基于粗糙集理论的知识发现方法研究
|
摘要
粗糙集理论是上世纪八十年代初由波兰数学家Z.Pawlak首先提出的一种用于数据分析的数学理论,它能处理含糊性和不精确性问题。自上世纪九十年代起,该理论日益受到重视,并成为国际学术界的研究热点之一。经过二十年的发展,粗糙集理论已在机器学习、模式识别、决策分析、过程控制、数据库知识发现、专家系统等领域获得成功应用。
本文主要对粗糙集理论在知识发现中应用的关键问题进行了研究。
第一章对知识发现进行了概述,介绍了知识发现的基本步骤、基本方法、基本任务等。而后对粗糙集理论进行了概述,介绍了粗糙集理论产生的背景、粗糙集理论的发展、以及对粗糙集应用于知识发现的优点作了阐述。
第二章介绍了粗糙集理论的一些基本概念,并将粗糙集与其他几种处理不确定性理论作了比较。
第三章对离散化问题进行了研究,从启发式方法和基于遗传算法的方法两个方面进行了研究。通过对初始断点集进行精简,将Nguyen S H提出的著名的离散化算法进行了改进,改进后的算法在空间复杂度和时间复杂度上都有较大程度的降低;另外,提出了一种免疫算法用于求解决策系统的离散化问题,它与启发式算法相比能获得更小且一致的离散化结果,为粗糙集中连续属性离散化提供了一种新的思想。
第四章对于决策系统属性约简问题,从信息论角度定义了一种新的属性重要性度量方法。与基于互信息增益的方法不同的是:这种度量方法不仅考虑了属性的值域的大小,而且还考虑了取值的分布。基于此度量,构造了相应的启发式算法,对多个数据集的实验结果表明该方法能更有效地对决策系统进行约简。
第五章研究了决策规则的获取,重点是针对不一致决策系统,提出了一种修改的基于分类一致性的规则获取算法,对每个决策类计算出相应的下近似集与上近似集,然后用决策类的下近似集获得确定性规则,上近似集获得概率性规则。在规则获取时采用属性重要性方法,与LEM2相比,它能一次获得多条规则。通过对Hayes数据集的实验表明了算法的有效性。
Rough set theory, introduced by Z. Pawlak in the early 1980s of the 20th century, is a mathematical theory of reasoning about data which can be also used to deal with vague and uncertain problems. Since 1990s of the last century, it has attracted much attention of researchers around the world and become a focus in the fields of computer science and information science. With about twenty years development, rough set theory has been successfully applied to many areas including machine learning, pattern recognition, decision analysis, process control, knowledge discovery from databases, and expert systems.
The key processes of the applying of rough set to knowledge discovery were studied, including the discretization problem, attribute reduction and the acquisition of decision rules were studied, and the corresponding algorithms were proposed in the thesis.
In Chapter1, the basic tasks, basic steps and basic methods of Knowledge Discovery are introduced. Consequently, the background of the emerging of rough set theory and developing of rough set theory are introduced. We also pointed out the virtues of applying rough set theory to knowledge discovery.
In Chapter 2, the basic concepts in rough set theory were introduced. Rough set theory was also compared with some other theory dealing with vagueness.
In Chapter 3, discretization problem was studied from two aspects: the heuristic method and the method based on genetic algorithm. A more efficient strategy of determination of candidate cuts was proposed contrasting to the strategy in the named method based on rough set and Boolean reasoning presented by Nguyen. Based on the strategy of determination of candidate cuts, an improved algorithm was constructed. The experiments show that the improved algorithm has lower space complexity and time complexity obviously. Additionally, a method based on immune algorithm was proposed which is easier to get small and consistent result.
In Chapter 4, the reduction problem was studied. In order to obtain good relative reduct in decision system, a new attribute importance measure defined from the viewpoint of information theory which considers value distribution of selected attributes besides the mutual information between selected conditional attributes and decision attribute was defined. An algorithm based on the measure was constructed and analyzed. The experiments show that the algorithm can reduce the decision system effectively.
In Chapter 5, the acquisition of decision rules was studied. We focused on inconsistent decision system. A modified algorithm was proposed. In the algorithm, the lower and upper of all decision classes were computed. Thus, the task of rule induction from inconsistent data is reduced to rule induction from consistent data. A set of certain rules can be induced from the lower approximation and a set of possible rules can be induced from the upper approximation. The induction process also made use of attribute importance method. Compared with the named LEM2 algorithm, the algorithm can acquire more than one rule at one time. The experiments on Hayes data show that the algorithm is effective.
本文主要对粗糙集理论在知识发现中应用的关键问题进行了研究。
第一章对知识发现进行了概述,介绍了知识发现的基本步骤、基本方法、基本任务等。而后对粗糙集理论进行了概述,介绍了粗糙集理论产生的背景、粗糙集理论的发展、以及对粗糙集应用于知识发现的优点作了阐述。
第二章介绍了粗糙集理论的一些基本概念,并将粗糙集与其他几种处理不确定性理论作了比较。
第三章对离散化问题进行了研究,从启发式方法和基于遗传算法的方法两个方面进行了研究。通过对初始断点集进行精简,将Nguyen S H提出的著名的离散化算法进行了改进,改进后的算法在空间复杂度和时间复杂度上都有较大程度的降低;另外,提出了一种免疫算法用于求解决策系统的离散化问题,它与启发式算法相比能获得更小且一致的离散化结果,为粗糙集中连续属性离散化提供了一种新的思想。
第四章对于决策系统属性约简问题,从信息论角度定义了一种新的属性重要性度量方法。与基于互信息增益的方法不同的是:这种度量方法不仅考虑了属性的值域的大小,而且还考虑了取值的分布。基于此度量,构造了相应的启发式算法,对多个数据集的实验结果表明该方法能更有效地对决策系统进行约简。
第五章研究了决策规则的获取,重点是针对不一致决策系统,提出了一种修改的基于分类一致性的规则获取算法,对每个决策类计算出相应的下近似集与上近似集,然后用决策类的下近似集获得确定性规则,上近似集获得概率性规则。在规则获取时采用属性重要性方法,与LEM2相比,它能一次获得多条规则。通过对Hayes数据集的实验表明了算法的有效性。
Rough set theory, introduced by Z. Pawlak in the early 1980s of the 20th century, is a mathematical theory of reasoning about data which can be also used to deal with vague and uncertain problems. Since 1990s of the last century, it has attracted much attention of researchers around the world and become a focus in the fields of computer science and information science. With about twenty years development, rough set theory has been successfully applied to many areas including machine learning, pattern recognition, decision analysis, process control, knowledge discovery from databases, and expert systems.
The key processes of the applying of rough set to knowledge discovery were studied, including the discretization problem, attribute reduction and the acquisition of decision rules were studied, and the corresponding algorithms were proposed in the thesis.
In Chapter1, the basic tasks, basic steps and basic methods of Knowledge Discovery are introduced. Consequently, the background of the emerging of rough set theory and developing of rough set theory are introduced. We also pointed out the virtues of applying rough set theory to knowledge discovery.
In Chapter 2, the basic concepts in rough set theory were introduced. Rough set theory was also compared with some other theory dealing with vagueness.
In Chapter 3, discretization problem was studied from two aspects: the heuristic method and the method based on genetic algorithm. A more efficient strategy of determination of candidate cuts was proposed contrasting to the strategy in the named method based on rough set and Boolean reasoning presented by Nguyen. Based on the strategy of determination of candidate cuts, an improved algorithm was constructed. The experiments show that the improved algorithm has lower space complexity and time complexity obviously. Additionally, a method based on immune algorithm was proposed which is easier to get small and consistent result.
In Chapter 4, the reduction problem was studied. In order to obtain good relative reduct in decision system, a new attribute importance measure defined from the viewpoint of information theory which considers value distribution of selected attributes besides the mutual information between selected conditional attributes and decision attribute was defined. An algorithm based on the measure was constructed and analyzed. The experiments show that the algorithm can reduce the decision system effectively.
In Chapter 5, the acquisition of decision rules was studied. We focused on inconsistent decision system. A modified algorithm was proposed. In the algorithm, the lower and upper of all decision classes were computed. Thus, the task of rule induction from inconsistent data is reduced to rule induction from consistent data. A set of certain rules can be induced from the lower approximation and a set of possible rules can be induced from the upper approximation. The induction process also made use of attribute importance method. Compared with the named LEM2 algorithm, the algorithm can acquire more than one rule at one time. The experiments on Hayes data show that the algorithm is effective.
