基于不一致决策表的知识约简方法研究
|
摘要
在知识发现过程中,为了解决数据带有噪声或不完整的问题,迫切需要能处理不精确、不确定数据的理论和方法。粗糙集理论是满足这种要求的重要新型数学工具之一。通过把粗糙集理论与方法应用在知识发现过程中,就能从相关数据中挖掘出有价值的、非平凡的模式。
知识约简是粗糙集理论研究的核心问题,虽然目前关于知识约简的研究目前已经取得很多研究成果,但其中很多成果是针对没有决策属性的信息系统或一致决策表提出来的,它们并不适用于不一致决策表情形。
对于一致决策表,基于D-S证据理论的知识约简与代数约简所得的结果是一致的。对于不一致决策表,具体算例能说明基于D-S证据理论的广义决策约简与代数约简在不一致决策表下的差异性,理论上证明广义决策约简仅与分配约简是等价的。在分析了广义决策约简与代数约简不同原因的基础上,给出一种将不一致决策表转化成一致决策表,再基于D-S证据理论求原始决策表代数约简的方法。通过建立信任函数与正区域基数之间的联系,给出了不需要转换过程,基于D-S证据理论直接求不一致决策表代数约简的新方法,数值算例验证了其正确性。
在基于决策强度知识约简中,决策强度知识约简与条件信息熵约简本质上被证明是等价的。从条件概率的角度,将基于近似分类质量的代数约简与基于决策强度的条件信息熵约简的数学模型在形式上给出统一表示,从而分析它们在一致决策表下是一致的以及在不一致决策表下是不一致的原因。通过定义一种与正区域相一致的新决策强度,证明新决策强度约简与代数约简是等价的,提出了基于该新决策强度的启发式约简算法,数值算例验证了其正确性。
将属性区分能力与差别矩阵结合起来研究,可建立差别矩阵中某属性集的可辩识属性集项数与其属性区分能力之间的关系。基于等价差别矩阵具有相同核属性和约简结果的思想,对现有差别矩阵进行改写,将基于知识量计算的方法推广到决策表情形,得到基于Hu差别矩阵知识约简和代数约简下的属性区分能力计算公式,提出一类以属性区分能力大小为启发式信息的决策表属性约简算法。该类方法的最大优点是以差别矩阵为参考但又不必通过构造差别矩阵来计算知识约简,从而巧妙避开基于差别矩阵方法的低效性问题,算法既有明显意义解释,又有坚实的理论基础。数值算例和仿真实验验证了该算法更易搜索到最优约简。同时,给出两类构造启发式算法的一般框架,为设计高效的启发式算法提供思路。
During the process of knowledge discovery, in order to solve the problem of information noise or information incompleteness, it is necessary to develop the theories and methods which can deal with imprecise and uncertain information. Rough set theory is one of important novel mathematical tool to meet those demands. The valuable and non-trivial patterns are mined by application of rough set theory and method in knowledge discovery.
Knowledge reduction is one of the fundamental contents in rough set theory. At present, many research results have been achieved, but most of them are just effective for information system without decision attributes or consistent decision table and invalid for inconsistent decision table.
For consistent decision table, the approach to knowledge reduction based on D-S evidence theory is consistent with algebraic reduction. For inconsistent decision table,the difference between generalized decision reduction based on D-S evidence theory and algebraic reduction has been illustrated by an example firstly. It is proved that generalized decision reduction is just equivalent to assignment reduction. The essential causes that algebraic reduction and generalized decision reduction obtain a different result for inconsistent decision table are analyzed. A new approach to algebraic reduction based on evidence theory is proposed by transferring the inconsistent decision table into consistent one. By establishing the relationship between positive region bases and belief function, a new approach which can obtain algebraic reduction based on D-S evidence theory is proposed and its correctness is illustrated by a numerical example.
It is proved that knowledge reduction based on decision power is equivalent to that based on conditional information entropy after knowledge reduction based on decision power discussion. From the view of conditional probability, because the mathematical models for algebraic and conditional information entropy reductions are unified formally, the reason of Consistency of their application in consistent decision table and inconsistency of their application in inconsistent decision table can be discussed. A new decision power which coincides with positive region is presented and a heuristic algorithm is proposed, which ensures to obtain an algebraic reduction, its correctness is illustrated by a numerical example.
Attribute discernibility and discernible matrix are studied to establish the relationship between attribute discernibility and the number of times in discernible matrix. Based on the thought that equivalent discernible matrix has the same attribute reduction and core, the existing discernible matrices are rewritten, and then, the method based on knowledge measurement computation is generalized to decision table. The calculation formulas of attribute discernibility for Hu's discernible matrix reduction and algebraic reduction are obtained. Accordingly, the heuristic reduction algorithms based on attribute discernibility are presented. The biggest advantage of these two algorithms is to calculate knowledge reduction without discernible matrices construction. Thus, they can avoid the low efficiency of discernible matrices. These methods have not only clear explanation but also solid theoretical foundation. Numerical examples and results of simulation experiment show that the proposed method can explore the optimal reduction more easily. At the same time, the new way to construct the high efficient heuristic reduction algorithm is given, by application of two general frameworks used to design heuristic reduction algorithm.
