基于粗糙集理论的不确定型决策系统研究
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摘要
随着社会的进步和发展,决策信息系统的研究和应用已取得很大的进展,但在信息社会到来的今天,人们所面临的决策问题日趋复杂,大量的、不完全的、有噪声的、模糊的、随机的实际数据干扰着决策者提取隐含的、有价值的决策信息。因此,提供一套解决含有此类不确定信息的决策信息系统一不确定型决策信息系统的决策方法已迫在眉睫。
粗糙集理论是二十世纪八十年代初由波兰数学家一Z.Pawlak提出的一种刻画不确定性和不完整性知识的数学工具,这为处理不确定型决策信息系统提供了一条新思路。该理论近年来日益受到广泛关注,己在人工智能、知识发现、故障诊断、模式识、专家系统等方面得到了成功的应用。以粗糙集为工具处理不确定型决策信息系统为我们提供了一条新思路。
本文通过对现有复杂决策问题特征的深入分析,在大量检索国内外资料、跟踪国际前沿技术,总结和借鉴前人经验的基础上,将粗糙集理论与决策问题相结合,本文的具体研究内容如下:
研究了决策信息系统的数据预处理过程,在噪音数据的有效识别问题上,提出了一种粗糙聚类算法。在属性约简方面,提出了基于同族矩阵的属性约简方法,并研究了同族矩阵的性质。在连续属性的离散化问题上,从聚类相似度以及分类质量、分类精度的角度对经典离散化方法进行了比较,得到了离散化方法相同的优劣序。
在不确定决策信息系统的设计上,将粗糙集与神经网络结合,构造了粗糙神经网络决策系统,实证分析表明粗糙神经网络缩短了网络的训练时间,同时分类精度也有了明显提升。
针对属性值为区间数的决策系统,提出一种新的离散化方法,并结合灰色系统理论,定义了决策规则,通过对比神经网络,该区间数型粗糙灰色决策系统简化了决策规则,提高了智能决策效率。
As social progress and development, research on Decision Information System and its application has made great progress, However, in the information society is coming, the decisioin problems we are facing are becoming more and more complicated, valuable information with large, incomplete, noisy, fuzzy, random data interfere with decision makers seeking interesting and valuable information. So it is urgent to provide a suit of decision methods which can solve the uncertain decision information system.
The rough set theory proposed by Pawlak (1982) is established on the basis of database, when database is uncertain or incomplete. It provides one new way for us to solve the uncertain decision information system. The rough set theory has preferable application on Artificial Intelligence and Knowledge Discovery, Pattern Recognition, Fault Detection, Expert Systems, etc.
Based on great searching of internal and external inofmration and following closely international advanced technology I deeply analyze the characteristic of the complex decision and combine rought sets theory with classical decision methods. The main contents of this paper are as follows:
On the data preprocessing of Decision Information System, on account of distinguishing noisy data, one rough cluster algorithm is proposed. In respect of attribute reduction, the redundant set of attributes is obtained by constituting homogenous matrix whose properties are discussed later, whereas that differs with classical method. In terms of discretization, four kinds of typical discretization algorithms were comparatively analyzed from two aspects with examples, one referred to the variable quality of classification and accuracy of approximation under different parameter, the other was the similarity degrees between reducted variable sets and the original variable set, Finally, the consistent conclusion on preference of discretization algorithms were gained.
As far as uncertain Decision Information System is concerned, an approach of back propagation neural network with rough set(RSBP) is presented, Simulation results indicate this model,compared with the conventional BP neural network model,can reduce the training time and improve the accuracy of classification.
In respect of Information System with interval numbers, a discretization algorithm is proposed. Combing with Grey System Theory, decision rules are defined, Simulation results indicate that Interval Rough—Grey Decision Information System Simplify the decision-making rules and improve the efficiency of intelligent decision-making.