引文
[1]陆汝钤.世纪之交的知识工程与知识科学.北京:清华大学出版社,2002
[2]Usma M.Fayyad,Gregory Piatetsky-Shapiro,Padhraic Smith,etc.Advnace in knowledge discovery and data mining.Cmabridge,MA:AAAIM/ITPress,1996
[3]Hart J W and Kambr M.Data mining------concepts and techniques.Morgan Kaufrnann Publishers,2001
[4]Peter F.Drueker.Knowledge Management.HarvardBusinessReview,1991(6):35-37
[5]Fayyad U M,Piatetsky Shapiro G,Smyth P.Know ledge discovery and data mining:towards a unifying frame work.Proc of KDD96.Menlo Park,CA:AAA I Press,1996:82-88
[6]Jiawei Han.Micbeline Kamber.Data mining:concepts and techniques.Beijing:higher education press.2002
[7]J.H.Friedman.A recursive partitioning decision rule for nonparametric classifiers.IEEE Trans.on Comp.:1977.404408
[8]L.Breiman.J.Friedman.R.Olsben.etc..Classification and regression trees.Monterey.CA,Wadswortb International Group.1984
[9]J.R.Quinlan.Unlmown attribute values in induction.In proc.6th Int.Workshop on machine learning.Itbaca.NY:1989.164168
[10]R.L Kemie:Y Lee.B.Van Roy.etc..Solving data mining problems through pattern recognition.Prentice Hall.Upper Saddle River.N J,1998
[11]D.Pyle.Data preparation for data mining.Morgan Kaufinaim:San Francisco.1999
[12]K.Ross and D.Srivastava.Fast computation of sparse datacubes.In proc.1997 Int.Conference Very Large Data Bases(VLDB'97).Athens.Greece:1977.116-125
[13]Agrawa R.and Srikant R.Fast Algorithms for Mining Association Rules in Large Databases.Proeeedings of the 20~(th)Intemational Conferenee on Very Large Data Bases,1994.1:487-499
[14] Pawlak Z. Rough Sets—Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht, 1991
[15] Pawlak Z, Grzymala-Bausse J, Slowinski R et al. Rough sets. Communications of the ACM, 1995, 38(11):89-95
[16] Pawlak Z, Skowron A. Rough Sets Rudiments, Bulletin of IRSS, 1999:67-70
[17]Polkowski L and Skowron A. Rough sets: A perspective. In: L. Polkowski and A. Skowron (eds.), Rough Sets in Knowledge Discovery 1: Methodology and Applications, Physica-Verlag, Heidelberg, 1998:31-56
[18] Ziarko W. Introduction to the special issue on rough sets and knowledge discovery. International Journal of Computational Intelligence, 1995,11(2):223-226
[19] Komorowski J, Pawlak Z, Polkowski L et al. Rough sets: A tutorial[A]. in: S.K. Pal and A. Skowron (eds.), Rough fuzzy hybridization: A new trend in decision-making, Springer-Verlag, Singapore, 1999:3-98
[20] Ohrn A, Komorowski J, Skowron A and Synak P. The design and implementation of a knowledge discovery toolkit based on rough sets- The ROSETTA system. In: L. Polkowski and A. Skowron (eds.), Rough Sets in Knowledge Discovery 1: Methodology and Applications, Physica-Verlag, Heidelberg, 1998:376-399
[21] Ohrn A, Komorowski J, Skowron A and Synak P. The ROSETTA software system. In: L. Polkowski and A. Skowron (eds.), Rough Sets in Knowledge Discovery 2: Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998:572-576
[22] Iwinski T B. Algebraic approach to rough sets. Bulletin of the Polish Academic of Sciences: Mathematics, 1987,35(9-10):673-683
[23] Pomykala J and Pomykala J A. The stone algebra of rough sets. Bulletin of the Polish Academic of Sciences: Mathematics, 1987,35(7-8):495-508
[24] Iwinski T B. Rough orders and rough concepts. Bulletin of the Polish Academic of Sciences: Mathematics, 1988,36(3-4): 187-192
[25] Wiweger A. On topological rough sets. Bulletin of the Polish Academic of Sciences: Mathematics, 1989,37(1-6): 89-93
[26] Pomykala J A. Approximation operations in approximation space. Bulletin of the Polish Academic of Sciences:Mathematics,1987,35(7-8):653-662
[27]Gehrke M and Walker E.On the structure of rough sets.Bulletin of the Polish Academic of Sciences:Mathematics,1992,40(3):235-245
[28]Duntsch I.Rough sets and algebras of relations.In Ewa Orlowska(eds.),Incomplete Information - Rough Set Analysis,Physica-Verlag,1997:95-108
[29]Duntsch I,Orlowska E and Wang H.Algebras of approximating regions.Fundamenta Informaticae,Vol.46,2001:71-82
[30]Yao Y Y.Constructive and algebraic methods of the theory of rough sets,Information Sciences,1998,109(1-4):21-47
[31]代建华.粗代数与三值Lukasiewicz代数.计算机学报,2007,30(2):161-167
[32]代建华,潘云鹤.粗代数研究.软件学报,2005,16(7):1197-1204
[33]Dai Jianhua,Lv Hanfei,Chen Weidong.Two Kinds of Rough Algebras and Brouwer-Zadeh Lattices.Proceedings of the 5~(th)International Conference on Rough Sets and Current Trends in Computing(RSCTC2006),LNAI 4259.Kobe,Japan,Nov.2006,p99-106
[34]Dai Jianhua,Chen Weidong,Pan Yunhe.Rough Sets and Brouwer-Zadeh Lattices.Proceedings of the 1~(st)International Conference on Rough Sets and Knowledge Technology(RSKT2006),LNAI 4062.Chongqing,China,Jul.2006,p200-207
[35]Kuroki N.Rough ideals in semigroups.Information Sciences,Vol.100,1997:139-163
[36]Stepaniuk J.Rough sets and similarity relations.Symulacja w badaniach i rozwoju,Trzecie Warsztaty Naukowe PTSK,Wigry,26-28 wrzesnia,1996,(red.)R.Bogacz,L.Bobrowski,Warszawa,1997:405-413
[37]Slowinski R and Vanderpooten D.A generalized definition of rough approximations based on similarity.IEEE Transactions on Knowledge and Data Engineering,2000,12(2):331-336
[38]Skowron A and Stepaniuk J.Tolerance approximation spaces.Fundamenta Informaticae,1996,27(2-3):245-253
[39]Jarvinen J.Approximations and rough sets based on tolerance.In:Ziarko W and Yao Y Y (eds.), Proceedings of 2nd International Conference, RSCTC2000, LNAI 2005, Banff, Canada, 2001: 182-189
[40] Yao Y Y and Lin T Y. Generalization of rough sets using modal logic, Intelligent Automation and Soft Computing An International Journal, 1996,2(2): 103-120
[41] Yao Y Y, Generalized rough set models, in: Rough Sets in Knowledge Discovery, Polkowski, L. and Skowron, A. (Eds.), Physica-Verlag, Heidelberg, 1998:286-318
[42] Yao Y Y, Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences, 1998,111 (1 -4):239-259
[43]Bodjanova S. Approximation of fuzzy concepts in decision making. Fuzzy Sets and System, Vol.85 1997:23-29
[44]Thiele H. On axiomatic characterizations of fuzzy approximation operators. In: Ziarko W and Yao Y Y (eds.), Proceedings of 2nd International Conference, RSCTC2000, LNAI 2005, Banff, Canada, 2001: 277-285
[45] Wong SKM, Wang L S and Yao Y Y. On modeling uncertainty with structures. Computational Intelligence, 1995, 11(2):406-426
[46]Ziarko W. Variable precision rough set model. Journal of Computer and System Sciences, Vol.46,1993:39-59
[47]Wybraniec-Skardowska U. On a generalization of approximation space. Bulletin of the Polish Academic of Sciences: Mathematics, 1989,37(1-6): 51-62
[48] J. Stepaniuk. Approximation spaces in extensions of rough set theory. Proceedings of the International Conference on Rough Sets and Current Trends in Computing, Warsaw, Poland, June 22-26, Lecture Notes in Artificial Intelligence 1424, Springer-Verlag, 1998:290-297
[49] Yao Y Y, Wong S K M and Lin TY, A review of rough set models, in: Rough Sets and Data Mining: Analysis for Imprecise Data, Lin, T.Y. and Cercone, N. (Eds.), Kluwer Academic Publishers, Boston, 1997:47-75
[50]Yao Y Y, On generalizing Pawlak approximation operators, Rough Sets and Current Trends in Computing, Proceedings of the First International Conference, RSCTC'98, Lecture Notes in Artificial Intelligence 1424, Warsaw, Poland,June 22-26,Polkowski,L.and Skowron,A.(Eds.),Springer-Verlag,Berlin,1998:298-307
[51]Jarvinen J.On the structure of rough approximations.In:Alpigini J J et al.(eds.)Proceedings of 3~(rd)International Conference,RSCTC2002,LNAI 2475,Malvern,PA,USA,2002:123-230
[52]Jarvinen J.On the structure of rough approximations.TUCS Technical Report 447,Turku Center for Computer Science,Turku,2002
[53]代建华.利用分子格对粗糙集理论进行推广.计算机学报,2004,27(10):1436-1440
[54]Dai J H.Structure of rough approximations based on molecular lattices.Proceedings of 4~(th)Internaltional Conference on Rough Sets and Current Trends in Computing,RSCTC2004,LNAI3066,Uppsala,Sweden,2004:69-77
