粗糙集和神经网络相结合的数据融合方法研究
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摘要
信息科学的飞速发展，对数据处理技术提出了新的、更高的要求。在多传感器系统中，由于传感器的精度、数据的采集成本、系统组成的多种环节以及外部环境等因素的影响，会导致多传感器系统中信息的不完备性。从而，使得传统的数据处理方法，不能满足工程应用对信息处理快速性和高精度的要求，这给数据融合带来困难。因此，对多传感器系统中不完备信息的处理已成为众多学者广泛关注的热点问题。本文将数据挖掘和数据融合技术相结合，用于多传感器系统中不完备信息的处理，所做的主要工作和创新性研究如下：
1．针对数据挖掘与数据融合技术在功能上互补的特点，研究了数据挖掘与数据融合技术相结合的基本概念和原理，并针对数据融合中先验信息难以获取，以及系统中存在大量冗余数据的问题，研究了基于粗糙集理论的数据融合模型。利用粗糙集理论的属性约简算法，剔除冗余信息得到了最简规则，并利用该规则进行数据融合。
2．研究了粗糙集理论中连续数据的离散化方法，提出了一种基于遗传算法的离散化方法。该方法以离散断点的数目最少和离散化后决策系统的一致性最大为优化目标，最大程度地保证了决策系统的一致性。
3．提出了一种直接在不完备信息系统上进行数据挖掘的方法。该方法从实际应用出发，考虑到属性获取的实时性、难易程度和成本等问题，将属性分层后进行递阶处理，求得最接近原始数据的规则。与经过完备化处理后进行挖掘的方法相比，该方法具有较强的实用性和有效性，并提高了知识约简的速度。
4．针对多传感器系统中不完备信息的融合问题，将数据挖掘方法和神经网络技术相结合，提出了一种基于粗糙集——模糊神经网络的融合系统设计方法。给出了系统的设计原理，设计步骤，系统各部分的算法以及网络的构造方法，并推导了网络的学习公式。仿真结果证明了该融合系统的可行性和有效性。
With the rapid development of information science, new and higher requirement is presented to data processing technique. Influenced by such factors as the precision of sensors, the cost of data collection, the variety of data mode and the external environment, the information in multi-sensor system is mostly incomplete. As a result, the traditional data processing methods can't satisfy the demands of high precision and rapid speed of information processing, which brings new challenge to data fusion. Therefore, the processing of incomplete information in multi-sensor system has been a hot spot concerned by many scholars. With the method of combing data mining and data fusion technology, the dissertation researches the processing method of incomplete information.
The main work and innovations are as follows:
Firstly, according to the complementary functions of data fusion and data mining, the basic concepts and the principle of combining both technologies are investigated. Moreover, in order to deal with the redundant data and the difficulty of obtaining prior knowledge, the fusion model based on rough sets is studied. By applying the reduction method, the redundant information is eliminated and the fusion algorithm is extracted.
Secondly, a discretization method based on genetic algorithm is proposed. In this method, the minimum set of cuts and the maximum consistency of decision system are the optimizing goals. Thus the consistency of the system is ensured at the maximal extent.
Thirdly, a data mining method based on rough sets theory for incomplete information system is proposed. From the practical application, in consideration of the real-time, difficulty and cost during obtaining the attributes, the attributes are partitioned into complete part and incomplete part. Thus the decision system is presented at two layers. Then the reduction method is hierarchically applied to each layer. This mining method has strong application and fast reduction speed.
Finally, the problem of incomplete information in multi-sensor system is investigated. By combining the above mining method and neural network, a design
1．针对数据挖掘与数据融合技术在功能上互补的特点，研究了数据挖掘与数据融合技术相结合的基本概念和原理，并针对数据融合中先验信息难以获取，以及系统中存在大量冗余数据的问题，研究了基于粗糙集理论的数据融合模型。利用粗糙集理论的属性约简算法，剔除冗余信息得到了最简规则，并利用该规则进行数据融合。
2．研究了粗糙集理论中连续数据的离散化方法，提出了一种基于遗传算法的离散化方法。该方法以离散断点的数目最少和离散化后决策系统的一致性最大为优化目标，最大程度地保证了决策系统的一致性。
3．提出了一种直接在不完备信息系统上进行数据挖掘的方法。该方法从实际应用出发，考虑到属性获取的实时性、难易程度和成本等问题，将属性分层后进行递阶处理，求得最接近原始数据的规则。与经过完备化处理后进行挖掘的方法相比，该方法具有较强的实用性和有效性，并提高了知识约简的速度。
4．针对多传感器系统中不完备信息的融合问题，将数据挖掘方法和神经网络技术相结合，提出了一种基于粗糙集——模糊神经网络的融合系统设计方法。给出了系统的设计原理，设计步骤，系统各部分的算法以及网络的构造方法，并推导了网络的学习公式。仿真结果证明了该融合系统的可行性和有效性。
With the rapid development of information science, new and higher requirement is presented to data processing technique. Influenced by such factors as the precision of sensors, the cost of data collection, the variety of data mode and the external environment, the information in multi-sensor system is mostly incomplete. As a result, the traditional data processing methods can't satisfy the demands of high precision and rapid speed of information processing, which brings new challenge to data fusion. Therefore, the processing of incomplete information in multi-sensor system has been a hot spot concerned by many scholars. With the method of combing data mining and data fusion technology, the dissertation researches the processing method of incomplete information.