粗糙集理论是二十世纪八十年代初由波兰数学家一Z.Pawlak提出的一种刻画不确定性和不完整性知识的数学工具,这为处理不确定型决策信息系统提供了一条新思路。该理论近年来日益受到广泛关注,己在人工智能、知识发现、故障诊断、模式识、专家系统等方面得到了成功的应用。以粗糙集为工具处理不确定型决策信息系统为我们提供了一条新思路。
本文通过对现有复杂决策问题特征的深入分析,在大量检索国内外资料、跟踪国际前沿技术,总结和借鉴前人经验的基础上,将粗糙集理论与决策问题相结合,本文的具体研究内容如下:
研究了决策信息系统的数据预处理过程,在噪音数据的有效识别问题上,提出了一种粗糙聚类算法。在属性约简方面,提出了基于同族矩阵的属性约简方法,并研究了同族矩阵的性质。在连续属性的离散化问题上,从聚类相似度以及分类质量、分类精度的角度对经典离散化方法进行了比较,得到了离散化方法相同的优劣序。
在不确定决策信息系统的设计上,将粗糙集与神经网络结合,构造了粗糙神经网络决策系统,实证分析表明粗糙神经网络缩短了网络的训练时间,同时分类精度也有了明显提升。
针对属性值为区间数的决策系统,提出一种新的离散化方法,并结合灰色系统理论,定义了决策规则,通过对比神经网络,该区间数型粗糙灰色决策系统简化了决策规则,提高了智能决策效率。
As social progress and development, research on Decision Information System and its application has made great progress, However, in the information society is coming, the decisioin problems we are facing are becoming more and more complicated, valuable information with large, incomplete, noisy, fuzzy, random data interfere with decision makers seeking interesting and valuable information. So it is urgent to provide a suit of decision methods which can solve the uncertain decision information system.
The rough set theory proposed by Pawlak (1982) is established on the basis of database, when database is uncertain or incomplete. It provides one new way for us to solve the uncertain decision information system. The rough set theory has preferable application on Artificial Intelligence and Knowledge Discovery, Pattern Recognition, Fault Detection, Expert Systems, etc.
Based on great searching of internal and external inofmration and following closely international advanced technology I deeply analyze the characteristic of the complex decision and combine rought sets theory with classical decision methods. The main contents of this paper are as follows:
On the data preprocessing of Decision Information System, on account of distinguishing noisy data, one rough cluster algorithm is proposed. In respect of attribute reduction, the redundant set of attributes is obtained by constituting homogenous matrix whose properties are discussed later, whereas that differs with classical method. In terms of discretization, four kinds of typical discretization algorithms were comparatively analyzed from two aspects with examples, one referred to the variable quality of classification and accuracy of approximation under different parameter, the other was the similarity degrees between reducted variable sets and the original variable set, Finally, the consistent conclusion on preference of discretization algorithms were gained.
As far as uncertain Decision Information System is concerned, an approach of back propagation neural network with rough set(RSBP) is presented, Simulation results indicate this model,compared with the conventional BP neural network model,can reduce the training time and improve the accuracy of classification.
In respect of Information System with interval numbers, a discretization algorithm is proposed. Combing with Grey System Theory, decision rules are defined, Simulation results indicate that Interval Rough—Grey Decision Information System Simplify the decision-making rules and improve the efficiency of intelligent decision-making.
引文
[1]胡寿松,何亚群.粗糙决策理论与应用.北京:北京航空航天大学出版社,2006.
[2]陶志,许宝栋,汪定伟等.基于遗传算法的粗糙集知识约简算法.系统工程,2003,21(4):116-122.
[3]周献中,黄兵.基于粗集的不完备信息系统属性约.南京理工大学学报,2003,27(8):631-633.
[4]薛锋,柯孔林.粗糙集神经网络系统在商业银行贷款五级分类中的应用.系统工程理论与实践.2008.1:40-45.
[5]Zeshui Xu,Qingli Da.Possibility degree method for ranking interval numbers andits application.Journal of Systems Engineering,2003,18(1):67-70.
