了逆P-信息规律推理与未知信息规律内-外发现定理。
The founding of Cantor set theory laid the foundation of modern mathematics theory and application research, which promoted the progress of some new science branches arising from the last century, for example information science, computer science, bioinformatics science. The finite Cantor set has three characteristics:I. Precision, II. Boundary certainty, III. Static characteristic. The characteristics are hided in the finite general set X for long years, which had not attract people's attention. Before1965, no one gave the new recognition for the characteristics Ⅰ～Ⅲ of finite general set. Perhaps people think the finite general set is only a definition or a mathematics concept, but it is not true.
In1965, L.A.Zadeh improved the finite general set and proposed fuzzy set by substituting boundary uncertainty for boundary certainty. Fuzzy set has become one of new research branches studying information science, system science and computer science. In1982, Z.Pawlak improved the finite general set and proposed rough set by substituting similarity for precision. Rough set has been applied into the research about data mining and knowledge discovery. Data mining and knowledge discovery is one of new research branches of information science, system science and computer science. The original works about fuzzy set and rough set expand the concept of Cantor set and supplement its faultiness. In2008, Professor Shi Kaiquan improved the finite general set X and proposed P-sets by substituting dynamic characteristic for static characteristic. In2011, function P-sets and its structure are presented by introducing the function concept into P-sets and improved it. P-sets and function P-sets have acquired lots of applications in the first class of dynamic information and dynamic information system. In2012, Professor Shi improved the finite general set X and put forward inverse P-sets by substituting dynamic characteristic for static characteristic. In2012, function inverse P-sets and its structure are presented by introducing the function concept into inverse P-sets and improved it. Inverse P-sets and function inverse P-sets have acquired lots of applications in another class of dynamic information and dynamic information system.
The information and information law in information science, system science and computer science has the dynamic characteristics, which are the real features of information system. By mathematics abstract for the information system, which can be studied using P-sets, function P-sets, inverse P-sets, function inverse P-sets and their general theories. P-sets, function P-sets, inverse P-sets, function inverse P-sets present people a novel study tool and theory support to study dynamic information and dynamic information law.
Based on the concepts and structures of P-sets, function P-sets, inverse P-sets and function inverse P-sets, the paper gives their further researches. Using the theory results, the paper gives the dynamic information characteristic researches of P-information, P-information law, inverse P-information and inverse P-information law, and gives the applications of information system(powcr information system). The main research results are follows.
(1) Using the dynamic characteristics of P-sets and P-information(power information), the paper gives the P-reasoning and its structure of P-information(power information), and presents the existence theorem, discovery theorem and delcted-supplemented theorem of P-reasoning, the relation theorem between P-reasoning and general reasoning. The paper gives P-reasoning information circle and the dynamic characteristic of information circle, internal concentric circles theorem, outer concentric circles theorem, P-informatin ring theorem and its dynamic characteristic theorem. Based on P-reasoning, it presents the backward P-reasoning and its structure of P-information, and then gives attributes residue discovery and attribtute supplemented-deleted theorem generated by backward P-reasoning, the relation theorem between backward P-reasoning and general reasoning. Using P-reasoning, the paper gives the application of P-reasoning mining-discovery in excellent workers selection in electric power enterprise.
(2) Using function P-sets and its information law characteristic, the paper gives interval invariability theorem, attribute control theorem, recovery-identification theorem, attribute dependence and attribute dependence theorem of P-information law(power information law), and presents attribute single-dependence transfer theorem, the internal point theorem of unit discret interval of attribute single-dependence, attribute single-double dependence theorem, the single dependence theorems between internal P-informaiton law, outer P-informatin law and their attributes. Based on the dynamic characteristics and its attribute dependence characteristics, the paper proposes P-information law reasoning and the internal-outer discovery theorem of unknown information law, and presents the existence theorem and attribute supplemented-deleted theorem of P-information iteration law. At last, the application of P-information law reasoning in power economy information law is given.
(3) Based on the dynamic characteristic of inverse P-information, the paper gives inverse P-reasoning and its structure, inverse P-reasoning discovery-identification theorem of inverse P-information(power information), the embedding-camouflage theorem and camouflage attribute theorem and camouflage-recovery theorem of inverse P-information. Final, the application of the embedding-camouflage and recovery in the security transmission of power fault information is given.
(4) Using function inverse P-sets and its inverse P-information law characteristic, the paper puts forward recovery theorem, attribute theorem and dynamic separation-discovery theorem of inverse P-information law(power information law). Based on the dynamic and law characteristics, the paper gives the inverse P-information law reasoning and its reasoning structure, the internal-outer discovery theorem of unknown information law.
1965年,L.A.Zadeh用“边界不确定性”代替“边界确定性”,改进了有限普通集合,提出模糊集合,模糊集合已成为研究信息科学、系统科学、计算机科学中的一个新兴的研究分支之一。1982年,Z.Pawlak用“近似性”代替“精确性”,改进有限普通集合,提出粗集合,粗集合已被成功的应用到数据挖掘-知识发现研究中。数据挖掘-知识发现是信息科学、系统科学、计算机科学中一个新的研究分支之一。2008年,史开泉教授用“动态性”代替“静态性”,改进有限普通集合X提出P-集合与它的结构。2011年,史开泉教授将函数概念引入到P-集合内并改进它,提出函数P-集合与它的结构。P-集合、函数P-集合在一类动态信息、一类动态信息规律系统中得到了多个应用。2012年,史开泉教授用“动态特性”代替“静态特性”,改进有限普通集合X提出逆P-集合与它的结构。2012年,史开泉将函数概念引入到逆P-集合内并改进它,提出函数逆P-集合与它的结构。逆P-集合、函数逆P-集合在另一类动态信息、另一类动态信息规律系统中得到了多个应用。
在信息科学、系统科学与计算机科学中的诸多工程问题中遇到的信息、信息规律都具有动态特性,动态特性是信息的真实面貌。抽掉信息系统(如电力信息系统)中的名称,把信息系统进行数学抽象,利用P-集合模型,逆P-集合模型、函数P-集合模型与函数逆P-集合模型与它的一般理论,居高临下的认识信息系统中包含的一些理论问题,给人们研究动态信息、动态信息规律提供了一个新的研究工具与新的理论支持。