The main work and innovations are as follows:
Firstly, according to the complementary functions of data fusion and data mining, the basic concepts and the principle of combining both technologies are investigated. Moreover, in order to deal with the redundant data and the difficulty of obtaining prior knowledge, the fusion model based on rough sets is studied. By applying the reduction method, the redundant information is eliminated and the fusion algorithm is extracted.
Secondly, a discretization method based on genetic algorithm is proposed. In this method, the minimum set of cuts and the maximum consistency of decision system are the optimizing goals. Thus the consistency of the system is ensured at the maximal extent.
Thirdly, a data mining method based on rough sets theory for incomplete information system is proposed. From the practical application, in consideration of the real-time, difficulty and cost during obtaining the attributes, the attributes are partitioned into complete part and incomplete part. Thus the decision system is presented at two layers. Then the reduction method is hierarchically applied to each layer. This mining method has strong application and fast reduction speed.
Finally, the problem of incomplete information in multi-sensor system is investigated. By combining the above mining method and neural network, a design
引文
[1] 杨万海．多传感器数据融合及其应用[M]．西安：西安电子科技大学出版社，2004．
[2] 刘同明，夏祖勋，谢洪成．数据融合技术及应用[M]．北京：国防工业出版社，2000．
[3] Hall D L, Linas J. An introduction to multi-sensor data fusion[J]. Proc IEEE, 1997, 85(1): 1～23.
[4] Bar-Shalom Y, Fortmann T E. Tracking and Data Association[M]. New York: Academic Press, 1988.
[5] Bar-Shalom Y, Li X R. Multitarget multisensor tracking: principles and techniques[M]. Storrs, CT: YBS, 1995.
[6] Blackman, Samual S. Multiple-Target Tracking with Radar Application[M]. Norwood: Artech House, 1986.
[7] Bar-Shalom Y. Multi target-multisensor tracking: Advanced applications[M]. Norwood Artech: House, 1992.
[8] 权太范．信息融合——神经网络—模糊推理理论与应用[M]．北京：国防工业出版社，2002．
[9] 何友，王国宏等．多传感器数据融合及其应用[M]．北京：电子工业出版社，2000．
[10] 康耀红．数据融合理论及其应用[M]．西安：西安电子科技大学出版社，1997．
[11] 王耀男，李树涛．多传感器信息融合及其应用综述[J]．控制与决策．2001，16(5)：518～522．
[12] 高翔，王勇．数据融合技术综述[J]．计算机测量与控制．2002，10(11)： 706～700．
[13] C. Ray Smith. Multisensor data fusion: Concepts and Principles[J]. IEEE Pacific Rim Conference on Communications, Computer and Signal Processing, 1991, 1: 235～237.
[14] Edward L, Waltz. Information Understanding: Integrating Data Fusion and Data Mining Processes. ISCA'98, Proceedings of the 1998 IEEE International Symposium on Circuits and Systems, 6: 553～556.
[15] Bin Han, Tie-Jun Wu. Data mining in multisensor system based on rough set theory[C]. American Control Conference, 2001. Proceedings of the 2001, 6: 4427～4431.
[16] Frawley W J, Piatetsky G.. Knowledge discovery in database: An overview of knowledge discovery in database[M]. AAAI/MIT press, 1991.
[17] 刘同明，曾富贵，刘伟．数据融合与数据挖掘相集成的自动目标识别系统[J]．计算机工程与应用．2002，3：92～95．
[18] 何剑斌，郑启伦，彭宏．数据融合与数据挖掘的集成研究[J]．计算机工程与应用．．2002，18：204～206．
[19] Kusiak A, Kurasek C. Data Mining of Printed-Circuit Board Defects[J]. IEEE Transactions on Robotics and Automation, 2001, 17(2): 191～196.