[55]Lin T Y,Liu Q.Rough approximate operators:Axiomatic rough set theory.In:Ziarko W P ed.Rough Sets,Fuzzy Sets and Knowledge Discovery.London:Springer-Verlag,1994:256-260
[56]代建华,潘云鹤.相似关系粗糙集理论的一个极小公理组.复旦学报,Vol.43,No.5,2004:856-859
[57]Dai Jianhua,Chen Weidong,Pan Yunhe.A Minimal Axiom Group of Rough Set Based on Quasi-ordering.Journal of Zhejiang University Science,Vol.5,No.7,2004:810-815
[58]Yao Y Y.A comparative study of fuzzy sets and rough sets,Information Sciences,1998,109(1-4):227-242
[59]Skowron A and Grzymala-Bausse J W.From rough set theory to evidence theory.In:Yager R R,Fedrizzi M and Kacprzyk Jet al(eds.),Advances in the Dempster-Shafter Theory of Evidence,New York 1994:193-236
[60]Yao Y Y and Lingras P J.Interpretations of belief functions in the theory of rough sets,Information Sciences,1998,104(1-2):81-106
[61]Szczuka M.Rough Sets and Artificial Neural Networks.In:L.Polkowski and
[62]Jelonek J,Krawiec K,Slowinski R.Rough Set Reduction of Attributes and their domains for neural networks.International Journal of Computational Intelligence,1995,11(2):339-347
[63]Lingras P.Unsupervised rough sets classification using GAs.Journal of Intelligent Information Systems,2001,16(3):215-228
[64]Szczerba L W.Rough quantifiers.Bulletin of the Polish Academic of Sciences:Mathematics,1987,35(3-4):251-254
[65]Szczerba L W.Rough quantifiers have no Tarski property.Bulletin of the Polish Academic of Sciences:Mathematics,1987,35(9-10):663-665
[66]Lin T Y and Liu Q.First-order rough logic I:Approximate reasoning via rough sets.Fundamenta Informaticae,1996,27(2-3):137-144
[67]刘清.算子Rough逻辑及其归结原理.计算机学报,1998,21(5):476-480
[68]Liu Q.The OI-resolution of operator rough logic.In Polkowski L and Skowron A(eds.),Proc.of the First International Conference on Rough Sets and Current Trends in Computing(RSCTC'98),LNAI 1424,Warsaw,Poland,1998:432-435
[69]刘清.邻域值信息表上的邻域逻辑及其数据推理.计算机学报,2001,24(4):405-410
[70]Liau C J and Liu D R.A logical approach to fuzzy data analysis.Proc.of the 3~(rd)European Conference on Principles and Practice of Knowledge Discovery in Databases,LNAI 1704,1999:412-417
[71]Fan T F,Hu W C and Liau C J.Decision Logics for Knowledge Representation in Data Mining.Proc.of the 25th Annual International Computer Software and Applications Conference(Workshop on Data Mining and E-Organizations),2001:626-631
[72]Yao Y Y and Liau C J.A generalized decision logic language for granular computing.Proceedings of the 11th IEEE International Conference on Fuzzy Systems,IEEE Press,2002:773-778
[73]Fan T-F,Liau C-J and Yao Y Y,On modal decision logics,in PAKDD 2002Workshop entitled "Towards Foundation of Data Mining",Communications of Institute of Information and Computing Machinery,2002,5(2):21-26
[74]Fan T F,Liau C J and Yao Y Y.On modal and fuzzy decision logics based on rough set theory, Fundamenta Informaticae, 2002, 52(4):323-344
[75]Liau C J. On rough quantifiers. Cybenetics and Systems'98,1998:175-180
[76]Liau C J. An overview of rough set semantics for modal and quantifier logics. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 2000, 8(1): 93-118
[77] Stepaniuk J. Rough relations and logics. In: L. Polkowski, A. Skowron (eds.), Rough Sets in Knowledge Discovery 1. Methodology and Applications, Physica Verlag, Heidelberg, 1998: 248-260
[78]刘清. Rough 集及Rough 推理. 北京: 科学出版社, 2003
[79]Nguyen S H. Discretization of real value attributes: Boolean reasoning approach[Ph.D Dissertation]. Poland: Warsaw University, 1997
[80]Nguyen S H and Skowron A. Quantization of real value attributes:Rough set and Boolean reasoning approach. Bulletin of Internation Rough Set Siciety, 1997,1(1):5-16.
[81]Nguyen S H and Nguyen H S. Discretization of real value attributes for control problems. In: Proceedings of the Fourth European Congress on Intelligent Techniques and Soft Computing (EUFIT'96) 1, September 2-5, Aachen, Germany, Verlag Mainz, 1996:188-191
[82]Nguyen S H and Nguyen H S. Discretization methods with back-tracking. In: Proceedings of the Fifth European Congress on Intelligent Techniques and Soft Computing, (EUFIT'97), September 8-11, Aachen, Germany, Verlag Mainz, 1997:201-205
[83]Nguyen S H and Nguyen H S. An Application of discretization methods in control. Proceedings of the Workshop on Robotics, Intelligent Control and Decision Support Systems, February 22-23, Polish-Japanese Institute of Information Technology, Warsaw, 1999:47-52
[84]Nguyen S H, Nguyen H S. Discretization Methods in Data Mining. In: Plokowski L, Skowron A(eds.): Rough Sets in Knowledge Discovery, Physica-Verlag, Heidelberg, 1998:451-482
[85]Chlebus B, Nguyen S H. On finding optimal discretization on two attributes. In: L. Polkowski,A.Skowron(eds.),Proc.of the first International Conference on Rough Sets and Current Trend in Computing(RSCTC'98),June 1998,Warsaw,Poland,1998:537-544
[86]Nguyen S H.Discretization Problems for Rough Set Methods.In:Polkowski L,Skowron A(eds.)Proc of the first International Conference on Rough Sets and Current Trend in Computing(RSCTC'98),Warsaw,Poland,1998:545-552
[87]Jia Ping,Dai Jianhua,Chen Weidong,Pan Yunhe,Zhu Miaoliang.Immune Algorithm for Discretization of Decision Systems in RoughSet Theory.Journal of Zhejiang University SCIENCE A,2006,7(4):602-606
[88]Hu X,Cercone N.Learning in Relational Database:A Rough Set Approach.International Journal of Computational Intelligence,1995,11(2):323-338
[89]王珏,王任,苗夺谦等.基于Rough Set理论的“数据浓缩”.计算机学报,1998,21(5):393-400
[90]Miao Duoqian,Wang Jue.An Information-based Algorithm for Reduction of Knowledge.IEEE ICIP'97,1997:1155-1158
[91]苗夺谦,胡桂荣.知识约简的一种启发式算法.计算机研究与发展,1999,36(6):681-684
[92]Wang J,Miao D Q.Analysis on Attribute Reduction strategies of Rough Set.Journal of Computer Science & Technology,1998,13(2):189-193
[93]Wroblewski J.Finding minimal reducts using genetic algorithm.ICS Research Report 16/95,Institute of computer science,Warsaw University of Technology,1995
[94]Dai J H and Li Y X.A hybrid genetic algorithm for reduct of attributes in decision system based on rough set theory.Wuhan University Journal of Natural Sciences,2002,7(3):285-289
[95]Slezak D.Approximate reducts in decision tables.In:Proc.of the sixth International Conference,Information Processing and Management of Uncertainty in Knowledge-based Systems(IPMU'96),Julyl-5,Granada,Spain,1996:1159-1164
[96]Slezak D.Searching for Dynamic Reducts in Inconsistent Decision Tables.In: Proceedings of the Seventh International Conference on Information Processing and Management of Uncertainty in Knowledge - Based Systems (IPMU'98),Paris,France,July6-10,1998:1362-1369
[97]Slezak D.Various approaches reasoning with frequency-based decision reducts:a survey.In:Polowski L,Lin T Y and Tsumoto S(eds.)Rough Sets in Soft Computing and Knowledge Discovery:New Developments,Physica-Verlag,Heidelberg,2000
[98]Nguyen S H,Skowron A.Boolean reasoning for feature extraction problems.In:Z.W.Ras,A.Skowron(eds.),Tenth International Symposium on Methodologies for Intelligent Systems,Foundations of Intelligent Systems (ISMIS'97),October 15-18,Charlotte,NC,USA,Lecture Notes in Artificial Intelligence 1325,Springer-Verlag,Berlin,1997:117-126
[99]Shao J.Finding Reducts with User Specified Criteria.In:Wagner R(eds.),Proc.of 8~(th)International Workshop on Database and Expert Systems Applications(DEXA'97),September 1-2,Toulouse,France,IEEE Computer Society Press,1997:352-357
[100]Skowron A and Stepaniuk J.Information Reduction Based on Constructive Neighborhood Systems.In:Proceedings of the Fifth International Workshop on Rough Sets Soft Computing(RSSC'97)at Third Annual Joint Conference on Information Sciences(JCIS'97).Duke University,Durham,NC,USA,1997:158-160
[101]Son H.Nguyen,A.Skowron.Boolean reasoning for feature extraction problems.In:Z.W.Ras,A.Skowron(eds.),Tenth International Symposium on Methodologies for Intelligent Systems,Foundations of Intelligent Systems (ISMIS'97),October 15-18,Charlotte,NC,USA,Lecture Notes in Artificial Intelligence 1325,Springer-Verlag,Berlin,1997:117-126