本文利用P-集合、函数P-集合、逆P-集合、函数逆P-集合,给出了P-信息、P-信息规律、逆P-信息、逆P-信息规律定义以及对它们的动态特性理论研究,并给出这些理论在信息系统(如电力信息系统)中的应用。主要研究内容如下：
(1)本文利用P-集合与P-信息的动态特性,给出P-信息(如电力信息)的P-推理及其结构,提出了P-推理的存在性定理,P-推理发现定理,P-推理的属性删除-补充定理,P-推理与普通推理的关系定理；给出了P-推理信息圆以及信息圆的动态特征,提出了内-同心圆定理,外-同心圆定理,P-信息环定理,P-推理信息环的动态特性定理。根据P-推理的结构,提出了P-信息的倒向P-推理及其结构,给出倒向P-推理生成的属性剩余发现,倒向P-推理的属性补充-删除定理,倒向P-推理与普通推理的关系定理。根据P-信息的P-推理及其定理,给出了未知动态信息的P-推理挖掘-发现在电力企业优秀职工评选中的应用。
(2)利用函数P-集合与它生成的信息规律及其特征,给出P-信息规律(如电力信息规律)的区间稳定定理、属性控制定理与恢复-辨识定理；给出P-信息规律的属性依赖与依赖定理,提出属性单依赖传递性定理,属性单依赖的单位离散区间内点定理,属性单依赖-属性双依赖定理,内P-信息规律与属性单依赖定理,外P-信息规律与属性单依赖定理,P-信息规律与属性单依赖定理。利用P-信息规律的动态特性,给出P-信息规律推理与未知信息规律内-外发现定理,提出P-信息迭代规律存在性定理,P-信息迭代规律属性补充-删除定理。利用P-信息规律推理,给出P-信息规律推理在电力经济信息规律中的应用。
(3)利用逆P-信息的动态特性,给出逆P-信息(如电力信息)的逆P-推理及其结构,提出逆P-信息的逆P-推理发现-辨识定理；给出逆P-信息的嵌入-伪装定理,逆P-信息的逆P-伪装属性定理,逆P-信息的逆P-伪装还原定理,逆P-信息的逆P-伪装辨识定理与不可辨识定理。利用逆P-信息的嵌入-伪装与还原定理,给出逆P-信息的嵌入-伪装与还原在电力故障信息安全传递中的应用。
(4)利用函数逆P-集合与它生成逆P-信息规律及其特征,给出了逆P-信息规律(如电力信息规律)还原定理,逆P-信息规律属性定理,逆P-信息规律的动态分离与发现定理；给出了逆P-信息规律推理及其推理结构,提出了逆P-信息规律推理与未知信息规律内-外发现定理。
The founding of Cantor set theory laid the foundation of modern mathematics theory and application research, which promoted the progress of some new science branches arising from the last century, for example information science, computer science, bioinformatics science. The finite Cantor set has three characteristics:I. Precision, II. Boundary certainty, III. Static characteristic. The characteristics are hided in the finite general set X for long years, which had not attract people's attention. Before1965, no one gave the new recognition for the characteristics Ⅰ～Ⅲ of finite general set. Perhaps people think the finite general set is only a definition or a mathematics concept, but it is not true.
In1965, L.A.Zadeh improved the finite general set and proposed fuzzy set by substituting boundary uncertainty for boundary certainty. Fuzzy set has become one of new research branches studying information science, system science and computer science. In1982, Z.Pawlak improved the finite general set and proposed rough set by substituting similarity for precision. Rough set has been applied into the research about data mining and knowledge discovery. Data mining and knowledge discovery is one of new research branches of information science, system science and computer science. The original works about fuzzy set and rough set expand the concept of Cantor set and supplement its faultiness. In2008, Professor Shi Kaiquan improved the finite general set X and proposed P-sets by substituting dynamic characteristic for static characteristic. In2011, function P-sets and its structure are presented by introducing the function concept into P-sets and improved it. P-sets and function P-sets have acquired lots of applications in the first class of dynamic information and dynamic information system. In2012, Professor Shi improved the finite general set X and put forward inverse P-sets by substituting dynamic characteristic for static characteristic. In2012, function inverse P-sets and its structure are presented by introducing the function concept into inverse P-sets and improved it. Inverse P-sets and function inverse P-sets have acquired lots of applications in another class of dynamic information and dynamic information system.
The information and information law in information science, system science and computer science has the dynamic characteristics, which are the real features of information system. By mathematics abstract for the information system, which can be studied using P-sets, function P-sets, inverse P-sets, function inverse P-sets and their general theories. P-sets, function P-sets, inverse P-sets, function inverse P-sets present people a novel study tool and theory support to study dynamic information and dynamic information law.
Based on the concepts and structures of P-sets, function P-sets, inverse P-sets and function inverse P-sets, the paper gives their further researches. Using the theory results, the paper gives the dynamic information characteristic researches of P-information, P-information law, inverse P-information and inverse P-information law, and gives the applications of information system(powcr information system). The main research results are follows.
(1) Using the dynamic characteristics of P-sets and P-information(power information), the paper gives the P-reasoning and its structure of P-information(power information), and presents the existence theorem, discovery theorem and delcted-supplemented theorem of P-reasoning, the relation theorem between P-reasoning and general reasoning. The paper gives P-reasoning information circle and the dynamic characteristic of information circle, internal concentric circles theorem, outer concentric circles theorem, P-informatin ring theorem and its dynamic characteristic theorem. Based on P-reasoning, it presents the backward P-reasoning and its structure of P-information, and then gives attributes residue discovery and attribtute supplemented-deleted theorem generated by backward P-reasoning, the relation theorem between backward P-reasoning and general reasoning. Using P-reasoning, the paper gives the application of P-reasoning mining-discovery in excellent workers selection in electric power enterprise.
(2) Using function P-sets and its information law characteristic, the paper gives interval invariability theorem, attribute control theorem, recovery-identification theorem, attribute dependence and attribute dependence theorem of P-information law(power information law), and presents attribute single-dependence transfer theorem, the internal point theorem of unit discret interval of attribute single-dependence, attribute single-double dependence theorem, the single dependence theorems between internal P-informaiton law, outer P-informatin law and their attributes. Based on the dynamic characteristics and its attribute dependence characteristics, the paper proposes P-information law reasoning and the internal-outer discovery theorem of unknown information law, and presents the existence theorem and attribute supplemented-deleted theorem of P-information iteration law. At last, the application of P-information law reasoning in power economy information law is given.
(3) Based on the dynamic characteristic of inverse P-information, the paper gives inverse P-reasoning and its structure, inverse P-reasoning discovery-identification theorem of inverse P-information(power information), the embedding-camouflage theorem and camouflage attribute theorem and camouflage-recovery theorem of inverse P-information. Final, the application of the embedding-camouflage and recovery in the security transmission of power fault information is given.