[20] Pawlak Z. Rough Sets[J]. International Journal of Computer and Information Sciences, 1982, 11: 341～356.
[21] 何友，彭应宁．多传感器数据融合模型综述[J]．清华大学学报．1996，36(9)： 14～20．
[22] White F E. Data fusion lexicon: Data fusion subpanel of the joint directors of laboratories technical panel for C~3[R]. San Diego, 1991.
[23] 孙红岩，毛士艺．多传感器目标识别的数据融合[J]．电子学报．1995(23)： 188～193．
[24] Karlheinz B, Jaeger K. Model-based sensor fusion for target recognition. Proceedings of SPIE. 1996(2756): 98～107.
[25] Linas J, Waltz. EMulti-sensor Data Fusion[M]. Boston, MA: Artech House, 1990.
[26] Fayyad U, Piatetsky-Shapiro. Advances in Knowledge Discovery and Data Mining[M]. AAA/MIT Press, 1996.
[27] 刘同明等．数据挖掘技术及其应用[M]．国防工业出版社，2001．
[28] A. Feelders. Methodological and Practical Aspects of Data Mining. Information Processing and Management, 2000.
[29] 员巧云，程刚．近年来我国数据挖掘研究综述[J]．情报学报．2005，24(2)： 250～256．
[30] Chen Ming yan, Han Jiawei, Philip S Yu. Data Mining: An overview from a database perspective[J]. IEEE Transactions on Knowledge and Data Engineering, 1996, 8 (6): 866～881.
[31] Yairi T, Kato Y, Hofi K. Fault Detection by Mining Association Rules from House-keeping Data. Proc. Robotics and Automation in Space, 2001.
[32] Mehmed Kantardzic．数据挖掘：概念、模型、方法和算法[M]．北京：清华大学出版社，2003．
[33] John F, Elder IV. A Comparison of Leading Data Mining Tools. Information Processing and Management, 2000.
[34] Pawlak Z. Rough set-theoretical aspects of reasoning about data[M]. Dordrecht: Kluwer Academic Publishers, 1991.
[35] 张文修，吴伟志．粗糙集理论介绍和研究综述[J]．模糊系统与数学，2000，14(4)：1～12．
[36] 李雄飞，李军．数据挖掘与知识发现[M]．北京：高等教育出版社，2003．
[37] 曾黄麟．粗集理论及其应用[M]．重庆：重庆大学出版社，1996．
[38] 王国胤．Rough集理论与知识获取[M]．西安：西安交通大学出版社，2001．
[39] 曾黄麟．智能计算[M]．重庆：重庆大学出版社，2004．
[40] Pawlak Z et al. Rough sets[J]. Communications of ACM, 1995, 38(11): 89～95.
[41] 李永敏，朱善君，陈湘晖等．基于粗糙集理论的数据挖掘模型[J]．清华大学学报(自然科学版)，1999，39(1)：29～33．
[42] 侯利娟，王国胤，聂能等．粗糙集理论中的离散化问题[J]．计算机科学，2000，27(2)：89～94．
[43] Nguyen H S. Discretization of Real Value Attributes: Boolean reasoning Approach[D]. Warsaw: Warsaw University, 1997.
[44] 米凯利维茨Z，何险峰．演化程序—遗传算法何数据编码的结合[M]．北京：科学出版社，2000．
[45] Jian-hua Dai, Yuan-xiang Li. Study on discretization based on rough set theory[C]. Proceedings of the First International Conference on Machine Learning and Cybernetics, Beijing, 2002.
[46] Nguyen H S, Skowron A. Quantization of real value attributes[C]. Proceedings of Second Joint Annual Conf on Information Science, Wrightsville Beach, North Carolina, 1995: 34～37.
[47] 曾志远．卫星遥感图像计算机分类与地学研究应用[M]．北京：科学出版社，2004．
[48] 乔斌．粗糙集理论分层递阶约简算法的研究[D]．浙江大学博士论文，2003．
[49] S. Tseng, K. Wang, C. Lee. A pre-processing method to deal with missing values by integrating clustering and regression techniques[J]. Applied Artificial Intelligence, 2003, 17 (5): 535～544.
[50] Dorian Pyle. Data Preparation for Data Mining[M]. San Francisco, Morgan Kaufmann Publishers, 1999.
