粗糙集约简算法及其应用的研究
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摘要
粗糙集理论不依赖于所需处理的数据集合之外的任何先验信息,它对不精确、不确定、不完整的信息和知识具有很强的分析处理能力。20世纪80年代末以来,关于粗糙集理论和应用的研究逐渐成为智能信息处理领域的热点问题。
知识约简是粗糙集理论的精髓之一。利用粗糙集理论及其约简算法可以进行知识获取、机器学习、决策制定、模型建立等,它和智能控制有着密切的关联。然而,知识约简离不开一系列的算法作支撑,包括判断属性的重要性、求核、属性约简和值约简等。约简算法的设计和实现是知识约简研究的重要内容之一。本文旨在研究一种简单有效的约简方法,并用粗糙集方法解决模糊信息系统问题。同时,探讨粗糙集方法在控制中的运用。
首先,本文总结了信息决策系统属性约简和值约简的一般方法,提出了一种基于二进制区分矩阵的约简方法。在该约简方法中,本文定义了二进制区分矩阵及运算规则并给出了相应的证明、基于二进制区分矩阵的最小约简判别及属性重要性的计算方法。在此基础上,给出了基于二进制区分矩阵的信息决策系统的求核算法、属性约简算法和值约简算法,并运用MATLAB编程实现。本文给出的基于二进制区分矩阵的算法以位操作为主,不包括复杂的逻辑化简和集合运算,在一定程度上简化了计算,提高了约简效率并易于计算机实现。约简过程不依赖信息决策表,具有一定的通用性。将该算法应用于数字电路设计的开关电路综合中,得到最简数字电路的逻辑表达,从而说明了算法的有效性。
然后,本文比较了粗糙集理论和模糊集理论,将本文的约简方法应用于模糊信息系统的属性约简算法,并与其他算法做了比较。实例验证了该算法的有效性。
最后,本文将粗糙集和模糊推理机制结合起来,利用粗糙集理论的知识获取能力,分析采集的观测数据,客观的将专家控制经验转化为控制规则,结合模糊推理方法建立了一种粗糙模糊控制器。通过对单级倒立摆的控制研究说明了该粗糙模糊控制器可以代替专家对被控对象进行控制。
Rough set theory is independent of any foregoing information which is excluded of processed data sets, and it is a new effective mathematic tool to deal with the uncertainty、 imprecision and incompletion. Since the end of 1980s, rough set has become hotspot gradually in the intellectual information processing field.Knowledge reduction is a kernel problem in the research of rough set theory. The reduction algorithm based on the rough set theory can be used in the areas of knowledge acquisition, machine learning, decision analysis, modeling and so on, and it is related to intelligent control nearly. However, knowledge reduction is dependent on a series of supporting algorithms such as the calculation of attribute significance、 finding core、 attribute reduction and value reduction. Design and implementation of reduction algorithm is one of important contents of rough set research. The purposes of this paper are researching a simple and effective reduction method and furthermore resolving fuzzy information system problem with rough set method, at the same time, discussing the application of rough set in control.Firstly, it is researched of existing relative reduction algorithms in Decision Information System in this paper. A novel reduction method based on the binary discernibility matrix is presented. In this reduction method, binary discernibility matrix and its operation rules are defined based on rough set, homologous prove of operation rules are given at the same time. In addition, minimal reduction discrimination and calculation method about attribute significance of binary discernibility matrix are redefined. Based on the definitions, finding core algorithm, relative attribute reduction algorithm and value reduction of information decision system are presented based on binary discernibility matrix. The algorithms are programmed by MATLAB. The proposed algorithms of binary discernibility matrix rely mainly on bit operation without complicated logic minimization and set operation. Therefore, compared to traditional reduction model, the advantage of novel method is that, calculation is simplified to some extent and reduction efficiency is improved to a certain extent. Reduction can be get only through binary matrix operation rather than depending on the concrete comment of information decision table. Therefore, the novel method has some generality. This method has been applied in switch circuit integration of digital circuit design and got the logic expression of briefest digital circuit, which can prove the validity of the algorithmSecondly, Rough set theory and fuzzy set theory are compared in this paper. The reduction method based on binary discernibility matrix has been applied in attribute reduction of a fuzzy information system. This algorithm is compared to others and an example is given to illustrate the validity of the algorithm.Finally, reduction algorithm of rough set theory and fuzzy reasoning mechanism are combined to construct a rough fuzzy controller in this paper. Through researching of one-order inverted pendulum it is explained that rough set reduction algorithm is an effective method to get rules; control experience of experts to some object can be objectively expressed through constructing rough fuzzy controller, therefore, it can replace experts to control the objects.