(4) Using function inverse P-sets and its inverse P-information law characteristic, the paper puts forward recovery theorem, attribute theorem and dynamic separation-discovery theorem of inverse P-information law(power information law). Based on the dynamic and law characteristics, the paper gives the inverse P-information law reasoning and its reasoning structure, the internal-outer discovery theorem of unknown information law.
引文
[1]L.A Zadeh. Fuzzy sets[J]. Information and Control,1965,8:338-353.
[2]汪培庄,模糊集合理论及其应用[M].上海科学技术出版社,1983.
[3]武庄,石柱,何新贵.基于模糊集合论的故障树分析方法及其应用[J].系统工程与电子技术,2000,22(9)：72-75.
[4]Habib Rajabi Mashhadi, Morteza Rahimiyan. Measurement of power supplier's Market power using a proposed fuzzy estimator[J]. IEEE Transaction on Power System,2011,26(4):1836-1844.
[5]Walid G.Morsi, M.E.EI-Hawary. Fuzzy-wavelet-based electric power quality assessment of distribution systems under stationary and nonstationary disturbances[J]. IEEE Transaction on Power Delivery,2009,24(4):2099-2106.
[6]Ignacio J Ramirez-Rosado, Jose Antonio Dominguez-Navarro. New multiob-jective tabu search algorithm for fuzzy optimal planning of power distribution systems[J]. IEEE Transaction on Power System,2006,21(1):224-233.
[7]李培强,李欣然,陈辉华,唐外文.基于模糊聚类的电力负荷特性的分类与综合[J].中国电机工程学报,2005,25(24)：73-78.
[8]吴剑飞,姚建刚,陈华林,龚陈雄,李昀.电力客户能效状态模糊综合评估[J].电力系统保护与控制,2010,38(13)：94-103.
[9]C.W. Cheong. Web access failure analysis-fuzzy reliability approach[J]. International Journal of the Computer, The Internet and Management,2004, 12(1):65-73.
[10]Y.H. Song, G..S. Wang, P.Y. Wang, A.T. Johns. Environmental/economic dispatch using fuzzy logic controlled genetic algorithms [J]. IEEE Proceedings-Generation, Transmission and Distribution,1997,144(4):377-382.
[11]Payman Dehghanian, Mahmud Fotuhi-Firuzabad, Saeed Bagheri-Shouraki, Ali Asghar Razi Kazemi. Critical component identification in reliability centered asset management of power distribution systems via fuzzy AHP[J]. IEEE Systems Journal,2012,6(4):593-602.
[12]Houzhong Yan, Peter B.Luh. A fuzzy optimization-based method for integrated power system scheduling and inter-utility power transaction with uncertainties [J]. IEEE Transaction on Power System,1997,12(2):756-763.
[13]Ignacio J.Ramirez-Rosado, Jose Antonio Dominguez-Navarro. Possibilistic model based on fuzzy sets for the multiobjective optimal planning of electric power distribution networks[J]. IEEE Transaction on Power System,2004, 19(4):1801-1810.
[14]Augustine O.Esogbue, Warren E.Hearnes. On replacement models via a fuzzy set theoretic framework[J]. IEEE Transaction on Systems, Man, and Cybernetics, Part C:Applications and Reviews,1998,28(4):549-560.
[15]武宏波,胡静.基于一种新的模糊运算方法实现电力系统模糊风险评估[J].华北电力大学学报,2011,38(6)：34-39.
[16]杨太华,基于模糊熵的综合评标法在电力工程项目招投标中的应用[J].上海电力学院学报,2011,27(1),91-95.
[17]陈连栋,吕春梅.基于模糊综合评判的电力风险评估方法的研究[J].电力科学与工程,2010,26(11)：50-54.
[18]Shubham Agrawal, B.K.Panigrahi, Manoj Kumar Tiwari. Multiobjective particle swarm algorithm with fuzzy clustering for electrical power dispatch[J]. IEEE Transactions on Evolutionary Computation,2008,12(5):529-541.
[19]A Mentes, I. Helvacioglu. An application of fuzzy fault tree analysis for spread mooring systems[J]. Ocean Engineering,2011,38:285-294.
[20]Z.Pawlak, Rough sets. International Journal of Computer and Information sciences,1982,11:341-356.
[21]王国胤.粗集理论与知识获取[M].西安交通大学出版社,2001.
[22]苗夺谦.粗集理论中连续属性的离散化方法[J].自动化学报,2001,27(3)：296-302.
[23]邱雅竹,付蓉.两个论域上的粗糙集模型及其应用[J].四川师范大学学报：自然科学版,2005,28：15-18.
[24]Hu Qinghua, Zhang Lei, Chen Degang. Gaussian kernel based fuzzy rough sets: Model, uncertainty measures and applications[J]. International Journal of Approximate Reasoning,2010,51(4):453-471.
[25]Biswas Subrata, Dey Debangshu, Chatterjee Biswendu, Chakravorti Sivaji. An approach based on rough set theory for identification of single and multiple partial discharge source[J]. International Journal of Electrical Power and Energy Systems,2013,46(1):163-174.
[26]汤义强,毛军军,李侠,程白彬.基于粗集属性约简的电力供应量SVM回归预测[J].计算机技术与发展,2010,20(9)：48-51.
[27]李秋丹,迟忠先,王大公.基于数据挖掘技术的负荷预测模型[J].大连理工大学学报,2003,43(6)：845-848.
[28]赵峰,苏宏升.证据理论和粗集在变电站故障诊断中的应用[J].电力系统及其自动化学报,2009,21(2)：42-46.
[29]Sovan Dalai, Biswendu Chatterjee, Debangshu Dey, Sivaji Chakravorti. Rough-set-based feature selection and classification for power quality sensing device employing correlation techniques[J]. IEEE Sensors Journal,2013,13(2): 563-573.
[30]Chen Yumin, Miao Duoqian, Wu Ruizhi, Wu Keshou. A rough set approach to feature selection based on power set tree[J]. Knowledge-based systems,2011, 24(2):275-281.
[31]Ma Wenbin, Ma Chao, Zheng Guixing, Zhao Rui. The fault location approach for grid network base on MAS of rough set theory[J]. Applied Mechanics and Materials,2011,127:460-465.
[32]L.P.Khoo, S.B.Tor, J.R.Li. A rough set approach to the ordering of basic events in a fault tree for fault diagnosis[J]. International Journal of Advanced Manufacturing Technology,2001,17(10):769-774.
[33]Zhou Yongyong, Zhou Quan, Liu Jiabin, Liu Yuming, Ren Haijun, Sun Caiyin, Liu Xu. Rough set theory based approach for fault diagnosis rule extraction of distribution system[J].2008,34(12):2713-2718.