[6]Quofang Qiu,Zuhuai Li.Measurement and Construct with Inclusion Degree for Priority of Interval Numbers.Operations Research and Management Science,2003,12(3):13-17.
[7]Saivatore Greco,Benedetto Matarazzo,Roman Slowinski.Rough sets methodology for sorting problems in presence of multiple attributes and criteria.European Journal of Operational Research,2002,138:247---259.
[8]W.Ziarko.Rough Sets,Fuzzy Sets and Knowledge Discovery.Proceeding of the International Workshop on Rough Sets and Knowledge Discovery.Springer--Verlag,Berlin,1994.
[9]A.G.Jackson,Z.pawlak,S.R.Leclair.Rough sets applied to the discovery of materials knowledge.Journal of Alloys and Compounds.1998(279):14-21.
[10]F.Questier,B.Walczak,D.L.Massart.Application of rough set theory to feature selection for unsupervised clustering.Chemometdcs and Intelligent Laboratory Systems.2002(63):155-167.
[11]Zhi Xiao,ShiJie Ye,Bo Zhong.BP neural network with rough set for short term load forecasting.Expert Systems with Applications,2007:1-7.
[12]Ebrahim A.Younes.Characterizing solutions of rough programming problems.European Journal of Operational Research,2006,168:1019-1029.
[13]B.Walczak,D.L.Massart.Rough sets theory.Chemometrics and Intelligent Laboratory Systems,1999,47:6-7.
[14]Kerber,ChiMerge.Discretization of Numberic Attributes[C]Proceeding of 10~(th) National Conference on Artificial Intelligence.MIT Press,1992:123-128.
[15]Daren Yu,Qinghua Hu,Wen Bao.Combining Rough Set Methodology and Fuzzy Clustering for Knowledge Discovery from Quantitative Data Journal of Chinese Electrical Engineering,2004(24):205-210.
[16]Pawan Lingras.Interval set clustering of web users with rough K-means.Journal of Intelligent Information Systems,2004,23:5-16.
[17] Wenxiu Zhang,Guofang Zhang.Uncertain Decision Making Based on Rough Sets.Beijing: the University of Tinghua Publishing Company,2005.
[18] Xinping Xiao.Theoretical Study and Reviews on the Computation Method of Grey Interconnet Degree. System Engineering Theory and Practice,1997,8:76-81.
[19] Wei Cuiping,Zhang Yuzhong1, Feng Xiangqian. Deriving Weights from Interval Comparison Matrics based on Consistency Test .System Engineering Theory and Practice,2007,27(10): 132- 139.
[20] Gerald Whittaker, Remegio Confesor Jr,Stephen M.Griffith.A hybrid genetic algorithm for multiobjective problems with activity Analysis-based local search. European Journal of Operational Research,2009(193): 195—203.
[21] M.Nasseri,K.Asghari,M.J.Abedini. Optimized scenario for rainfall forecasting using genetic algorithm coupled with artificial neural network.Expert Systems with Application,2008,35(3): 1415—1421.
[22] Zdzislaw Pawlak. Rough sets,decision algorithms and Bayes'theorem. European Journal of Operation Research,2002(136):182- 184.
[23] Zdzislaw Pawlak.Rough sets and intelligent data analysis.Information Sciences,2002(147):1-12.
[24] Asultan K S,Selim S. A global algorithm for the fuzzy clustering problem. Pattern Recognition, 1994,2(27):321-329.
[25] Martin T.Hagan, Howard B.Demuth,Mark Beale.Neural Network Design.PWS Publishing Company, 1996.
[26] Philippe Fortemps,Salvatore Greco,Roman Slowinski.Multicriteria decision support using rules that represent rough-graded preference relations. European Journal of Operational Research,2008(188):206-223.
[27] Jerzy Blaszczynski,Salvatore Greco,Roman Slowinski.Multi-criteria classification - A new scheme for application of dominance based decision rules. European Journal of Operational Research,2007( 181): 1030-1044.