知识约简是粗糙集理论的精髓之一。利用粗糙集理论及其约简算法可以进行知识获取、机器学习、决策制定、模型建立等,它和智能控制有着密切的关联。然而,知识约简离不开一系列的算法作支撑,包括判断属性的重要性、求核、属性约简和值约简等。约简算法的设计和实现是知识约简研究的重要内容之一。本文旨在研究一种简单有效的约简方法,并用粗糙集方法解决模糊信息系统问题。同时,探讨粗糙集方法在控制中的运用。
首先,本文总结了信息决策系统属性约简和值约简的一般方法,提出了一种基于二进制区分矩阵的约简方法。在该约简方法中,本文定义了二进制区分矩阵及运算规则并给出了相应的证明、基于二进制区分矩阵的最小约简判别及属性重要性的计算方法。在此基础上,给出了基于二进制区分矩阵的信息决策系统的求核算法、属性约简算法和值约简算法,并运用MATLAB编程实现。本文给出的基于二进制区分矩阵的算法以位操作为主,不包括复杂的逻辑化简和集合运算,在一定程度上简化了计算,提高了约简效率并易于计算机实现。约简过程不依赖信息决策表,具有一定的通用性。将该算法应用于数字电路设计的开关电路综合中,得到最简数字电路的逻辑表达,从而说明了算法的有效性。
然后,本文比较了粗糙集理论和模糊集理论,将本文的约简方法应用于模糊信息系统的属性约简算法,并与其他算法做了比较。实例验证了该算法的有效性。
最后,本文将粗糙集和模糊推理机制结合起来,利用粗糙集理论的知识获取能力,分析采集的观测数据,客观的将专家控制经验转化为控制规则,结合模糊推理方法建立了一种粗糙模糊控制器。通过对单级倒立摆的控制研究说明了该粗糙模糊控制器可以代替专家对被控对象进行控制。
Rough set theory is independent of any foregoing information which is excluded of processed data sets, and it is a new effective mathematic tool to deal with the uncertainty、 imprecision and incompletion. Since the end of 1980s, rough set has become hotspot gradually in the intellectual information processing field.Knowledge reduction is a kernel problem in the research of rough set theory. The reduction algorithm based on the rough set theory can be used in the areas of knowledge acquisition, machine learning, decision analysis, modeling and so on, and it is related to intelligent control nearly. However, knowledge reduction is dependent on a series of supporting algorithms such as the calculation of attribute significance、 finding core、 attribute reduction and value reduction. Design and implementation of reduction algorithm is one of important contents of rough set research. The purposes of this paper are researching a simple and effective reduction method and furthermore resolving fuzzy information system problem with rough set method, at the same time, discussing the application of rough set in control.Firstly, it is researched of existing relative reduction algorithms in Decision Information System in this paper. A novel reduction method based on the binary discernibility matrix is presented. In this reduction method, binary discernibility matrix and its operation rules are defined based on rough set, homologous prove of operation rules are given at the same time. In addition, minimal reduction discrimination and calculation method about attribute significance of binary discernibility matrix are redefined. Based on the definitions, finding core algorithm, relative attribute reduction algorithm and value reduction of information decision system are presented based on binary discernibility matrix. The algorithms are programmed by MATLAB. The proposed algorithms of binary discernibility matrix rely mainly on bit operation without complicated logic minimization and set operation. Therefore, compared to traditional reduction model, the advantage of novel method is that, calculation is simplified to some extent and reduction efficiency is improved to a certain extent. Reduction can be get only through binary matrix operation rather than depending on the concrete comment of information decision table. Therefore, the novel method has some generality. This method has been applied in switch circuit integration of digital circuit design and got the logic expression of briefest digital circuit, which can prove the validity of the algorithmSecondly, Rough set theory and fuzzy set theory are compared in this paper. The reduction method based on binary discernibility matrix has been applied in attribute reduction of a fuzzy information system. This algorithm is compared to others and an example is given to illustrate the validity of the algorithm.Finally, reduction algorithm of rough set theory and fuzzy reasoning mechanism are combined to construct a rough fuzzy controller in this paper. Through researching of one-order inverted pendulum it is explained that rough set reduction algorithm is an effective method to get rules; control experience of experts to some object can be objectively expressed through constructing rough fuzzy controller, therefore, it can replace experts to control the objects.