[102]贾平,代建华,潘云鹤,朱淼良.一种基于互信息增益率的新属性约简算法.浙江大学学报(工学版),2006,40(6):1041-1044
[103]Bazan J,Skowron A and Synak P.Discovery of decision rules from experimental data.Research Report40/94,Institute of Mathematics,Warsaw University, 1994
[104] Bazan J G, Skowron A, Synak P. Dynamic reducts as a tool for extracting laws from decision tables. Proc. of the Symposium on Methodologies for Intelligent Systems, Charlotte, NC, October 16-19, LNAI 869, Springer-Verlag, Berlin, 1994:346-355
[105] Bazan J G Dynamic reducts and statistical inference. In: Proceedings of the Sixth International Conference, Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMIU'96) vol. III, July 1-5, Granada, Spain, vol. III, 1996:1147-1152
[106] Bazan J G A Comparison of Dynamic and non-Dynamic Rough Set Methods for Extracting Laws from Decision Table. In: L. Polkowski, A. Skowron (eds.), Rough Sets in Knowledge Discovery, Physica - Verlag, Heidelberg, 1998:321-365
[107] Skowron A and Polkowski L. Synthesis of decision systems from data tables. In: T.Y. Lin, N. Cercone (eds.), Rough sets and data mining: Analysis of imprecise data, Kluwer Academic Publisher, Dordrecht, 1997: 259-299
[108] Stefanowski J. On rough set based approaches to induction of decision rules. In Polkowski L, Skowron A(eds.) Rough Sets in Data Mining and Knowledge Discovery vol. 1, Physica-Verlag, 1998:500-529
[109] Stefanowski J. Rough set based rule induction techniques for classification problems, In Porc. 6th European Congress on Intelligent Techniques and Soft Computing vol. 1, Aachen, 1998:109-113
[110] Nguyen H S. Discovery of generalized patterns. Proceedings of the Eleventh International Symposium on Methodologies for Intelligent Systems, Foundations of Intelligent Systems (ISMIS'99), June 8-11, Warsaw, Lecture Notes in Artificial Intelligence 1609, Springer - Verlag, Berlin, 1999: 574-582
[111] Polkowski L and Skowron A. Decision algorithms: A survay of rough set theoretic methods. Fundamenta Informaticae, 1997, 30(3-4):345-358
[112] Bazan J G, Nguyen S H, Nguyen T T, Skowron A and Stepaniuk J. Decision rules synthesis for object classificatioa In: E. Orowska (ed.), Incomplete Information:Rough Set Analysis,Physica - Verlag,Heidelberg,1998:23-57
[113]Nguyen H S,Nguyen T T,Polkowski L,Skowron A,Synak P and Wroblewski J.Decision Rules for Large Data Tables.in:P.Borne,G.Dauphin-Tanguy.C.Sueur and S.El Khattabi(eds.),CESA'96:Proceedings of CESA'96 IMACS Multiconference:Computational Engineering in Systems Applications 3/4,July 9-12,Lille,France,Gerf EC Lille - Cite Scientifique,1996:942-947
[114]Nguyen H S,Nguyen T T,Skowron A and Synak P.Knowledge discovery by rough set methods.In:Nagib C.Callaos(eds.),ISAS-96:Proc.of the International Conference on Information Systems Analysis and Synthesis,July 22-26,Orlando,USA,1996:26-33
[115]Polkowski L,Skowron A,Synak P and Wroblewski J.Searching for approximate description of decision classes.In:S.Tsumoto,S.Kobayashi,T.Yokomori,H.Tanaka and A.Nakamura(eds.),The Fourth International Workshop on Rough Sets,Fuzzy Sets,and Machine Discovery(RSFD'96),University of Tokyo,November 6-8,1996:153-161
[116]Mollestad T and Skowron A.A rough set framework for data mining of propositional default rules.In:Z.W.Ras and M.Michalewicz(eds.),ISMIS-96:Ninth International Symposium on Methodologies for Intelligent Systems,Zakopane,Poland,June 10-13,Lecture Notes in Artificial Intelligence 1079,Springer - Verlag,Berlin,1996:448-457
[117]代建华,潘云鹤.一种基于分类一致性的决策规则获取算法.控制与决策,2004,19(10):1086-1091
[118]Golan R,Ziarko W.Methodology for stock market analysis rough set theory.Proc.of IEEE/IAFE Conference on Computational Intelligence for Financial Engineering,New Jersey,1995:32-40
[119]Tsumoto S and Tanaka H.PRIMEROSE:Probabilistic rule induction method based on rough sets and resampling methods.Computational Intelligence,1995,11(2):389-405
[120]Tsumoto S,Tanaka H.Induction of Disease Description based on Rough Sets.The 1~(st)online workshop on soft computing,Aug,1996
[121] Tsumoto S. Automated extraction of medical expert system rules from clinical databases based on rough set theory. Information Sciences, 1998,112(1-4):67-84
[122] Tsumoto S. Modelling medical diagnostic rules based on rough sets. In Polkowski L and Skowron A(eds.), Proc. of the First International Conference on Rough Sets and Current Trends in Computing(RSCTC98), LNAI 1424, Warsaw, Poland, 1998:475-482
[123] Stepaniuk J. Rough Set Data Mining of Diabetes Mellitus Data. In: Ras Z W, Skowron A(eds.) Foundations of Intelligent Systems, 11th Inernational Symposium, ISMIS'99, Warsaw, Poland, Proceedings Springer Lecture Notes in Computer Science 1609,1999
[124] Pawlak Z. An inquiry into anatomy of conflicts. Information Sciences, 1998, 109(1-4):65-78
[125] Jelonek J, Krawiec K and Slowinski R. Rough set reduction of attributes and their domains for neural networks. Computational Intelligence, 1995,11(2):339-347
[126] Plonka L and Mrozek A. rule-based stabilization of the inverted pendulum. Computational Intelligence, 1995,11(2):348-356
[127] Czogala E et al. Ideas of a rough fuzzy controllers and its application of the stabilization of a pendulum-car system. Fuzzy Sets and Systems, 1995, 72(1):61-73
[128] Hu X H and Cercone N. Learning maximal generalized decision rules via discretization, generalization and rough set feature reduction. In: Proc. of the 9th IEEE International Conference on Tools with Artificial Intelligence. 1997:548-556
[129] Hu X. Knowledge Discovery in Database: An Attribute-Oriented Rough Set Approach[Ph.D Dissertation]. Canada: University of Regina, 1995
[130] Shan Ning and Wojciech Ziarko. Data-based acquisition and incremental modification of classification rules. Computational Intelligence, 1995,11(2):357-370
[131] Shan N, Ziarko W, Hamilton H J et al. Using rough sets as tools for knowledge discovery[A]. in Fayyad U M (eds.), First International Conference on Knowledge Discovery and Data Mining[C] , Menlo Park, Canada, 1995:268-273
[132] Chan C. A rough set approach to attribute generalization in data mining. Information Sciences, 1998,107(1-4):169-176
[133] Nejman D. A rough set based of handwritten numerals classification. Institute of Computer Science Reports, Warsaw University of Technology, Warsaw, Poland, 1994
[134] Teghem J et al. Use of rough sets method to draw premonitory factors for earthquakes by emphasizing gas geochemistry. In Slowinski R(eds.) Intelligent Decision Support : Handbook of Applications and Advances of Rough Set Theory, Dordrecht: Kluwer Academic 1992:165-179
[135] Slowinski R. Rough set approach to decision analysis. AI Expert, 1995, March: 19-25
[136] Ruhe G and Gesselschaft F. Rough set based data analysis in goal-oriented software measurement. In Proc. of IEEE International Software Metrics Symposium, Los Alamitos, 1996:10-19
[137] Wojcik Z et al. Structural modelling using rough sets, in Proc. of IEEE International Conference on Fuzzy Systems, New Jersey, 1999:761-766
[138] Ryszard N. Evaluation of vibroacoustic diagnostic symptoms by means of the rough set theory. Computers in Industry, 1992, 20(2): 141-152
[139] Fayyad U M, Piatetsky-Shapiro G and Smyth P. Knowledge discovery and data mining: Towards a unifying framework. In Proceedings of Second International Conference on Knowledge Discovery and Data Mining, Mento Park, Canada, AAAI Press, 1996:82-88
[140] Douherty J, Kohavi R and Sahami M. Supervised and Unsupervised Discretizations of Continuous Features. In : Proceedings of the 12th International Conference on Machine Learning, Morgan Kaufinann Publishers, 1995:194-202
[141] Susmaga R. Analyzing Discretizations of Continuous Attributes Given a Monotonic Discrimination Function. Intelligent Data Analysis, 1997:157-179