[28] Dembczynski Krzysztof,Greco Salvatore,Slowinski Roman. Second-order rough approximations in multi-criteria classification with imprecise evaluations and assignments.The 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing,Canada,2005,3641:54—63.
[29] Yager Ronald R.. Level sets and the extension principle for interval valued fuzzy sets and its application to uncertainty measures. Information Sciences,2008,178(18):3565—3576.
[30] Yuchuan Chang, Shyiming Chen,Churnjung Liau.Fuzzy interpolative reasoning for sparse fuzzy-rule-based systems based on the areas of fuzzy sets. IEEE Transactions on Fuzzy Systems, 2008, 16(5):1285-1301.
[31] Meilian Liang,Jiarong Liang,Chen Guo.Generation of optimal decision rules from incomplete information systems. Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 2004:2231-2235.
[32] Mingli Hu,Sifeng Liu.A rough analysis method of multi-attribute decision making for handling decision system with incomplete information.Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, 2007:936—941.
[33] Greco S, Matarazzo B, Slowinski R. Rough set approach to multi-attribute choice and ranking problems. The proceedings of the 12th International Conference on Multiple Criteria Decision Making, 1997:318—329.
[34] Greco S,Matarazzo B, Slowinski R. Rough set theory for multicriteria decision analysis. European Journal of Operational Research,2001,129 (1):1 —47.
[35] Slowinski R, Greco S, Matarazzo B. Mining decision-rule preference model from rough approximation of preference relation.The proceedings of the 26th IEEE Annual International Conference on Computer Software and Applications. IEEE Press,2002:1129-1134.
[36] B. Walczak, D.L. Massart.Rough sets theory. Chemometrics and Intelligent Laboratory Systems, 1999,47:1 -16.
[37] Dembczynski Krzysztof, Greco Salvatore, Kotlowski Wojciech.Quality of rough approximation in multi-criteria classification problems.The 5th International Conference on Rough Sets and Current Trends in Computing, Japan ,Nov 6-8 2006:318—327.
[38] Kotlowski Wojciech, Dembczynski Krzysztof, Greco Salvatore.Stochastic dominance-based rough set model for ordinal classification.Information Sciences,2008,178(21 ):4019-4037.
[39] Sushmita Mitra. An evolutionary rough partitive clustering, Pattern Recognition Letters,2004,25:1439-1449.
[40] Ebrahim A. Youness. Characterizing solutions of rough programming problems, European Journal of Operational Research,2006,168:1019—1029.
[41] Lian-Yin Zhai, Li-Pheng Khoo , Zhao-Wei Zhong. Design concept evaluation in product development using rough sets and grey relation analysis, Expert Systems with Applications,2008,35:1617 - 1621.
[42] Renpu Li, Zheng-ou Wang. Mining classification rules using rough sets and neural networks, European Journal of Operational Research,2004,157:439—448.
[43] Chao-Ton Su, Jyh-Hwa Hsu. Precision parameter in the variable precision rough sets model:an application,The International Journal of Management Science.2006,34:149—157.
[44] Malcolm Beynon.Reducts within the variable precision rough sets model:A further investigation, European Journal of Operational Research.2001,134:592—605.
[45] Pradeep Kumar. Rough clustering of sequential data, Data & Knowledge Engineering.2007,63:183 - 199.
[46] Georg Peters. Some refinements of rough k-means clustering, Pattern Recognition,2006,39:1481 - 1491.
[47] Zdzislaw Pawlak. Some remarks on conflict analysis, European Journal of Operational Research.2005,166:649-654.
[48] Gang Xie, Jinlong Zhang. Variable precision rough set for group decision-making:An application, International Journal of Approximate Reasoning.2007,33:1643 — 1652.
[49] Blaszczynski Jerzy, Greco Salvatore, Slowinski Roman.Multi-criteria classification - A new scheme for application of dominance-based decision rules. European Journal of Operational Research,2007,181(3):1030- 1044.