[34]Pisicabreve I., P. Postolache. Rough set theory and its applications in electrical power engineering[J]. University "Politehnica" of Bucharest, Scientific Bulletin Series C:Electrical Engineering,2010,72(1):211-222.
[35]I. Pisicabreve. A note on rough set theory applications in power engineering[J]. University "Politehnica" of Bucharest, Scientific Bulletin Series C:Electrical Engineering,2010,72(3):313-318.
[36]Dong Lixin, Xiao Dengming, Liang Yishan. Rough set and fuzzy wavelet neural network integrated with least square weighted fusion algorithm based fault diagnosis research for power transformers[J]. Electric Power Systems Research,2008,78(1):129-136.
[37]Cai Jinding. An improved three-ratio fault diagnosis based on rough set theory for power transformer[J]. Advanced Technology of Electrical Engineering and Energy,2004,23(4):8-12.
[38]罗治强,张焰,朱杰.粗集理论在电力系统负荷预测中的应用[J].电网技术,2004,28(3)：29-32.
[39]庞清乐,孙同景,钟麦英,杨福刚.基于粗集理论的小电流接地系统故障选线[J].中国电机工程学报,2007,27(4)：60-64.
[40]A. Kusiak. Rough set theory:a data mining tool for semiconductor manufac-turing[J]. IEEE Transactions on Electronics Packaging Manufacturing,2001, 24(1):44-50.
[41]Chen Degang, Zhao Suyun, Zhang Lei, Yang Yongping, Zhang Xiao. Sample pair selection for attribute reduction with rough set[J]. IEEE Transaction on Knowledge and Data Engineering,2012,24(11):2080-2093.
[42]史开泉.P-集合[J].山东大学学报理学版,2008,43(11)：77-84.
[43]史开泉.函数P-集合[J].山东大学学报：理学版,2011,46(2)：62-69.
[44]Shi Kaiquan. Function P-sets [J]. International Journal of Machine Learning and Cybernetics,2011,2(4):281-288.
[45]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.
[46]史开泉.逆P-集合[J].山东大学学报：理学版,2012,47(1)：98-109.
[47]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.
[48]闫立梅.逆P-推理与未知信息推理-搜索与发现[J].计算机科学,2012,39(8)：268-272.
[49]史开泉.P-集合与它的应用特性[J].计算机科学,2010,37(8)：1-8.
[50]Shi Kaiquan. P-sets and its applications[J]. An International Journal Advances in Systems Science and Applications,2009,9(2):209-219.
[51]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.
[52]汤积华,陈保会,史开泉.P-集合与(F,F)数据生成-辨识[J].山东大学学报：理学版,2009,44(11)：83-92.
[53]李豫颖,谢维奇,史开泉.F-残缺数据的辨识与恢复[J].山东大学学报：理学版,2009,45(9)：57-64.
[54]Shi Kaiquan, Li Xiuhong. Camouflaged information identification and its application [J]. An International Journal Advances in Systems Science and Applications,2010,10(2):157-167.
[55]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.
[56]张飞,陈萍,张丽.P-集合的P-分离与应用[J].山东大学学报理学版,2010,45(3)：18-22.
[57]Zhang Li, Cui Yuquan. Outer P-sets and data internal recovery[J]. An International Journal Advances in Systems Science and Applications,2010, 10(2):189-199.
[58]Zhang Li, Xiu Ming, Shi Kaiquan. P-sets and applications of internal-outer data circle[J]. Quantitative Logic and Soft Computing,2010,1(2):581-592.
[59]Li Yuying, Zhang Li, Shi Kailua. Generation and Recovery of Compressed data and Redundant data[J]. Quantitative Logic and Soft Computing,2010,1(2): 661-672.
[60]Xiu Ming, Shi Kaiquan, Zhang Li. P-sets and F-data Selection-Discovery [J]. Quantitative Logic and Soft Computing,2010, 1(2):791-800.
[61]周玉华,张冠宇,张丽.内-外数据圆与动态数据-恢复[J].山东大学学报：理学版,2010,45(8)：21-26.
[62]Lin Hongkang, Li Yuying. P-sets and its P-separation theorems[J]. An International Journal Advances in Systems Science and Applications,2010, 10(2):209-215
[63]周玉华,张冠宇,史开泉.P-集合与双信息规律生成[J].数学的实践与认识,2010,40(13)：71-80
[64]Wang Yang, Geng Hongqin, Shi Kaiquan. The mining of dynamic information based on P-sets and its application[J]. An International Journal Advances in Systems Science and Applications,2010,10(2):234-240.
[65]Zhang Guanyu, Li Enzhong. Information gene and identification of its information Knock-out/Knock-in [J]. An International Journal Advances in Systems Science and Applications,2010,10(2):308-315
[66]Huang Shunliang, Wang Wei, Geng Dianyou. P-sets and its internal P-memory Characteristics[J]. An International Journal Advances in Systems Science and Applications,2010,10(2):216-222
[67]Liu Jiqin. P-Probabilities and its application[J]. An International Journal Advances in Systems Science and Applications,2010,10(2):200-222.
[68]汤积华,张凌,张龙.P-集合的信度特征[J].计算机工程与应用.2010,46(34)：50-122.
[69]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
[70]于秀清.P-集合的识别与筛选[J].山东大学学报：理学版,2010,45(1)：94-98.
[71]于秀清.迭代F-内嵌入信息生成及其遗传发现-应用[J].系统工程与电子技术,2011,33(12)：2691-2731
[72]刘若慧,刘保仓,史开泉.外P-集合与F-信息伪装[J].系统工程与电子技术,2011,33(1)：116-119.
[73]耿红琴,张冠宇,史开泉.F-信息伪装与伪装-还原辨识[J].计算机科学,2011,38(2)：241-245.
[74]汪洋,张冠宇,史开泉.P-集合与F-记忆信息特征-应用[J].计算机科学,2011,38(2)：246-249.
[75]于秀清.P-集合与F-外嵌入信息辨识-发现[J].计算机科学,2011,38(2)：250-253.
[76]杜英玲,孙宗保.F-粗规律分离与风L机盘运行-识别[J].山东大学学报：理学版,2011,46(6)：110-114
[77]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
[78]汪洋,张冠宇,张丽.P-集合与F-信息的动态分离特征[J].山东大学学报：理学版,2011,46(3)：35-40.
[79]郭华龙,邱育峰,陈保会.P-集合与它的f-遗传[J].计算机工程与应用2011,47(36)：41-43.
[80]李豫颖.(F,F-)-信息的辨识-过滤[J].计算机工程与应用,2011,47(34)：74-77.