[51] 张文修，吴伟业，梁吉业等．粗糙集理论与方法[M]．北京：科学出版社，2001． system[J]. Information Science, 1998, 39 (1): 110～113.
[53] Xiaolu Huang. A pseudo-nearest-neighbor approach for missing data recovery on Gaussian random data sets[J]. Pattern Recognition Letters, 2002, 23: 1613～1622.
[54] J W Grzymala-Busse, M Hu. A comparison of several approaches to missing attribute values in data mining. Proc of the 2nd Int' Conf on Rough Sets and Current Trends in Computing, Berlin: Springer-Verlag, 2000, 378～3852.
[55] Joe Schafer. Multiple imputation: a primer[J]. Statistical Methods in Medical Research, 1999, 8: 3～15.
[56] Marzena Kryszkiewicz. Rules in incomplete information systems[J]. Information Sciences, 1999, 113: 271～292.
[57] 吴今培，孙德山．现代数据分析[M]．北京：机械工业出版社，2006．
[58] 郭昱葵，熊友山，姚海林等．模糊数学在当宜高速公路膨胀土判别和分类中的应用[J]．岩土力学，1999，20(3)：61～65．
[59] 杨杰，胡英，全勇．集成数据融合和数据挖掘技术的信息智能处理平台[J]．高技术通信，2003，1：57～61．
[60] T. L. Huntsberger, S. N. Jayaramanurthy. A framework for multi-sensor fusion in the presence of uncertainty[J]. Proc, Workshop Spatial Reasoning and Multi-sensor Fusion, 1987: 345～350.
[61] Thomopoulos Stelios C, Wann Chin-Der. Clustering with unsupervised neural networks with applications to data fusion. SPIE, 1994, 2093: 621～632.
[62] 曲晓慧，安钢．数据融合方法综述及展望[J]．舰船电子工程，2003(2)： 2～4．
[63] X. Dai, S. Khorram. Data fusion using artificial neural networks: a case study on multitemporal change analysis[J]. Computers, Environment and Urban Systems, 1999, 23(1): 19～31.
[64] 魏海坤．神经网络结构设计的理论与方法[M]．北京：国防工业出版社，2005．
[65] 陈文林，郝丽娜，徐心和．粗糙集—神经网络—专家系统混合系统及其应用[J]．计算机工程．2003，9(9)：147～149．
[66] 赵卫东，陈国华．粗集和神经网络的集成技术研究[J]．系统工程与电子技术，2002，24(10)：103～106．
[67] Pawan Lingras. Comparision of Neofuzzy and Rough Neural Networks[J]. Journal of Information Science, 1998, 110: 207～215.
[68] Lazar Alina, Sethi Ishwar K. Decision Rule Extraction from Trained Neural Networks Using Rough Sets[J]. Intelligent Engineering Systems Through Artificial Neural Networks, 1999, 9: 493～498.
[69] Chung Young-June, Jun Hyo-Byung,etal. A Study on the Structure Optimization of Multilayer Neural Networks Using Rough Set Theory[J]. Transactions of the Korean Institute of Electrical Engineers, 1999, 48(1): 82～91.
[70] 王璿，高社生，赵霞．基于粗糙集理论的模糊神经网络构造方法[J]．计算机测量与控制．2006，14(6)：782～784．
[2] 刘同明，夏祖勋，谢洪成．数据融合技术及应用[M]．北京：国防工业出版社，2000．
[3] Hall D L, Linas J. An introduction to multi-sensor data fusion[J]. Proc IEEE, 1997, 85(1): 1～23.
[4] Bar-Shalom Y, Fortmann T E. Tracking and Data Association[M]. New York: Academic Press, 1988.
[5] Bar-Shalom Y, Li X R. Multitarget multisensor tracking: principles and techniques[M]. Storrs, CT: YBS, 1995.
[6] Blackman, Samual S. Multiple-Target Tracking with Radar Application[M]. Norwood: Artech House, 1986.
[7] Bar-Shalom Y. Multi target-multisensor tracking: Advanced applications[M]. Norwood Artech: House, 1992.
[8] 权太范．信息融合——神经网络—模糊推理理论与应用[M]．北京：国防工业出版社，2002．
[9] 何友，王国宏等．多传感器数据融合及其应用[M]．北京：电子工业出版社，2000．
[10] 康耀红．数据融合理论及其应用[M]．西安：西安电子科技大学出版社，1997．
[11] 王耀男，李树涛．多传感器信息融合及其应用综述[J]．控制与决策．2001，16(5)：518～522．
[12] 高翔，王勇．数据融合技术综述[J]．计算机测量与控制．2002，10(11)： 706～700．
[13] C. Ray Smith. Multisensor data fusion: Concepts and Principles[J]. IEEE Pacific Rim Conference on Communications, Computer and Signal Processing, 1991, 1: 235～237.