[50] Zhang W X, Leung Y. Theory of including degrees and its applications to uncertainty inferences. Soft Computing in Intelligent Systems and Information Processing. New York:IEEE,1996,496-501.
[51] Hsin-Hung Wu. A Comparative Study of Using Grey Relational Analysis in Multiple Attribute Decision Making Problems. QUALITY ENGINEERING, 2002,15(2):209- 217.
[52] Nguyen H.S., Skowron A. Quantization of real values attributes, rough set and Boolean reasoning approaches. Proceedings of the 2nd Joint Annual Conference on Information Science, Wrightsville Beach,NC,1995,34-37.
[53] W.Pedrycz, L.Han. Calibration of software quality: Fuzzy neural and rough neural computing approaches.Neurocomputing,2001,36:149— 170.
[54] Sushmita Mitra, Pabitra Mitra, Sankar K. Pal. Evolutionary modular design of rough knowledge-based network using fuzzy attributes. Neurocomputing, 2001,36:45-66.
[55] Pawan Lingras.Fuzzy-rough and rough-fuzzy serial combinations in Neurocomputing. 2001,36:29-44.
[56] Witold Pedrycz, George Vukovich.Granular neural networks. Neurocomputing, 2001,36:205-224.
[57] Andrzej Czyzewski, Rafa Krohikowski. Neuro-rough control of masking thresholds for audio signal enhancement. Neurocomputing, 2001,36:5—27.
[58] Marcin Szczuka. Neuro-wavelet classi"ers for EEG signals based on rough set methods. Neurocomputing, 2001,36:103—122.
[59] Roman W. Swiniarski, Larry Hargis. Rough sets as a front end of neural-networks texture classi"ers. Neurocomputing, 2001,36:85—102.
[60] Zhiqiang Geng, Qunxiong Zhu. Rough set-based heuristic hybrid recognizer and its application in fault diagnosis. Expert Systems with Applications.2008,32:103— 112.
[2]陶志,许宝栋,汪定伟等.基于遗传算法的粗糙集知识约简算法.系统工程,2003,21(4):116-122.
[3]周献中,黄兵.基于粗集的不完备信息系统属性约.南京理工大学学报,2003,27(8):631-633.
[4]薛锋,柯孔林.粗糙集神经网络系统在商业银行贷款五级分类中的应用.系统工程理论与实践.2008.1:40-45.
[5]Zeshui Xu,Qingli Da.Possibility degree method for ranking interval numbers andits application.Journal of Systems Engineering,2003,18(1):67-70.
[6]Quofang Qiu,Zuhuai Li.Measurement and Construct with Inclusion Degree for Priority of Interval Numbers.Operations Research and Management Science,2003,12(3):13-17.
[7]Saivatore Greco,Benedetto Matarazzo,Roman Slowinski.Rough sets methodology for sorting problems in presence of multiple attributes and criteria.European Journal of Operational Research,2002,138:247---259.
[8]W.Ziarko.Rough Sets,Fuzzy Sets and Knowledge Discovery.Proceeding of the International Workshop on Rough Sets and Knowledge Discovery.Springer--Verlag,Berlin,1994.
[9]A.G.Jackson,Z.pawlak,S.R.Leclair.Rough sets applied to the discovery of materials knowledge.Journal of Alloys and Compounds.1998(279):14-21.
[10]F.Questier,B.Walczak,D.L.Massart.Application of rough set theory to feature selection for unsupervised clustering.Chemometdcs and Intelligent Laboratory Systems.2002(63):155-167.
[11]Zhi Xiao,ShiJie Ye,Bo Zhong.BP neural network with rough set for short term load forecasting.Expert Systems with Applications,2007:1-7.
[12]Ebrahim A.Younes.Characterizing solutions of rough programming problems.European Journal of Operational Research,2006,168:1019-1029.
[13]B.Walczak,D.L.Massart.Rough sets theory.Chemometrics and Intelligent Laboratory Systems,1999,47:6-7.