[142] Quinlan J R. Improved use of continuous attributes in C4.5. Journal of Artificial Intelligence Research, 1996(4):77-90
[143] Ting K M. Discretization of continuous-valued attributes and instance-based learning. Technical Report 491, University of Sydney, 1994
[144] Kurgan L and Cios K J. Discretization Algorithm that Uses Class-Attribute Interdependence Maximization. Proc. of the 2001 International Conference on Artificial Intelligence(IC-AI2001), Las Vegas, Nevada, 2001:980-987
[145] Wang K and Liu B. Concurrent Discretization of Multiple Attributes. The Pacific Rim International Conference on Artificial Intelligence(PRICAI98), Singapore, 1998:250-259
[146] Wang K and Han C G Minimum Splits Based Discretization for Continuous Features. The International Joint Conference on Artificial Intelligence, Nagoya, Japan, 1997:942-947
[147] Ching J Y, Wong A K C and Chan K C C. Class Dependence Discretization for Inductive Learning from Continuous and Mixed-Mode Data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17(7):641-645
[148] Liu H and Setiono R. Chi2:Feature Selection and Discretization of Numeric Attributes. Proc. of the 7th IEEE International Conference on Tools with Artificial Intelligence(TAI'95), Washington D C, USA, 1995:388-391
[149] Jun B H, Kim C S and Song H Y et al. A New Criterion in Selection and Discretization of Attributes for the Generation of Decision Trees. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(12):1371-1375
[150] Elomaa T and Rousu J. Finding Optional Multi-Splits for Numerical Attributes in Decision Tree Learning. Technical Report NC-TR-96-041, University of Helsinki, Finland, 1996
[151] Berka P and Bruha I. Discretization and grouping : preprocessing steps for Data Mining. In: Quafafou Z(eds.) Proc. Principles of Data Mining and Knowledge Discovery(PKDD'98), LNAI 1510, Springer, 1998:239-245
[152] Frank E and Witten I H. Making Better Use of Global Discretization. Proc. International Conference on Machine Learning, Bled Slovenia, Morgan Kaufmann, 1999:115-123
[153] Kohavi R and Sahami M. Error-based and entropy-based discretization of Continuous Features. In Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, Menlo Park, 1996:114-119
[154] Ho K M and Scott P D. Zeta: A global method for discretization of continuous variables. Technical Report CSM-287, University of Essex, Australia, 1997
[155] Chun, K. S., Jung, H. K., Yahn, S. Y., Shape optimization of electromagnetic devieces using immune algorithm, IEEE Tran. Magnetics, 1997, 33(2): 1876-1879
[156] Chun, K. S., Jung, H. K., Yahn, S. Y, A study on comparison of optimizing performances between immune algorithm and other heuristic algorithms, IEEE Tran. Magnetics, 1998, 34(5): 2972-2975
[157] JonTimmis, MarkNeal, JohnHunt. An artificial immune system for data analysis. BioSystems,2000(55): 143-150
[158] Skowron A. Extracting laws from decision tables: A rough set approach. Computational Intelligence, 1995,11(2):371-388
[159] Grzymala-Bausse D M and Grzymala-Busse J W. The usefulness of machine learning approach to knowledge acquisition. Computational Intelligence, 1995, 11(2):268-279
[160] Wu X. Induction by attribute elimination. IEEE Transactions on Knowledge and Data Engineering, 1999,ll(5):805-812
[161] Khoo L P and Zhai L Y. A prototype genetic algorithm enhanced rough set-based rule induction system. Computers in Industry, Vol.46, 2001:95-106
[162] Liu J, Kwok T Y An Extended Genetic Rule Induction Algorithm. Proceedings of the Congress on Evolutionary Computation(CEC'2000), La Jolla, California, USA, 2000: 458-463
[163]Kwedlo W and Kretowski M.An evolutionary algorithm integrating diseretization of continuous-valued attributes with learning decision rules.Proc.of the Workshop on Intelligent Information System Ⅷ,Ustron,Poland,Junl4-18,1999
[164]Noda E,Freitas A A and Lopes H S.Discovering interesting prediction rules with a genetic algorithm.Proc.Congress on Evolutionary Computation (CEC-99),Washington D.C.,USA,July,1999:1322-1329
[165]Freitas A A.A survey of evolutionary algorithms for data mining and knowledge discovery.In:A.Ghosh and S.Tsutsui.(Eds.)Advances in Evolutionary Computation.Springer-Verlag,2002
[2]Usma M.Fayyad,Gregory Piatetsky-Shapiro,Padhraic Smith,etc.Advnace in knowledge discovery and data mining.Cmabridge,MA:AAAIM/ITPress,1996
[3]Hart J W and Kambr M.Data mining------concepts and techniques.Morgan Kaufrnann Publishers,2001
[4]Peter F.Drueker.Knowledge Management.HarvardBusinessReview,1991(6):35-37
[5]Fayyad U M,Piatetsky Shapiro G,Smyth P.Know ledge discovery and data mining:towards a unifying frame work.Proc of KDD96.Menlo Park,CA:AAA I Press,1996:82-88
[6]Jiawei Han.Micbeline Kamber.Data mining:concepts and techniques.Beijing:higher education press.2002
[7]J.H.Friedman.A recursive partitioning decision rule for nonparametric classifiers.IEEE Trans.on Comp.:1977.404408
[8]L.Breiman.J.Friedman.R.Olsben.etc..Classification and regression trees.Monterey.CA,Wadswortb International Group.1984
[9]J.R.Quinlan.Unlmown attribute values in induction.In proc.6th Int.Workshop on machine learning.Itbaca.NY:1989.164168
[10]R.L Kemie:Y Lee.B.Van Roy.etc..Solving data mining problems through pattern recognition.Prentice Hall.Upper Saddle River.N J,1998
[11]D.Pyle.Data preparation for data mining.Morgan Kaufinaim:San Francisco.1999
[12]K.Ross and D.Srivastava.Fast computation of sparse datacubes.In proc.1997 Int.Conference Very Large Data Bases(VLDB'97).Athens.Greece:1977.116-125
[13]Agrawa R.and Srikant R.Fast Algorithms for Mining Association Rules in Large Databases.Proeeedings of the 20~(th)Intemational Conferenee on Very Large Data Bases,1994.1:487-499
[14] Pawlak Z. Rough Sets—Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht, 1991
[15] Pawlak Z, Grzymala-Bausse J, Slowinski R et al. Rough sets. Communications of the ACM, 1995, 38(11):89-95
[16] Pawlak Z, Skowron A. Rough Sets Rudiments, Bulletin of IRSS, 1999:67-70
[17]Polkowski L and Skowron A. Rough sets: A perspective. In: L. Polkowski and A. Skowron (eds.), Rough Sets in Knowledge Discovery 1: Methodology and Applications, Physica-Verlag, Heidelberg, 1998:31-56
[18] Ziarko W. Introduction to the special issue on rough sets and knowledge discovery. International Journal of Computational Intelligence, 1995,11(2):223-226
[19] Komorowski J, Pawlak Z, Polkowski L et al. Rough sets: A tutorial[A]. in: S.K. Pal and A. Skowron (eds.), Rough fuzzy hybridization: A new trend in decision-making, Springer-Verlag, Singapore, 1999:3-98
[20] Ohrn A, Komorowski J, Skowron A and Synak P. The design and implementation of a knowledge discovery toolkit based on rough sets- The ROSETTA system. In: L. Polkowski and A. Skowron (eds.), Rough Sets in Knowledge Discovery 1: Methodology and Applications, Physica-Verlag, Heidelberg, 1998:376-399
[21] Ohrn A, Komorowski J, Skowron A and Synak P. The ROSETTA software system. In: L. Polkowski and A. Skowron (eds.), Rough Sets in Knowledge Discovery 2: Applications, Case Studies and Software Systems, Physica-Verlag, Heidelberg, 1998:572-576
[22] Iwinski T B. Algebraic approach to rough sets. Bulletin of the Polish Academic of Sciences: Mathematics, 1987,35(9-10):673-683
[23] Pomykala J and Pomykala J A. The stone algebra of rough sets. Bulletin of the Polish Academic of Sciences: Mathematics, 1987,35(7-8):495-508
[24] Iwinski T B. Rough orders and rough concepts. Bulletin of the Polish Academic of Sciences: Mathematics, 1988,36(3-4): 187-192
[25] Wiweger A. On topological rough sets. Bulletin of the Polish Academic of Sciences: Mathematics, 1989,37(1-6): 89-93
[26] Pomykala J A. Approximation operations in approximation space. Bulletin of the Polish Academic of Sciences:Mathematics,1987,35(7-8):653-662
[27]Gehrke M and Walker E.On the structure of rough sets.Bulletin of the Polish Academic of Sciences:Mathematics,1992,40(3):235-245