[81]李豫颖.半P-集合(XF,X)与噪声数据剔除-应用[J].计算机科学,2011,38(8),221-225.
[82]刘保仓,刘若慧,史开泉.P-集合与信息F-伪装-辨识[J].计算机工程与应 用,2011,47(18)：32-35.
[83]谢维奇,于秀清.P-集合与数据内搜索-应用[J].计算机科学,2011,38(1)：236-239.
[84]闫立梅,徐风生,史开泉.P-模糊集(AF,AF)及其应用[J].计算机科学,2011,38(5)：194-198.
[85]林宏康,李豫颖,阮群生.数据依赖与异常数据分离-应用[J].计算机科学,2011,38(5)：203-207.
[86]于秀清.F-嵌入信息与F-遗传辨识-应用[J].计算机科学,2011,38(5),208-248.
[87]汪洋,史金昌,史开泉.P-集合与F-记忆信息特性-应用[J].计算机科学,2011,38(5)：212-243.
[88]李豫颖.半P-集合(XF,X)与信息的内-真度环特征[J].计算机科学,2011,38(4)：239-248.
[89]陈萍.P-集合与信息图像外变换-还原[J].太原理工大学学报,2012,43(2)：126-130.
[90]于秀清.P-集合与系统状态预测-识别[J].计算机工程与应用,2011,47(2)：46-120.
[91]李豫颖,林宏康.外-残缺数据的生成-辨识[J].计算机科学,2011,38(1)：253-267.
[92]郭志林.随机P-集合的数据筛选过滤[J].河南科技大学学报：自然科学版,2012,33(2)：83-91.
[93]于秀清.内Pp-集合与元素迁移概率特征-应用[J].计算机工程与应用,2012,48(3)：49-51.
[94]李豫颖,林宏康.内-递推信息与内-递推二叉树特征-辨识[J].山东大学学报：理学版,2012,47(8)：86-102.
[95]林宏康,李豫颖,熊国敏.动态数据距离与动态数据几何辨识-恢复[J].山东大学学报：理学版,2012,47(8)：92-97.
[96]张景晓,刘新华.函数P-集合与同物系物质结构-物性规律发现[J].山东大学学报：理学版,2012,47(8)：98-10.
[97]林蓉,史开泉,函数P-集合与信息规律的属性控制[J].计算机科学,2012,39(7),225-228.
[98]张景晓,徐风生,史开泉.P-集合与它的动态等价类特征[J].计算机科学2012,39(3)：246-249.
[99]闫立梅.内P-模糊集并-分离及其属性特征[J].山东大学学报：理学版,2012,47(1),104-109.
[100]张世良,李豫颖,林宏康.半P-集合(X’,X‘)与F-导航数据的路径匹配[J].山东大学学报：理学版,2012,47(1)：116-1120.
[101]阎红灿,王坚,刘保相.基于P-集合的本体形式背景抽取[J].计算机应用研究,2012,29(6)：2196-2204.
[102]Sun Xiyan, Liu Xidong, Fan Chengxian. P-sets and its application in the unknown information identification[J]. Journal of Theoretical and Applied Information Technology,2012,45(1),67-71.
[103]Lin Hongkang, Li Yuying, Fan Chengxian. Information outer-camouflage and true-false information[J]. International Journal of Digital Content Technology and its Applications,2012,6(13),19-29.
[104]李豫颖,范成贤.史开泉.混合记忆信息与记忆筛选[J].系统工程与电子技术,2011,33(8)：1824-1828.
[105]Lin Rong, Fan Chengxian. P-sets and identification of inward-Convergence information[J]. An International Journal of Convergence Information Techno-logy,2012,7(7):157-164.
[106]Hu Haiqing, Fan Chengxian, Wang Yan. P-sets and embedded-extrapolativc laws in electronic power system[J]. Journal of Information and Computational Science,2011,8(10):1977-1984.
[107]Fan Chengxian, Liu Shuqin, Li Kejun. Function P-sets and its application in the information system[J]. International of Advances in Information Science and Service Science,2012,4(18):380-386.
[108]林蓉,范成贤.函数P-集合与信息规律动态特征[J].山东大学学报：理学版,2012,47(1),121-126.
[109]赵文菊,范成贤.函数P-集合属性依赖与应用[J].山东大学学报：理学版,2011,46(6)：115-120
[110]Fan Chengxian, Liu Shuqin, Li Kejun. P-reasoning and the status information identification of power system [J]. Energy Education Science and Technology Part A:Energy Science and Research,2013,30(2),1023-1030.
[111]Fan Chengxian, Lin Hongkang, P-sets and the reasoning-identification of disaster information[J]. An International Journal of Convergence Information Technology,2012,7(1):337-345.
[112]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.
[113]于秀清,徐风生.P-规律推理与未知规律发现-应用[J].山东大学学报：理学版,2012,47(1)：110-115.
[114]徐风生,于秀清,史开泉.内P-推理与内收敛信息的辨识[J].计算机科学,2012,39(3)：212-215.
[115]刘道广,史开泉.外-遗传信息与它的外P-推理辨识[J].山东大学学报：理学版,2012,47(8)：81-85.
[116]Fan Chengxian, Liu Jiahe. Backward P-reasoning and fault status identification-discovery in electronic system[J]. Lecture Notes in Electrical Engineering,2013,3:301-307.
[117]林宏康,范成贤,史开泉.倒向P-推理与属性剩余发现-应用[J].计算机科学,2011,38(10)：189-198.
[118]赵树理,范成贤,史开泉.倒向P-推理与内P-属性类特征[J].计算机科学,2012,39(7)：245-249.
[119]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.
[120]Lin Hongkang, Fan Chengxian. Embedding-camouflage of inverse P-information and application[J]. An International Journal of Convergence Information Technology,2012,7(20):471-480.
[121]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.
[122]Fan Chengxian, Huang Shunliang, Inverse P-reasoning discovery identific-ation of inverse P-information[J]. International Journal of Digital Content Technology and Applications,2012,6(20):735-744.
[123]赵树理,王军昌,史开泉.逆P-等价类的逆P-推理分离-还原[J].山东大学学报：理学版,2013,48(1)：62-67.
[124]史开泉.函数S-粗集,函数粗集与信息规律系统规律拆分-合成[J].计算机 科学,2010,37(10)：1-10.
[125]W. Stallings. Cryptography and Network Security Principles and Practice, London:Prentic-Hall Int Ltd,1999:193-206.
[126]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.
[127]Shi Kaiquan, Zhao Jianli. Function S-rough sets and security-authentication of hiding law[J]. Science in China F:Information Science,2008,51(7):924-935.