[14]Kerber,ChiMerge.Discretization of Numberic Attributes[C]Proceeding of 10~(th) National Conference on Artificial Intelligence.MIT Press,1992:123-128.
[15]Daren Yu,Qinghua Hu,Wen Bao.Combining Rough Set Methodology and Fuzzy Clustering for Knowledge Discovery from Quantitative Data Journal of Chinese Electrical Engineering,2004(24):205-210.
[16]Pawan Lingras.Interval set clustering of web users with rough K-means.Journal of Intelligent Information Systems,2004,23:5-16.
[17] Wenxiu Zhang,Guofang Zhang.Uncertain Decision Making Based on Rough Sets.Beijing: the University of Tinghua Publishing Company,2005.
[18] Xinping Xiao.Theoretical Study and Reviews on the Computation Method of Grey Interconnet Degree. System Engineering Theory and Practice,1997,8:76-81.
[19] Wei Cuiping,Zhang Yuzhong1, Feng Xiangqian. Deriving Weights from Interval Comparison Matrics based on Consistency Test .System Engineering Theory and Practice,2007,27(10): 132- 139.
[20] Gerald Whittaker, Remegio Confesor Jr,Stephen M.Griffith.A hybrid genetic algorithm for multiobjective problems with activity Analysis-based local search. European Journal of Operational Research,2009(193): 195—203.
[21] M.Nasseri,K.Asghari,M.J.Abedini. Optimized scenario for rainfall forecasting using genetic algorithm coupled with artificial neural network.Expert Systems with Application,2008,35(3): 1415—1421.
[22] Zdzislaw Pawlak. Rough sets,decision algorithms and Bayes'theorem. European Journal of Operation Research,2002(136):182- 184.
[23] Zdzislaw Pawlak.Rough sets and intelligent data analysis.Information Sciences,2002(147):1-12.
[24] Asultan K S,Selim S. A global algorithm for the fuzzy clustering problem. Pattern Recognition, 1994,2(27):321-329.
[25] Martin T.Hagan, Howard B.Demuth,Mark Beale.Neural Network Design.PWS Publishing Company, 1996.
[26] Philippe Fortemps,Salvatore Greco,Roman Slowinski.Multicriteria decision support using rules that represent rough-graded preference relations. European Journal of Operational Research,2008(188):206-223.
[27] Jerzy Blaszczynski,Salvatore Greco,Roman Slowinski.Multi-criteria classification - A new scheme for application of dominance based decision rules. European Journal of Operational Research,2007( 181): 1030-1044.
[28] Dembczynski Krzysztof,Greco Salvatore,Slowinski Roman. Second-order rough approximations in multi-criteria classification with imprecise evaluations and assignments.The 10th International Conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing,Canada,2005,3641:54—63.
[29] Yager Ronald R.. Level sets and the extension principle for interval valued fuzzy sets and its application to uncertainty measures. Information Sciences,2008,178(18):3565—3576.
[30] Yuchuan Chang, Shyiming Chen,Churnjung Liau.Fuzzy interpolative reasoning for sparse fuzzy-rule-based systems based on the areas of fuzzy sets. IEEE Transactions on Fuzzy Systems, 2008, 16(5):1285-1301.
[31] Meilian Liang,Jiarong Liang,Chen Guo.Generation of optimal decision rules from incomplete information systems. Proceedings of 2004 International Conference on Machine Learning and Cybernetics, 2004:2231-2235.
[32] Mingli Hu,Sifeng Liu.A rough analysis method of multi-attribute decision making for handling decision system with incomplete information.Proceedings of 2007 IEEE International Conference on Grey Systems and Intelligent Services, 2007:936—941.
[33] Greco S, Matarazzo B, Slowinski R. Rough set approach to multi-attribute choice and ranking problems. The proceedings of the 12th International Conference on Multiple Criteria Decision Making, 1997:318—329.