[28]Duntsch I.Rough sets and algebras of relations.In Ewa Orlowska(eds.),Incomplete Information - Rough Set Analysis,Physica-Verlag,1997:95-108
[29]Duntsch I,Orlowska E and Wang H.Algebras of approximating regions.Fundamenta Informaticae,Vol.46,2001:71-82
[30]Yao Y Y.Constructive and algebraic methods of the theory of rough sets,Information Sciences,1998,109(1-4):21-47
[31]代建华.粗代数与三值Lukasiewicz代数.计算机学报,2007,30(2):161-167
[32]代建华,潘云鹤.粗代数研究.软件学报,2005,16(7):1197-1204
[33]Dai Jianhua,Lv Hanfei,Chen Weidong.Two Kinds of Rough Algebras and Brouwer-Zadeh Lattices.Proceedings of the 5~(th)International Conference on Rough Sets and Current Trends in Computing(RSCTC2006),LNAI 4259.Kobe,Japan,Nov.2006,p99-106
[34]Dai Jianhua,Chen Weidong,Pan Yunhe.Rough Sets and Brouwer-Zadeh Lattices.Proceedings of the 1~(st)International Conference on Rough Sets and Knowledge Technology(RSKT2006),LNAI 4062.Chongqing,China,Jul.2006,p200-207
[35]Kuroki N.Rough ideals in semigroups.Information Sciences,Vol.100,1997:139-163
[36]Stepaniuk J.Rough sets and similarity relations.Symulacja w badaniach i rozwoju,Trzecie Warsztaty Naukowe PTSK,Wigry,26-28 wrzesnia,1996,(red.)R.Bogacz,L.Bobrowski,Warszawa,1997:405-413
[37]Slowinski R and Vanderpooten D.A generalized definition of rough approximations based on similarity.IEEE Transactions on Knowledge and Data Engineering,2000,12(2):331-336
[38]Skowron A and Stepaniuk J.Tolerance approximation spaces.Fundamenta Informaticae,1996,27(2-3):245-253
[39]Jarvinen J.Approximations and rough sets based on tolerance.In:Ziarko W and Yao Y Y (eds.), Proceedings of 2nd International Conference, RSCTC2000, LNAI 2005, Banff, Canada, 2001: 182-189
[40] Yao Y Y and Lin T Y. Generalization of rough sets using modal logic, Intelligent Automation and Soft Computing An International Journal, 1996,2(2): 103-120
[41] Yao Y Y, Generalized rough set models, in: Rough Sets in Knowledge Discovery, Polkowski, L. and Skowron, A. (Eds.), Physica-Verlag, Heidelberg, 1998:286-318
[42] Yao Y Y, Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences, 1998,111 (1 -4):239-259
[43]Bodjanova S. Approximation of fuzzy concepts in decision making. Fuzzy Sets and System, Vol.85 1997:23-29
[44]Thiele H. On axiomatic characterizations of fuzzy approximation operators. In: Ziarko W and Yao Y Y (eds.), Proceedings of 2nd International Conference, RSCTC2000, LNAI 2005, Banff, Canada, 2001: 277-285
[45] Wong SKM, Wang L S and Yao Y Y. On modeling uncertainty with structures. Computational Intelligence, 1995, 11(2):406-426
[46]Ziarko W. Variable precision rough set model. Journal of Computer and System Sciences, Vol.46,1993:39-59
[47]Wybraniec-Skardowska U. On a generalization of approximation space. Bulletin of the Polish Academic of Sciences: Mathematics, 1989,37(1-6): 51-62
[48] J. Stepaniuk. Approximation spaces in extensions of rough set theory. Proceedings of the International Conference on Rough Sets and Current Trends in Computing, Warsaw, Poland, June 22-26, Lecture Notes in Artificial Intelligence 1424, Springer-Verlag, 1998:290-297
[49] Yao Y Y, Wong S K M and Lin TY, A review of rough set models, in: Rough Sets and Data Mining: Analysis for Imprecise Data, Lin, T.Y. and Cercone, N. (Eds.), Kluwer Academic Publishers, Boston, 1997:47-75
[50]Yao Y Y, On generalizing Pawlak approximation operators, Rough Sets and Current Trends in Computing, Proceedings of the First International Conference, RSCTC'98, Lecture Notes in Artificial Intelligence 1424, Warsaw, Poland,June 22-26,Polkowski,L.and Skowron,A.(Eds.),Springer-Verlag,Berlin,1998:298-307
[51]Jarvinen J.On the structure of rough approximations.In:Alpigini J J et al.(eds.)Proceedings of 3~(rd)International Conference,RSCTC2002,LNAI 2475,Malvern,PA,USA,2002:123-230
[52]Jarvinen J.On the structure of rough approximations.TUCS Technical Report 447,Turku Center for Computer Science,Turku,2002
[53]代建华.利用分子格对粗糙集理论进行推广.计算机学报,2004,27(10):1436-1440
[54]Dai J H.Structure of rough approximations based on molecular lattices.Proceedings of 4~(th)Internaltional Conference on Rough Sets and Current Trends in Computing,RSCTC2004,LNAI3066,Uppsala,Sweden,2004:69-77
[55]Lin T Y,Liu Q.Rough approximate operators:Axiomatic rough set theory.In:Ziarko W P ed.Rough Sets,Fuzzy Sets and Knowledge Discovery.London:Springer-Verlag,1994:256-260
[56]代建华,潘云鹤.相似关系粗糙集理论的一个极小公理组.复旦学报,Vol.43,No.5,2004:856-859
[57]Dai Jianhua,Chen Weidong,Pan Yunhe.A Minimal Axiom Group of Rough Set Based on Quasi-ordering.Journal of Zhejiang University Science,Vol.5,No.7,2004:810-815
[58]Yao Y Y.A comparative study of fuzzy sets and rough sets,Information Sciences,1998,109(1-4):227-242
[59]Skowron A and Grzymala-Bausse J W.From rough set theory to evidence theory.In:Yager R R,Fedrizzi M and Kacprzyk Jet al(eds.),Advances in the Dempster-Shafter Theory of Evidence,New York 1994:193-236
[60]Yao Y Y and Lingras P J.Interpretations of belief functions in the theory of rough sets,Information Sciences,1998,104(1-2):81-106
[61]Szczuka M.Rough Sets and Artificial Neural Networks.In:L.Polkowski and
[62]Jelonek J,Krawiec K,Slowinski R.Rough Set Reduction of Attributes and their domains for neural networks.International Journal of Computational Intelligence,1995,11(2):339-347
[63]Lingras P.Unsupervised rough sets classification using GAs.Journal of Intelligent Information Systems,2001,16(3):215-228
[64]Szczerba L W.Rough quantifiers.Bulletin of the Polish Academic of Sciences:Mathematics,1987,35(3-4):251-254
[65]Szczerba L W.Rough quantifiers have no Tarski property.Bulletin of the Polish Academic of Sciences:Mathematics,1987,35(9-10):663-665
[66]Lin T Y and Liu Q.First-order rough logic I:Approximate reasoning via rough sets.Fundamenta Informaticae,1996,27(2-3):137-144
[67]刘清.算子Rough逻辑及其归结原理.计算机学报,1998,21(5):476-480
[68]Liu Q.The OI-resolution of operator rough logic.In Polkowski L and Skowron A(eds.),Proc.of the First International Conference on Rough Sets and Current Trends in Computing(RSCTC'98),LNAI 1424,Warsaw,Poland,1998:432-435
[69]刘清.邻域值信息表上的邻域逻辑及其数据推理.计算机学报,2001,24(4):405-410
[70]Liau C J and Liu D R.A logical approach to fuzzy data analysis.Proc.of the 3~(rd)European Conference on Principles and Practice of Knowledge Discovery in Databases,LNAI 1704,1999:412-417
[71]Fan T F,Hu W C and Liau C J.Decision Logics for Knowledge Representation in Data Mining.Proc.of the 25th Annual International Computer Software and Applications Conference(Workshop on Data Mining and E-Organizations),2001:626-631
[72]Yao Y Y and Liau C J.A generalized decision logic language for granular computing.Proceedings of the 11th IEEE International Conference on Fuzzy Systems,IEEE Press,2002:773-778
[73]Fan T-F,Liau C-J and Yao Y Y,On modal decision logics,in PAKDD 2002Workshop entitled "Towards Foundation of Data Mining",Communications of Institute of Information and Computing Machinery,2002,5(2):21-26
[74]Fan T F,Liau C J and Yao Y Y.On modal and fuzzy decision logics based on rough set theory, Fundamenta Informaticae, 2002, 52(4):323-344
[75]Liau C J. On rough quantifiers. Cybenetics and Systems'98,1998:175-180
[76]Liau C J. An overview of rough set semantics for modal and quantifier logics. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems, 2000, 8(1): 93-118
[77] Stepaniuk J. Rough relations and logics. In: L. Polkowski, A. Skowron (eds.), Rough Sets in Knowledge Discovery 1. Methodology and Applications, Physica Verlag, Heidelberg, 1998: 248-260
[78]刘清. Rough 集及Rough 推理. 北京: 科学出版社, 2003
[79]Nguyen S H. Discretization of real value attributes: Boolean reasoning approach[Ph.D Dissertation]. Poland: Warsaw University, 1997
[80]Nguyen S H and Skowron A. Quantization of real value attributes:Rough set and Boolean reasoning approach. Bulletin of Internation Rough Set Siciety, 1997,1(1):5-16.