[14] Edward L, Waltz. Information Understanding: Integrating Data Fusion and Data Mining Processes. ISCA'98, Proceedings of the 1998 IEEE International Symposium on Circuits and Systems, 6: 553～556.
[15] Bin Han, Tie-Jun Wu. Data mining in multisensor system based on rough set theory[C]. American Control Conference, 2001. Proceedings of the 2001, 6: 4427～4431.
[16] Frawley W J, Piatetsky G.. Knowledge discovery in database: An overview of knowledge discovery in database[M]. AAAI/MIT press, 1991.
[17] 刘同明，曾富贵，刘伟．数据融合与数据挖掘相集成的自动目标识别系统[J]．计算机工程与应用．2002，3：92～95．
[18] 何剑斌，郑启伦，彭宏．数据融合与数据挖掘的集成研究[J]．计算机工程与应用．．2002，18：204～206．
[19] Kusiak A, Kurasek C. Data Mining of Printed-Circuit Board Defects[J]. IEEE Transactions on Robotics and Automation, 2001, 17(2): 191～196.
[20] Pawlak Z. Rough Sets[J]. International Journal of Computer and Information Sciences, 1982, 11: 341～356.
[21] 何友，彭应宁．多传感器数据融合模型综述[J]．清华大学学报．1996，36(9)： 14～20．
[22] White F E. Data fusion lexicon: Data fusion subpanel of the joint directors of laboratories technical panel for C~3[R]. San Diego, 1991.
[23] 孙红岩，毛士艺．多传感器目标识别的数据融合[J]．电子学报．1995(23)： 188～193．
[24] Karlheinz B, Jaeger K. Model-based sensor fusion for target recognition. Proceedings of SPIE. 1996(2756): 98～107.
[25] Linas J, Waltz. EMulti-sensor Data Fusion[M]. Boston, MA: Artech House, 1990.
[26] Fayyad U, Piatetsky-Shapiro. Advances in Knowledge Discovery and Data Mining[M]. AAA/MIT Press, 1996.
[27] 刘同明等．数据挖掘技术及其应用[M]．国防工业出版社，2001．
[28] A. Feelders. Methodological and Practical Aspects of Data Mining. Information Processing and Management, 2000.
[29] 员巧云，程刚．近年来我国数据挖掘研究综述[J]．情报学报．2005，24(2)： 250～256．
[30] Chen Ming yan, Han Jiawei, Philip S Yu. Data Mining: An overview from a database perspective[J]. IEEE Transactions on Knowledge and Data Engineering, 1996, 8 (6): 866～881.
[31] Yairi T, Kato Y, Hofi K. Fault Detection by Mining Association Rules from House-keeping Data. Proc. Robotics and Automation in Space, 2001.
[32] Mehmed Kantardzic．数据挖掘：概念、模型、方法和算法[M]．北京：清华大学出版社，2003．
[33] John F, Elder IV. A Comparison of Leading Data Mining Tools. Information Processing and Management, 2000.
[34] Pawlak Z. Rough set-theoretical aspects of reasoning about data[M]. Dordrecht: Kluwer Academic Publishers, 1991.
[35] 张文修，吴伟志．粗糙集理论介绍和研究综述[J]．模糊系统与数学，2000，14(4)：1～12．
[36] 李雄飞，李军．数据挖掘与知识发现[M]．北京：高等教育出版社，2003．
[37] 曾黄麟．粗集理论及其应用[M]．重庆：重庆大学出版社，1996．
[38] 王国胤．Rough集理论与知识获取[M]．西安：西安交通大学出版社，2001．
[39] 曾黄麟．智能计算[M]．重庆：重庆大学出版社，2004．
[40] Pawlak Z et al. Rough sets[J]. Communications of ACM, 1995, 38(11): 89～95.
[41] 李永敏，朱善君，陈湘晖等．基于粗糙集理论的数据挖掘模型[J]．清华大学学报(自然科学版)，1999，39(1)：29～33．
[42] 侯利娟，王国胤，聂能等．粗糙集理论中的离散化问题[J]．计算机科学，2000，27(2)：89～94．
[43] Nguyen H S. Discretization of Real Value Attributes: Boolean reasoning Approach[D]. Warsaw: Warsaw University, 1997.