[128]Koblitz N. Elliptic Curve Cryptosystems[J]. Mathematics and Computer,1987, 21(1):203-209.
[2]汪培庄,模糊集合理论及其应用[M].上海科学技术出版社,1983.
[3]武庄,石柱,何新贵.基于模糊集合论的故障树分析方法及其应用[J].系统工程与电子技术,2000,22(9)：72-75.
[4]Habib Rajabi Mashhadi, Morteza Rahimiyan. Measurement of power supplier's Market power using a proposed fuzzy estimator[J]. IEEE Transaction on Power System,2011,26(4):1836-1844.
[5]Walid G.Morsi, M.E.EI-Hawary. Fuzzy-wavelet-based electric power quality assessment of distribution systems under stationary and nonstationary disturbances[J]. IEEE Transaction on Power Delivery,2009,24(4):2099-2106.
[6]Ignacio J Ramirez-Rosado, Jose Antonio Dominguez-Navarro. New multiob-jective tabu search algorithm for fuzzy optimal planning of power distribution systems[J]. IEEE Transaction on Power System,2006,21(1):224-233.
[7]李培强,李欣然,陈辉华,唐外文.基于模糊聚类的电力负荷特性的分类与综合[J].中国电机工程学报,2005,25(24)：73-78.
[8]吴剑飞,姚建刚,陈华林,龚陈雄,李昀.电力客户能效状态模糊综合评估[J].电力系统保护与控制,2010,38(13)：94-103.
[9]C.W. Cheong. Web access failure analysis-fuzzy reliability approach[J]. International Journal of the Computer, The Internet and Management,2004, 12(1):65-73.
[10]Y.H. Song, G..S. Wang, P.Y. Wang, A.T. Johns. Environmental/economic dispatch using fuzzy logic controlled genetic algorithms [J]. IEEE Proceedings-Generation, Transmission and Distribution,1997,144(4):377-382.
[11]Payman Dehghanian, Mahmud Fotuhi-Firuzabad, Saeed Bagheri-Shouraki, Ali Asghar Razi Kazemi. Critical component identification in reliability centered asset management of power distribution systems via fuzzy AHP[J]. IEEE Systems Journal,2012,6(4):593-602.
[12]Houzhong Yan, Peter B.Luh. A fuzzy optimization-based method for integrated power system scheduling and inter-utility power transaction with uncertainties [J]. IEEE Transaction on Power System,1997,12(2):756-763.
[13]Ignacio J.Ramirez-Rosado, Jose Antonio Dominguez-Navarro. Possibilistic model based on fuzzy sets for the multiobjective optimal planning of electric power distribution networks[J]. IEEE Transaction on Power System,2004, 19(4):1801-1810.
[14]Augustine O.Esogbue, Warren E.Hearnes. On replacement models via a fuzzy set theoretic framework[J]. IEEE Transaction on Systems, Man, and Cybernetics, Part C:Applications and Reviews,1998,28(4):549-560.
[15]武宏波,胡静.基于一种新的模糊运算方法实现电力系统模糊风险评估[J].华北电力大学学报,2011,38(6)：34-39.
[16]杨太华,基于模糊熵的综合评标法在电力工程项目招投标中的应用[J].上海电力学院学报,2011,27(1),91-95.
[17]陈连栋,吕春梅.基于模糊综合评判的电力风险评估方法的研究[J].电力科学与工程,2010,26(11)：50-54.
[18]Shubham Agrawal, B.K.Panigrahi, Manoj Kumar Tiwari. Multiobjective particle swarm algorithm with fuzzy clustering for electrical power dispatch[J]. IEEE Transactions on Evolutionary Computation,2008,12(5):529-541.
[19]A Mentes, I. Helvacioglu. An application of fuzzy fault tree analysis for spread mooring systems[J]. Ocean Engineering,2011,38:285-294.
[20]Z.Pawlak, Rough sets. International Journal of Computer and Information sciences,1982,11:341-356.
[21]王国胤.粗集理论与知识获取[M].西安交通大学出版社,2001.
[22]苗夺谦.粗集理论中连续属性的离散化方法[J].自动化学报,2001,27(3)：296-302.
[23]邱雅竹,付蓉.两个论域上的粗糙集模型及其应用[J].四川师范大学学报：自然科学版,2005,28：15-18.
[24]Hu Qinghua, Zhang Lei, Chen Degang. Gaussian kernel based fuzzy rough sets: Model, uncertainty measures and applications[J]. International Journal of Approximate Reasoning,2010,51(4):453-471.
[25]Biswas Subrata, Dey Debangshu, Chatterjee Biswendu, Chakravorti Sivaji. An approach based on rough set theory for identification of single and multiple partial discharge source[J]. International Journal of Electrical Power and Energy Systems,2013,46(1):163-174.
[26]汤义强,毛军军,李侠,程白彬.基于粗集属性约简的电力供应量SVM回归预测[J].计算机技术与发展,2010,20(9)：48-51.
[27]李秋丹,迟忠先,王大公.基于数据挖掘技术的负荷预测模型[J].大连理工大学学报,2003,43(6)：845-848.
[28]赵峰,苏宏升.证据理论和粗集在变电站故障诊断中的应用[J].电力系统及其自动化学报,2009,21(2)：42-46.
[29]Sovan Dalai, Biswendu Chatterjee, Debangshu Dey, Sivaji Chakravorti. Rough-set-based feature selection and classification for power quality sensing device employing correlation techniques[J]. IEEE Sensors Journal,2013,13(2): 563-573.
[30]Chen Yumin, Miao Duoqian, Wu Ruizhi, Wu Keshou. A rough set approach to feature selection based on power set tree[J]. Knowledge-based systems,2011, 24(2):275-281.
[31]Ma Wenbin, Ma Chao, Zheng Guixing, Zhao Rui. The fault location approach for grid network base on MAS of rough set theory[J]. Applied Mechanics and Materials,2011,127:460-465.
[32]L.P.Khoo, S.B.Tor, J.R.Li. A rough set approach to the ordering of basic events in a fault tree for fault diagnosis[J]. International Journal of Advanced Manufacturing Technology,2001,17(10):769-774.
[33]Zhou Yongyong, Zhou Quan, Liu Jiabin, Liu Yuming, Ren Haijun, Sun Caiyin, Liu Xu. Rough set theory based approach for fault diagnosis rule extraction of distribution system[J].2008,34(12):2713-2718.
[34]Pisicabreve I., P. Postolache. Rough set theory and its applications in electrical power engineering[J]. University "Politehnica" of Bucharest, Scientific Bulletin Series C:Electrical Engineering,2010,72(1):211-222.