[34] Greco S,Matarazzo B, Slowinski R. Rough set theory for multicriteria decision analysis. European Journal of Operational Research,2001,129 (1):1 —47.
[35] Slowinski R, Greco S, Matarazzo B. Mining decision-rule preference model from rough approximation of preference relation.The proceedings of the 26th IEEE Annual International Conference on Computer Software and Applications. IEEE Press,2002:1129-1134.
[36] B. Walczak, D.L. Massart.Rough sets theory. Chemometrics and Intelligent Laboratory Systems, 1999,47:1 -16.
[37] Dembczynski Krzysztof, Greco Salvatore, Kotlowski Wojciech.Quality of rough approximation in multi-criteria classification problems.The 5th International Conference on Rough Sets and Current Trends in Computing, Japan ,Nov 6-8 2006:318—327.
[38] Kotlowski Wojciech, Dembczynski Krzysztof, Greco Salvatore.Stochastic dominance-based rough set model for ordinal classification.Information Sciences,2008,178(21 ):4019-4037.
[39] Sushmita Mitra. An evolutionary rough partitive clustering, Pattern Recognition Letters,2004,25:1439-1449.
[40] Ebrahim A. Youness. Characterizing solutions of rough programming problems, European Journal of Operational Research,2006,168:1019—1029.
[41] Lian-Yin Zhai, Li-Pheng Khoo , Zhao-Wei Zhong. Design concept evaluation in product development using rough sets and grey relation analysis, Expert Systems with Applications,2008,35:1617 - 1621.
[42] Renpu Li, Zheng-ou Wang. Mining classification rules using rough sets and neural networks, European Journal of Operational Research,2004,157:439—448.
[43] Chao-Ton Su, Jyh-Hwa Hsu. Precision parameter in the variable precision rough sets model:an application,The International Journal of Management Science.2006,34:149—157.
[44] Malcolm Beynon.Reducts within the variable precision rough sets model:A further investigation, European Journal of Operational Research.2001,134:592—605.
[45] Pradeep Kumar. Rough clustering of sequential data, Data & Knowledge Engineering.2007,63:183 - 199.
[46] Georg Peters. Some refinements of rough k-means clustering, Pattern Recognition,2006,39:1481 - 1491.
[47] Zdzislaw Pawlak. Some remarks on conflict analysis, European Journal of Operational Research.2005,166:649-654.
[48] Gang Xie, Jinlong Zhang. Variable precision rough set for group decision-making:An application, International Journal of Approximate Reasoning.2007,33:1643 — 1652.
[49] Blaszczynski Jerzy, Greco Salvatore, Slowinski Roman.Multi-criteria classification - A new scheme for application of dominance-based decision rules. European Journal of Operational Research,2007,181(3):1030- 1044.
[50] Zhang W X, Leung Y. Theory of including degrees and its applications to uncertainty inferences. Soft Computing in Intelligent Systems and Information Processing. New York:IEEE,1996,496-501.
[51] Hsin-Hung Wu. A Comparative Study of Using Grey Relational Analysis in Multiple Attribute Decision Making Problems. QUALITY ENGINEERING, 2002,15(2):209- 217.
[52] Nguyen H.S., Skowron A. Quantization of real values attributes, rough set and Boolean reasoning approaches. Proceedings of the 2nd Joint Annual Conference on Information Science, Wrightsville Beach,NC,1995,34-37.
[53] W.Pedrycz, L.Han. Calibration of software quality: Fuzzy neural and rough neural computing approaches.Neurocomputing,2001,36:149— 170.
[54] Sushmita Mitra, Pabitra Mitra, Sankar K. Pal. Evolutionary modular design of rough knowledge-based network using fuzzy attributes. Neurocomputing, 2001,36:45-66.
[55] Pawan Lingras.Fuzzy-rough and rough-fuzzy serial combinations in Neurocomputing. 2001,36:29-44.
[56] Witold Pedrycz, George Vukovich.Granular neural networks. Neurocomputing, 2001,36:205-224.
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