[81]Nguyen S H and Nguyen H S. Discretization of real value attributes for control problems. In: Proceedings of the Fourth European Congress on Intelligent Techniques and Soft Computing (EUFIT'96) 1, September 2-5, Aachen, Germany, Verlag Mainz, 1996:188-191
[82]Nguyen S H and Nguyen H S. Discretization methods with back-tracking. In: Proceedings of the Fifth European Congress on Intelligent Techniques and Soft Computing, (EUFIT'97), September 8-11, Aachen, Germany, Verlag Mainz, 1997:201-205
[83]Nguyen S H and Nguyen H S. An Application of discretization methods in control. Proceedings of the Workshop on Robotics, Intelligent Control and Decision Support Systems, February 22-23, Polish-Japanese Institute of Information Technology, Warsaw, 1999:47-52
[84]Nguyen S H, Nguyen H S. Discretization Methods in Data Mining. In: Plokowski L, Skowron A(eds.): Rough Sets in Knowledge Discovery, Physica-Verlag, Heidelberg, 1998:451-482
[85]Chlebus B, Nguyen S H. On finding optimal discretization on two attributes. In: L. Polkowski,A.Skowron(eds.),Proc.of the first International Conference on Rough Sets and Current Trend in Computing(RSCTC'98),June 1998,Warsaw,Poland,1998:537-544
[86]Nguyen S H.Discretization Problems for Rough Set Methods.In:Polkowski L,Skowron A(eds.)Proc of the first International Conference on Rough Sets and Current Trend in Computing(RSCTC'98),Warsaw,Poland,1998:545-552
[87]Jia Ping,Dai Jianhua,Chen Weidong,Pan Yunhe,Zhu Miaoliang.Immune Algorithm for Discretization of Decision Systems in RoughSet Theory.Journal of Zhejiang University SCIENCE A,2006,7(4):602-606
[88]Hu X,Cercone N.Learning in Relational Database:A Rough Set Approach.International Journal of Computational Intelligence,1995,11(2):323-338
[89]王珏,王任,苗夺谦等.基于Rough Set理论的“数据浓缩”.计算机学报,1998,21(5):393-400
[90]Miao Duoqian,Wang Jue.An Information-based Algorithm for Reduction of Knowledge.IEEE ICIP'97,1997:1155-1158
[91]苗夺谦,胡桂荣.知识约简的一种启发式算法.计算机研究与发展,1999,36(6):681-684
[92]Wang J,Miao D Q.Analysis on Attribute Reduction strategies of Rough Set.Journal of Computer Science & Technology,1998,13(2):189-193
[93]Wroblewski J.Finding minimal reducts using genetic algorithm.ICS Research Report 16/95,Institute of computer science,Warsaw University of Technology,1995
[94]Dai J H and Li Y X.A hybrid genetic algorithm for reduct of attributes in decision system based on rough set theory.Wuhan University Journal of Natural Sciences,2002,7(3):285-289
[95]Slezak D.Approximate reducts in decision tables.In:Proc.of the sixth International Conference,Information Processing and Management of Uncertainty in Knowledge-based Systems(IPMU'96),Julyl-5,Granada,Spain,1996:1159-1164
[96]Slezak D.Searching for Dynamic Reducts in Inconsistent Decision Tables.In: Proceedings of the Seventh International Conference on Information Processing and Management of Uncertainty in Knowledge - Based Systems (IPMU'98),Paris,France,July6-10,1998:1362-1369
[97]Slezak D.Various approaches reasoning with frequency-based decision reducts:a survey.In:Polowski L,Lin T Y and Tsumoto S(eds.)Rough Sets in Soft Computing and Knowledge Discovery:New Developments,Physica-Verlag,Heidelberg,2000
[98]Nguyen S H,Skowron A.Boolean reasoning for feature extraction problems.In:Z.W.Ras,A.Skowron(eds.),Tenth International Symposium on Methodologies for Intelligent Systems,Foundations of Intelligent Systems (ISMIS'97),October 15-18,Charlotte,NC,USA,Lecture Notes in Artificial Intelligence 1325,Springer-Verlag,Berlin,1997:117-126
[99]Shao J.Finding Reducts with User Specified Criteria.In:Wagner R(eds.),Proc.of 8~(th)International Workshop on Database and Expert Systems Applications(DEXA'97),September 1-2,Toulouse,France,IEEE Computer Society Press,1997:352-357
[100]Skowron A and Stepaniuk J.Information Reduction Based on Constructive Neighborhood Systems.In:Proceedings of the Fifth International Workshop on Rough Sets Soft Computing(RSSC'97)at Third Annual Joint Conference on Information Sciences(JCIS'97).Duke University,Durham,NC,USA,1997:158-160
[101]Son H.Nguyen,A.Skowron.Boolean reasoning for feature extraction problems.In:Z.W.Ras,A.Skowron(eds.),Tenth International Symposium on Methodologies for Intelligent Systems,Foundations of Intelligent Systems (ISMIS'97),October 15-18,Charlotte,NC,USA,Lecture Notes in Artificial Intelligence 1325,Springer-Verlag,Berlin,1997:117-126
[102]贾平,代建华,潘云鹤,朱淼良.一种基于互信息增益率的新属性约简算法.浙江大学学报(工学版),2006,40(6):1041-1044
[103]Bazan J,Skowron A and Synak P.Discovery of decision rules from experimental data.Research Report40/94,Institute of Mathematics,Warsaw University, 1994
[104] Bazan J G, Skowron A, Synak P. Dynamic reducts as a tool for extracting laws from decision tables. Proc. of the Symposium on Methodologies for Intelligent Systems, Charlotte, NC, October 16-19, LNAI 869, Springer-Verlag, Berlin, 1994:346-355
[105] Bazan J G Dynamic reducts and statistical inference. In: Proceedings of the Sixth International Conference, Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMIU'96) vol. III, July 1-5, Granada, Spain, vol. III, 1996:1147-1152
[106] Bazan J G A Comparison of Dynamic and non-Dynamic Rough Set Methods for Extracting Laws from Decision Table. In: L. Polkowski, A. Skowron (eds.), Rough Sets in Knowledge Discovery, Physica - Verlag, Heidelberg, 1998:321-365
[107] Skowron A and Polkowski L. Synthesis of decision systems from data tables. In: T.Y. Lin, N. Cercone (eds.), Rough sets and data mining: Analysis of imprecise data, Kluwer Academic Publisher, Dordrecht, 1997: 259-299
[108] Stefanowski J. On rough set based approaches to induction of decision rules. In Polkowski L, Skowron A(eds.) Rough Sets in Data Mining and Knowledge Discovery vol. 1, Physica-Verlag, 1998:500-529
[109] Stefanowski J. Rough set based rule induction techniques for classification problems, In Porc. 6th European Congress on Intelligent Techniques and Soft Computing vol. 1, Aachen, 1998:109-113
[110] Nguyen H S. Discovery of generalized patterns. Proceedings of the Eleventh International Symposium on Methodologies for Intelligent Systems, Foundations of Intelligent Systems (ISMIS'99), June 8-11, Warsaw, Lecture Notes in Artificial Intelligence 1609, Springer - Verlag, Berlin, 1999: 574-582
[111] Polkowski L and Skowron A. Decision algorithms: A survay of rough set theoretic methods. Fundamenta Informaticae, 1997, 30(3-4):345-358
[112] Bazan J G, Nguyen S H, Nguyen T T, Skowron A and Stepaniuk J. Decision rules synthesis for object classificatioa In: E. Orowska (ed.), Incomplete Information:Rough Set Analysis,Physica - Verlag,Heidelberg,1998:23-57
[113]Nguyen H S,Nguyen T T,Polkowski L,Skowron A,Synak P and Wroblewski J.Decision Rules for Large Data Tables.in:P.Borne,G.Dauphin-Tanguy.C.Sueur and S.El Khattabi(eds.),CESA'96:Proceedings of CESA'96 IMACS Multiconference:Computational Engineering in Systems Applications 3/4,July 9-12,Lille,France,Gerf EC Lille - Cite Scientifique,1996:942-947
[114]Nguyen H S,Nguyen T T,Skowron A and Synak P.Knowledge discovery by rough set methods.In:Nagib C.Callaos(eds.),ISAS-96:Proc.of the International Conference on Information Systems Analysis and Synthesis,July 22-26,Orlando,USA,1996:26-33
[115]Polkowski L,Skowron A,Synak P and Wroblewski J.Searching for approximate description of decision classes.In:S.Tsumoto,S.Kobayashi,T.Yokomori,H.Tanaka and A.Nakamura(eds.),The Fourth International Workshop on Rough Sets,Fuzzy Sets,and Machine Discovery(RSFD'96),University of Tokyo,November 6-8,1996:153-161
[116]Mollestad T and Skowron A.A rough set framework for data mining of propositional default rules.In:Z.W.Ras and M.Michalewicz(eds.),ISMIS-96:Ninth International Symposium on Methodologies for Intelligent Systems,Zakopane,Poland,June 10-13,Lecture Notes in Artificial Intelligence 1079,Springer - Verlag,Berlin,1996:448-457
[117]代建华,潘云鹤.一种基于分类一致性的决策规则获取算法.控制与决策,2004,19(10):1086-1091
[118]Golan R,Ziarko W.Methodology for stock market analysis rough set theory.Proc.of IEEE/IAFE Conference on Computational Intelligence for Financial Engineering,New Jersey,1995:32-40
[119]Tsumoto S and Tanaka H.PRIMEROSE:Probabilistic rule induction method based on rough sets and resampling methods.Computational Intelligence,1995,11(2):389-405