[35]I. Pisicabreve. A note on rough set theory applications in power engineering[J]. University "Politehnica" of Bucharest, Scientific Bulletin Series C:Electrical Engineering,2010,72(3):313-318.
[36]Dong Lixin, Xiao Dengming, Liang Yishan. Rough set and fuzzy wavelet neural network integrated with least square weighted fusion algorithm based fault diagnosis research for power transformers[J]. Electric Power Systems Research,2008,78(1):129-136.
[37]Cai Jinding. An improved three-ratio fault diagnosis based on rough set theory for power transformer[J]. Advanced Technology of Electrical Engineering and Energy,2004,23(4):8-12.
[38]罗治强,张焰,朱杰.粗集理论在电力系统负荷预测中的应用[J].电网技术,2004,28(3)：29-32.
[39]庞清乐,孙同景,钟麦英,杨福刚.基于粗集理论的小电流接地系统故障选线[J].中国电机工程学报,2007,27(4)：60-64.
[40]A. Kusiak. Rough set theory:a data mining tool for semiconductor manufac-turing[J]. IEEE Transactions on Electronics Packaging Manufacturing,2001, 24(1):44-50.
[41]Chen Degang, Zhao Suyun, Zhang Lei, Yang Yongping, Zhang Xiao. Sample pair selection for attribute reduction with rough set[J]. IEEE Transaction on Knowledge and Data Engineering,2012,24(11):2080-2093.
[42]史开泉.P-集合[J].山东大学学报理学版,2008,43(11)：77-84.
[43]史开泉.函数P-集合[J].山东大学学报：理学版,2011,46(2)：62-69.
[44]Shi Kaiquan. Function P-sets [J]. International Journal of Machine Learning and Cybernetics,2011,2(4):281-288.
[45]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.
[46]史开泉.逆P-集合[J].山东大学学报：理学版,2012,47(1)：98-109.
[47]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.
[48]闫立梅.逆P-推理与未知信息推理-搜索与发现[J].计算机科学,2012,39(8)：268-272.
[49]史开泉.P-集合与它的应用特性[J].计算机科学,2010,37(8)：1-8.
[50]Shi Kaiquan. P-sets and its applications[J]. An International Journal Advances in Systems Science and Applications,2009,9(2):209-219.
[51]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.
[52]汤积华,陈保会,史开泉.P-集合与(F,F)数据生成-辨识[J].山东大学学报：理学版,2009,44(11)：83-92.
[53]李豫颖,谢维奇,史开泉.F-残缺数据的辨识与恢复[J].山东大学学报：理学版,2009,45(9)：57-64.
[54]Shi Kaiquan, Li Xiuhong. Camouflaged information identification and its application [J]. An International Journal Advances in Systems Science and Applications,2010,10(2):157-167.
[55]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.
[56]张飞,陈萍,张丽.P-集合的P-分离与应用[J].山东大学学报理学版,2010,45(3)：18-22.
[57]Zhang Li, Cui Yuquan. Outer P-sets and data internal recovery[J]. An International Journal Advances in Systems Science and Applications,2010, 10(2):189-199.
[58]Zhang Li, Xiu Ming, Shi Kaiquan. P-sets and applications of internal-outer data circle[J]. Quantitative Logic and Soft Computing,2010,1(2):581-592.
[59]Li Yuying, Zhang Li, Shi Kailua. Generation and Recovery of Compressed data and Redundant data[J]. Quantitative Logic and Soft Computing,2010,1(2): 661-672.
[60]Xiu Ming, Shi Kaiquan, Zhang Li. P-sets and F-data Selection-Discovery [J]. Quantitative Logic and Soft Computing,2010, 1(2):791-800.
[61]周玉华,张冠宇,张丽.内-外数据圆与动态数据-恢复[J].山东大学学报：理学版,2010,45(8)：21-26.
[62]Lin Hongkang, Li Yuying. P-sets and its P-separation theorems[J]. An International Journal Advances in Systems Science and Applications,2010, 10(2):209-215
[63]周玉华,张冠宇,史开泉.P-集合与双信息规律生成[J].数学的实践与认识,2010,40(13)：71-80
[64]Wang Yang, Geng Hongqin, Shi Kaiquan. The mining of dynamic information based on P-sets and its application[J]. An International Journal Advances in Systems Science and Applications,2010,10(2):234-240.
[65]Zhang Guanyu, Li Enzhong. Information gene and identification of its information Knock-out/Knock-in [J]. An International Journal Advances in Systems Science and Applications,2010,10(2):308-315
[66]Huang Shunliang, Wang Wei, Geng Dianyou. P-sets and its internal P-memory Characteristics[J]. An International Journal Advances in Systems Science and Applications,2010,10(2):216-222
[67]Liu Jiqin. P-Probabilities and its application[J]. An International Journal Advances in Systems Science and Applications,2010,10(2):200-222.
[68]汤积华,张凌,张龙.P-集合的信度特征[J].计算机工程与应用.2010,46(34)：50-122.
[69]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
[70]于秀清.P-集合的识别与筛选[J].山东大学学报：理学版,2010,45(1)：94-98.
[71]于秀清.迭代F-内嵌入信息生成及其遗传发现-应用[J].系统工程与电子技术,2011,33(12)：2691-2731
[72]刘若慧,刘保仓,史开泉.外P-集合与F-信息伪装[J].系统工程与电子技术,2011,33(1)：116-119.
[73]耿红琴,张冠宇,史开泉.F-信息伪装与伪装-还原辨识[J].计算机科学,2011,38(2)：241-245.
[74]汪洋,张冠宇,史开泉.P-集合与F-记忆信息特征-应用[J].计算机科学,2011,38(2)：246-249.
[75]于秀清.P-集合与F-外嵌入信息辨识-发现[J].计算机科学,2011,38(2)：250-253.
[76]杜英玲,孙宗保.F-粗规律分离与风L机盘运行-识别[J].山东大学学报：理学版,2011,46(6)：110-114
[77]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
[78]汪洋,张冠宇,张丽.P-集合与F-信息的动态分离特征[J].山东大学学报：理学版,2011,46(3)：35-40.
[79]郭华龙,邱育峰,陈保会.P-集合与它的f-遗传[J].计算机工程与应用2011,47(36)：41-43.
[80]李豫颖.(F,F-)-信息的辨识-过滤[J].计算机工程与应用,2011,47(34)：74-77.
[81]李豫颖.半P-集合(XF,X)与噪声数据剔除-应用[J].计算机科学,2011,38(8),221-225.