引文
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[3] 韩祯祥,张琦,文福拴.粗糙集理论及其应用综述[J].控制理论及应用.1999,16(2):153-157
[4] 高隽.智能信息处理方法导论.机械工业出版社.2004
[5] Z. Pawlak. Rough Set Theory for Intelligent Industrial Applications [A] IPMM'99. The Second International Conference on Intelligent Processing and Manufacturing of Materials[C], Honolulu, Hawaii, July 10-15, 1999 vol. 1: 37-44
[6] R. Slowinski. Rough Set Approach to Decision Analysis. AI Expert. 1995(10), 18-25
[7] R. Slowinski. Rough Set Theory and Its Applications to Decision aid[J]. Belgian Journal of Operation Research. Special Issue Francoro. 1995, 35(3-4): 81-90
[8] R. Slowinski. Rough Set Reasioning about uncertain data[J]. Fundamenta Information. 1996, 27 (2-3): 229-243
[9] Z. Pawlak. Rough Set Communications of ACM, 1995, 38(11): 89-95
[10] Tsumoto S. Automated extraction of medical expert system rules from clinical data based on Rough Set theory [J]. Tournal of Information Sciences. 1998, 112: 67-84
[11] Hu X. Mining knowledge rules from databases: a Rough Set Approach[D], Data ngineering. Proceedings of the Twelfth International Conferenceon 1996, 96-105
[12] Jelonek J, Krawiec K, Slowinski R. Rough Set reduction of attributes and their domains for neural networks [J]. Computational Intelligence. 1995, 11(2): 339-347
[13] Beaubouef T, Petty F E. A rough set model for relational databases [A]. ZiarkoW P eds, Proc of RSED'93 [C], spring-verlag,. 1994, 100-107
[14] Nejman D. A rough set based method of hand written numerals classification, Institute of Computer Science Reports, Waraw University of Technology Waraw, 1994
[15] Mrozek A. Rough sets and dependency analysis among attributes in computer implementations of expert's inference models. International Journal of Mart Machine Studies. 1989, 30(4): 457-473
[16] Muraszkieqiez M, Rybinski li. Towards a Parallel Rough Sets Computer. Rough sets, Fuzzy Sets and Knowledge Discovery. Springer-Verlag. 1994, 227-236
[17] 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,Vol.14,No.4:1-12
[18] 胡可云,陆玉昌,石纯一.粗糙集理论及其应用进展[J].清华大学学报.2001,Vol.41,No.1:64-68
[19] Wong S. K. M., Ziarko W. On optional Decision Rule in Decision Table. Bulletin of Polish Academy of science. 1985(33): 693-696
[20] Lin M, Software system for intelligent data processing and discovering based on the fuzzy-rough sets theory [D], San Diego: San Diego State University. 1995
[21] 唐建国,谭明术.粗糙集理论中的求核与约简[J].控制与决策.2002,Vol.18,No.4:449-452
[22] 常梨云,王国胤.一种基于Rough set理论的属性约简及规则提取方法[J].软件学报.1999.10(11):1206-1211
[23] Fujimori S, Kaiya T, Jnoue T. Analysis of dischange currents with discernibility matrices [A]. Proceedings of 1998 International Symposium on Electrical Insulating Materials [C]. 1998: 649-652
[24] 徐一新,叶东毅.知识约简的差别矩阵启发式算法[J].福州大学学报,2000,28(3);120-123
[25] 徐德友,胡寿松.一种基于粗糙集的近似质量求取属性约简的决策算法[J].控制与决策.Vol.18,No.3:313-316
[26] 何苗,李春葆.一种结合粗糙集理论和启发式知识的特征选取算法[J].计算机应用.2003,Vol.23,No.2:113-115
[27] 李雄飞等.基于粗集理论的约简算法.吉林大学学报(工学报),2003 Vol 33,No.6
[28] Hu Xiaohua. Knowledge discovery in databases an attribute-oriented rough set approach [D]. Regina University. 1995
[29] Felix R, Ushio T. Rough sets-based machine learning using a binary discernibility matrix [A]. Proceeding of the second International Conference on Intelligent Proceeding and Manufacturing of Materials [C], 1999, 1: 299-305
[30] J. W. Guan, D. A. Bell, Z. Guan. Matrix Computation for information systems, Information sciences. 131(2001): 129-156
[31] 支云天,苗夺谦.二进制可辨矩阵的变换及高效属性约简算法的构造[J].计算机科学.2002,Vol.29,No.2:140-143
[32] 周海岩,杨汀.基于二进制可辨矩阵的属性约简算法的改进[J].计算机工程与设计.2003,Vol.24,No.12:35-39
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