[120]Tsumoto S,Tanaka H.Induction of Disease Description based on Rough Sets.The 1~(st)online workshop on soft computing,Aug,1996
[121] Tsumoto S. Automated extraction of medical expert system rules from clinical databases based on rough set theory. Information Sciences, 1998,112(1-4):67-84
[122] Tsumoto S. Modelling medical diagnostic rules based on rough sets. In Polkowski L and Skowron A(eds.), Proc. of the First International Conference on Rough Sets and Current Trends in Computing(RSCTC98), LNAI 1424, Warsaw, Poland, 1998:475-482
[123] Stepaniuk J. Rough Set Data Mining of Diabetes Mellitus Data. In: Ras Z W, Skowron A(eds.) Foundations of Intelligent Systems, 11th Inernational Symposium, ISMIS'99, Warsaw, Poland, Proceedings Springer Lecture Notes in Computer Science 1609,1999
[124] Pawlak Z. An inquiry into anatomy of conflicts. Information Sciences, 1998, 109(1-4):65-78
[125] Jelonek J, Krawiec K and Slowinski R. Rough set reduction of attributes and their domains for neural networks. Computational Intelligence, 1995,11(2):339-347
[126] Plonka L and Mrozek A. rule-based stabilization of the inverted pendulum. Computational Intelligence, 1995,11(2):348-356
[127] Czogala E et al. Ideas of a rough fuzzy controllers and its application of the stabilization of a pendulum-car system. Fuzzy Sets and Systems, 1995, 72(1):61-73
[128] Hu X H and Cercone N. Learning maximal generalized decision rules via discretization, generalization and rough set feature reduction. In: Proc. of the 9th IEEE International Conference on Tools with Artificial Intelligence. 1997:548-556
[129] Hu X. Knowledge Discovery in Database: An Attribute-Oriented Rough Set Approach[Ph.D Dissertation]. Canada: University of Regina, 1995
[130] Shan Ning and Wojciech Ziarko. Data-based acquisition and incremental modification of classification rules. Computational Intelligence, 1995,11(2):357-370
[131] Shan N, Ziarko W, Hamilton H J et al. Using rough sets as tools for knowledge discovery[A]. in Fayyad U M (eds.), First International Conference on Knowledge Discovery and Data Mining[C] , Menlo Park, Canada, 1995:268-273
[132] Chan C. A rough set approach to attribute generalization in data mining. Information Sciences, 1998,107(1-4):169-176
[133] Nejman D. A rough set based of handwritten numerals classification. Institute of Computer Science Reports, Warsaw University of Technology, Warsaw, Poland, 1994
[134] Teghem J et al. Use of rough sets method to draw premonitory factors for earthquakes by emphasizing gas geochemistry. In Slowinski R(eds.) Intelligent Decision Support : Handbook of Applications and Advances of Rough Set Theory, Dordrecht: Kluwer Academic 1992:165-179
[135] Slowinski R. Rough set approach to decision analysis. AI Expert, 1995, March: 19-25
[136] Ruhe G and Gesselschaft F. Rough set based data analysis in goal-oriented software measurement. In Proc. of IEEE International Software Metrics Symposium, Los Alamitos, 1996:10-19
[137] Wojcik Z et al. Structural modelling using rough sets, in Proc. of IEEE International Conference on Fuzzy Systems, New Jersey, 1999:761-766
[138] Ryszard N. Evaluation of vibroacoustic diagnostic symptoms by means of the rough set theory. Computers in Industry, 1992, 20(2): 141-152
[139] Fayyad U M, Piatetsky-Shapiro G and Smyth P. Knowledge discovery and data mining: Towards a unifying framework. In Proceedings of Second International Conference on Knowledge Discovery and Data Mining, Mento Park, Canada, AAAI Press, 1996:82-88
[140] Douherty J, Kohavi R and Sahami M. Supervised and Unsupervised Discretizations of Continuous Features. In : Proceedings of the 12th International Conference on Machine Learning, Morgan Kaufinann Publishers, 1995:194-202
[141] Susmaga R. Analyzing Discretizations of Continuous Attributes Given a Monotonic Discrimination Function. Intelligent Data Analysis, 1997:157-179
[142] Quinlan J R. Improved use of continuous attributes in C4.5. Journal of Artificial Intelligence Research, 1996(4):77-90
[143] Ting K M. Discretization of continuous-valued attributes and instance-based learning. Technical Report 491, University of Sydney, 1994
[144] Kurgan L and Cios K J. Discretization Algorithm that Uses Class-Attribute Interdependence Maximization. Proc. of the 2001 International Conference on Artificial Intelligence(IC-AI2001), Las Vegas, Nevada, 2001:980-987
[145] Wang K and Liu B. Concurrent Discretization of Multiple Attributes. The Pacific Rim International Conference on Artificial Intelligence(PRICAI98), Singapore, 1998:250-259
[146] Wang K and Han C G Minimum Splits Based Discretization for Continuous Features. The International Joint Conference on Artificial Intelligence, Nagoya, Japan, 1997:942-947
[147] Ching J Y, Wong A K C and Chan K C C. Class Dependence Discretization for Inductive Learning from Continuous and Mixed-Mode Data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1995, 17(7):641-645
[148] Liu H and Setiono R. Chi2:Feature Selection and Discretization of Numeric Attributes. Proc. of the 7th IEEE International Conference on Tools with Artificial Intelligence(TAI'95), Washington D C, USA, 1995:388-391
[149] Jun B H, Kim C S and Song H Y et al. A New Criterion in Selection and Discretization of Attributes for the Generation of Decision Trees. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(12):1371-1375
[150] Elomaa T and Rousu J. Finding Optional Multi-Splits for Numerical Attributes in Decision Tree Learning. Technical Report NC-TR-96-041, University of Helsinki, Finland, 1996
[151] Berka P and Bruha I. Discretization and grouping : preprocessing steps for Data Mining. In: Quafafou Z(eds.) Proc. Principles of Data Mining and Knowledge Discovery(PKDD'98), LNAI 1510, Springer, 1998:239-245
[152] Frank E and Witten I H. Making Better Use of Global Discretization. Proc. International Conference on Machine Learning, Bled Slovenia, Morgan Kaufmann, 1999:115-123
[153] Kohavi R and Sahami M. Error-based and entropy-based discretization of Continuous Features. In Proceedings of the Second International Conference on Knowledge Discovery and Data Mining, Menlo Park, 1996:114-119
[154] Ho K M and Scott P D. Zeta: A global method for discretization of continuous variables. Technical Report CSM-287, University of Essex, Australia, 1997
[155] Chun, K. S., Jung, H. K., Yahn, S. Y., Shape optimization of electromagnetic devieces using immune algorithm, IEEE Tran. Magnetics, 1997, 33(2): 1876-1879
[156] Chun, K. S., Jung, H. K., Yahn, S. Y, A study on comparison of optimizing performances between immune algorithm and other heuristic algorithms, IEEE Tran. Magnetics, 1998, 34(5): 2972-2975
[157] JonTimmis, MarkNeal, JohnHunt. An artificial immune system for data analysis. BioSystems,2000(55): 143-150
[158] Skowron A. Extracting laws from decision tables: A rough set approach. Computational Intelligence, 1995,11(2):371-388
[159] Grzymala-Bausse D M and Grzymala-Busse J W. The usefulness of machine learning approach to knowledge acquisition. Computational Intelligence, 1995, 11(2):268-279
[160] Wu X. Induction by attribute elimination. IEEE Transactions on Knowledge and Data Engineering, 1999,ll(5):805-812
[161] Khoo L P and Zhai L Y. A prototype genetic algorithm enhanced rough set-based rule induction system. Computers in Industry, Vol.46, 2001:95-106
[162] Liu J, Kwok T Y An Extended Genetic Rule Induction Algorithm. Proceedings of the Congress on Evolutionary Computation(CEC'2000), La Jolla, California, USA, 2000: 458-463
[163]Kwedlo W and Kretowski M.An evolutionary algorithm integrating diseretization of continuous-valued attributes with learning decision rules.Proc.of the Workshop on Intelligent Information System Ⅷ,Ustron,Poland,Junl4-18,1999
[164]Noda E,Freitas A A and Lopes H S.Discovering interesting prediction rules with a genetic algorithm.Proc.Congress on Evolutionary Computation (CEC-99),Washington D.C.,USA,July,1999:1322-1329
[165]Freitas A A.A survey of evolutionary algorithms for data mining and knowledge discovery.In:A.Ghosh and S.Tsutsui.(Eds.)Advances in Evolutionary Computation.Springer-Verlag,2002