[44] 米凯利维茨Z，何险峰．演化程序—遗传算法何数据编码的结合[M]．北京：科学出版社，2000．
[45] Jian-hua Dai, Yuan-xiang Li. Study on discretization based on rough set theory[C]. Proceedings of the First International Conference on Machine Learning and Cybernetics, Beijing, 2002.
[46] Nguyen H S, Skowron A. Quantization of real value attributes[C]. Proceedings of Second Joint Annual Conf on Information Science, Wrightsville Beach, North Carolina, 1995: 34～37.
[47] 曾志远．卫星遥感图像计算机分类与地学研究应用[M]．北京：科学出版社，2004．
[48] 乔斌．粗糙集理论分层递阶约简算法的研究[D]．浙江大学博士论文，2003．
[49] S. Tseng, K. Wang, C. Lee. A pre-processing method to deal with missing values by integrating clustering and regression techniques[J]. Applied Artificial Intelligence, 2003, 17 (5): 535～544.
[50] Dorian Pyle. Data Preparation for Data Mining[M]. San Francisco, Morgan Kaufmann Publishers, 1999.
[51] 张文修，吴伟业，梁吉业等．粗糙集理论与方法[M]．北京：科学出版社，2001． system[J]. Information Science, 1998, 39 (1): 110～113.
[53] Xiaolu Huang. A pseudo-nearest-neighbor approach for missing data recovery on Gaussian random data sets[J]. Pattern Recognition Letters, 2002, 23: 1613～1622.
[54] J W Grzymala-Busse, M Hu. A comparison of several approaches to missing attribute values in data mining. Proc of the 2nd Int' Conf on Rough Sets and Current Trends in Computing, Berlin: Springer-Verlag, 2000, 378～3852.
[55] Joe Schafer. Multiple imputation: a primer[J]. Statistical Methods in Medical Research, 1999, 8: 3～15.
[56] Marzena Kryszkiewicz. Rules in incomplete information systems[J]. Information Sciences, 1999, 113: 271～292.
[57] 吴今培，孙德山．现代数据分析[M]．北京：机械工业出版社，2006．
[58] 郭昱葵，熊友山，姚海林等．模糊数学在当宜高速公路膨胀土判别和分类中的应用[J]．岩土力学，1999，20(3)：61～65．
[59] 杨杰，胡英，全勇．集成数据融合和数据挖掘技术的信息智能处理平台[J]．高技术通信，2003，1：57～61．
[60] T. L. Huntsberger, S. N. Jayaramanurthy. A framework for multi-sensor fusion in the presence of uncertainty[J]. Proc, Workshop Spatial Reasoning and Multi-sensor Fusion, 1987: 345～350.
[61] Thomopoulos Stelios C, Wann Chin-Der. Clustering with unsupervised neural networks with applications to data fusion. SPIE, 1994, 2093: 621～632.
[62] 曲晓慧，安钢．数据融合方法综述及展望[J]．舰船电子工程，2003(2)： 2～4．
[63] X. Dai, S. Khorram. Data fusion using artificial neural networks: a case study on multitemporal change analysis[J]. Computers, Environment and Urban Systems, 1999, 23(1): 19～31.
[64] 魏海坤．神经网络结构设计的理论与方法[M]．北京：国防工业出版社，2005．
[65] 陈文林，郝丽娜，徐心和．粗糙集—神经网络—专家系统混合系统及其应用[J]．计算机工程．2003，9(9)：147～149．
[66] 赵卫东，陈国华．粗集和神经网络的集成技术研究[J]．系统工程与电子技术，2002，24(10)：103～106．
[67] Pawan Lingras. Comparision of Neofuzzy and Rough Neural Networks[J]. Journal of Information Science, 1998, 110: 207～215.
[68] Lazar Alina, Sethi Ishwar K. Decision Rule Extraction from Trained Neural Networks Using Rough Sets[J]. Intelligent Engineering Systems Through Artificial Neural Networks, 1999, 9: 493～498.
[69] Chung Young-June, Jun Hyo-Byung,etal. A Study on the Structure Optimization of Multilayer Neural Networks Using Rough Set Theory[J]. Transactions of the Korean Institute of Electrical Engineers, 1999, 48(1): 82～91.
[70] 王璿，高社生，赵霞．基于粗糙集理论的模糊神经网络构造方法[J]．计算机测量与控制．2006，14(6)：782～784．