[82]刘保仓,刘若慧,史开泉.P-集合与信息F-伪装-辨识[J].计算机工程与应 用,2011,47(18)：32-35.
[83]谢维奇,于秀清.P-集合与数据内搜索-应用[J].计算机科学,2011,38(1)：236-239.
[84]闫立梅,徐风生,史开泉.P-模糊集(AF,AF)及其应用[J].计算机科学,2011,38(5)：194-198.
[85]林宏康,李豫颖,阮群生.数据依赖与异常数据分离-应用[J].计算机科学,2011,38(5)：203-207.
[86]于秀清.F-嵌入信息与F-遗传辨识-应用[J].计算机科学,2011,38(5),208-248.
[87]汪洋,史金昌,史开泉.P-集合与F-记忆信息特性-应用[J].计算机科学,2011,38(5)：212-243.
[88]李豫颖.半P-集合(XF,X)与信息的内-真度环特征[J].计算机科学,2011,38(4)：239-248.
[89]陈萍.P-集合与信息图像外变换-还原[J].太原理工大学学报,2012,43(2)：126-130.
[90]于秀清.P-集合与系统状态预测-识别[J].计算机工程与应用,2011,47(2)：46-120.
[91]李豫颖,林宏康.外-残缺数据的生成-辨识[J].计算机科学,2011,38(1)：253-267.
[92]郭志林.随机P-集合的数据筛选过滤[J].河南科技大学学报：自然科学版,2012,33(2)：83-91.
[93]于秀清.内Pp-集合与元素迁移概率特征-应用[J].计算机工程与应用,2012,48(3)：49-51.
[94]李豫颖,林宏康.内-递推信息与内-递推二叉树特征-辨识[J].山东大学学报：理学版,2012,47(8)：86-102.
[95]林宏康,李豫颖,熊国敏.动态数据距离与动态数据几何辨识-恢复[J].山东大学学报：理学版,2012,47(8)：92-97.
[96]张景晓,刘新华.函数P-集合与同物系物质结构-物性规律发现[J].山东大学学报：理学版,2012,47(8)：98-10.
[97]林蓉,史开泉,函数P-集合与信息规律的属性控制[J].计算机科学,2012,39(7),225-228.
[98]张景晓,徐风生,史开泉.P-集合与它的动态等价类特征[J].计算机科学2012,39(3)：246-249.
[99]闫立梅.内P-模糊集并-分离及其属性特征[J].山东大学学报：理学版,2012,47(1),104-109.
[100]张世良,李豫颖,林宏康.半P-集合(X’,X‘)与F-导航数据的路径匹配[J].山东大学学报：理学版,2012,47(1)：116-1120.
[101]阎红灿,王坚,刘保相.基于P-集合的本体形式背景抽取[J].计算机应用研究,2012,29(6)：2196-2204.
[102]Sun Xiyan, Liu Xidong, Fan Chengxian. P-sets and its application in the unknown information identification[J]. Journal of Theoretical and Applied Information Technology,2012,45(1),67-71.
[103]Lin Hongkang, Li Yuying, Fan Chengxian. Information outer-camouflage and true-false information[J]. International Journal of Digital Content Technology and its Applications,2012,6(13),19-29.
[104]李豫颖,范成贤.史开泉.混合记忆信息与记忆筛选[J].系统工程与电子技术,2011,33(8)：1824-1828.
[105]Lin Rong, Fan Chengxian. P-sets and identification of inward-Convergence information[J]. An International Journal of Convergence Information Techno-logy,2012,7(7):157-164.
[106]Hu Haiqing, Fan Chengxian, Wang Yan. P-sets and embedded-extrapolativc laws in electronic power system[J]. Journal of Information and Computational Science,2011,8(10):1977-1984.
[107]Fan Chengxian, Liu Shuqin, Li Kejun. Function P-sets and its application in the information system[J]. International of Advances in Information Science and Service Science,2012,4(18):380-386.
[108]林蓉,范成贤.函数P-集合与信息规律动态特征[J].山东大学学报：理学版,2012,47(1),121-126.
[109]赵文菊,范成贤.函数P-集合属性依赖与应用[J].山东大学学报：理学版,2011,46(6)：115-120
[110]Fan Chengxian, Liu Shuqin, Li Kejun. P-reasoning and the status information identification of power system [J]. Energy Education Science and Technology Part A:Energy Science and Research,2013,30(2),1023-1030.
[111]Fan Chengxian, Lin Hongkang, P-sets and the reasoning-identification of disaster information[J]. An International Journal of Convergence Information Technology,2012,7(1):337-345.
[112]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.
[113]于秀清,徐风生.P-规律推理与未知规律发现-应用[J].山东大学学报：理学版,2012,47(1)：110-115.
[114]徐风生,于秀清,史开泉.内P-推理与内收敛信息的辨识[J].计算机科学,2012,39(3)：212-215.
[115]刘道广,史开泉.外-遗传信息与它的外P-推理辨识[J].山东大学学报：理学版,2012,47(8)：81-85.
[116]Fan Chengxian, Liu Jiahe. Backward P-reasoning and fault status identification-discovery in electronic system[J]. Lecture Notes in Electrical Engineering,2013,3:301-307.
[117]林宏康,范成贤,史开泉.倒向P-推理与属性剩余发现-应用[J].计算机科学,2011,38(10)：189-198.
[118]赵树理,范成贤,史开泉.倒向P-推理与内P-属性类特征[J].计算机科学,2012,39(7)：245-249.
[119]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.
[120]Lin Hongkang, Fan Chengxian. Embedding-camouflage of inverse P-information and application[J]. An International Journal of Convergence Information Technology,2012,7(20):471-480.
[121]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.
[122]Fan Chengxian, Huang Shunliang, Inverse P-reasoning discovery identific-ation of inverse P-information[J]. International Journal of Digital Content Technology and Applications,2012,6(20):735-744.
[123]赵树理,王军昌,史开泉.逆P-等价类的逆P-推理分离-还原[J].山东大学学报：理学版,2013,48(1)：62-67.
[124]史开泉.函数S-粗集,函数粗集与信息规律系统规律拆分-合成[J].计算机 科学,2010,37(10)：1-10.
[125]W. Stallings. Cryptography and Network Security Principles and Practice, London:Prentic-Hall Int Ltd,1999:193-206.
[126]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.
[127]Shi Kaiquan, Zhao Jianli. Function S-rough sets and security-authentication of hiding law[J]. Science in China F:Information Science,2008,51(7):924-935.
[128]Koblitz N. Elliptic Curve Cryptosystems[J]. Mathematics and Computer,1987, 21(1):203-209.