知识约简是粗糙集理论研究的核心问题,虽然目前关于知识约简的研究目前已经取得很多研究成果,但其中很多成果是针对没有决策属性的信息系统或一致决策表提出来的,它们并不适用于不一致决策表情形。
对于一致决策表,基于D-S证据理论的知识约简与代数约简所得的结果是一致的。对于不一致决策表,具体算例能说明基于D-S证据理论的广义决策约简与代数约简在不一致决策表下的差异性,理论上证明广义决策约简仅与分配约简是等价的。在分析了广义决策约简与代数约简不同原因的基础上,给出一种将不一致决策表转化成一致决策表,再基于D-S证据理论求原始决策表代数约简的方法。通过建立信任函数与正区域基数之间的联系,给出了不需要转换过程,基于D-S证据理论直接求不一致决策表代数约简的新方法,数值算例验证了其正确性。
在基于决策强度知识约简中,决策强度知识约简与条件信息熵约简本质上被证明是等价的。从条件概率的角度,将基于近似分类质量的代数约简与基于决策强度的条件信息熵约简的数学模型在形式上给出统一表示,从而分析它们在一致决策表下是一致的以及在不一致决策表下是不一致的原因。通过定义一种与正区域相一致的新决策强度,证明新决策强度约简与代数约简是等价的,提出了基于该新决策强度的启发式约简算法,数值算例验证了其正确性。
将属性区分能力与差别矩阵结合起来研究,可建立差别矩阵中某属性集的可辩识属性集项数与其属性区分能力之间的关系。基于等价差别矩阵具有相同核属性和约简结果的思想,对现有差别矩阵进行改写,将基于知识量计算的方法推广到决策表情形,得到基于Hu差别矩阵知识约简和代数约简下的属性区分能力计算公式,提出一类以属性区分能力大小为启发式信息的决策表属性约简算法。该类方法的最大优点是以差别矩阵为参考但又不必通过构造差别矩阵来计算知识约简,从而巧妙避开基于差别矩阵方法的低效性问题,算法既有明显意义解释,又有坚实的理论基础。数值算例和仿真实验验证了该算法更易搜索到最优约简。同时,给出两类构造启发式算法的一般框架,为设计高效的启发式算法提供思路。
During the process of knowledge discovery, in order to solve the problem of information noise or information incompleteness, it is necessary to develop the theories and methods which can deal with imprecise and uncertain information. Rough set theory is one of important novel mathematical tool to meet those demands. The valuable and non-trivial patterns are mined by application of rough set theory and method in knowledge discovery.
Knowledge reduction is one of the fundamental contents in rough set theory. At present, many research results have been achieved, but most of them are just effective for information system without decision attributes or consistent decision table and invalid for inconsistent decision table.
For consistent decision table, the approach to knowledge reduction based on D-S evidence theory is consistent with algebraic reduction. For inconsistent decision table,the difference between generalized decision reduction based on D-S evidence theory and algebraic reduction has been illustrated by an example firstly. It is proved that generalized decision reduction is just equivalent to assignment reduction. The essential causes that algebraic reduction and generalized decision reduction obtain a different result for inconsistent decision table are analyzed. A new approach to algebraic reduction based on evidence theory is proposed by transferring the inconsistent decision table into consistent one. By establishing the relationship between positive region bases and belief function, a new approach which can obtain algebraic reduction based on D-S evidence theory is proposed and its correctness is illustrated by a numerical example.
It is proved that knowledge reduction based on decision power is equivalent to that based on conditional information entropy after knowledge reduction based on decision power discussion. From the view of conditional probability, because the mathematical models for algebraic and conditional information entropy reductions are unified formally, the reason of Consistency of their application in consistent decision table and inconsistency of their application in inconsistent decision table can be discussed. A new decision power which coincides with positive region is presented and a heuristic algorithm is proposed, which ensures to obtain an algebraic reduction, its correctness is illustrated by a numerical example.
Attribute discernibility and discernible matrix are studied to establish the relationship between attribute discernibility and the number of times in discernible matrix. Based on the thought that equivalent discernible matrix has the same attribute reduction and core, the existing discernible matrices are rewritten, and then, the method based on knowledge measurement computation is generalized to decision table. The calculation formulas of attribute discernibility for Hu's discernible matrix reduction and algebraic reduction are obtained. Accordingly, the heuristic reduction algorithms based on attribute discernibility are presented. The biggest advantage of these two algorithms is to calculate knowledge reduction without discernible matrices construction. Thus, they can avoid the low efficiency of discernible matrices. These methods have not only clear explanation but also solid theoretical foundation. Numerical examples and results of simulation experiment show that the proposed method can explore the optimal reduction more easily. At the same time, the new way to construct the high efficient heuristic reduction algorithm is given, by application of two general frameworks used to design heuristic reduction algorithm.
引文
[1]焦李成,刘芳,缑水平等.智能数据挖掘与知识发现.西安:西安电子科学技术大学出版社,2006.1-534
[2]Fayyad U M,Piatestsky-Shapiro G,Smyth P.Knowledge discovery and data mining:towards a unifying framework,in:Simoudis E,Han J W,Fayyad U M.eds.Proceedings of Second International Conference on Knowledge Discovery and DataMining(KDD-96).Menlo Park,California:AAAI Press,1996.82-88
[3]Fayyad U M,Piatestsky-Shapiro G,Smyth P.The KDD process for extracting useful knowledge from volumes of data.Communition of the ACM,1996,39(11):27-34
[4]Han J W,Kamber M.Data Mining:Concepts and Techniques.New York:Morgan Kaufmann Publisher,2000,1-14
[5]史忠植.知识发现.北京:清华大学出版社,2002.1-416
[6]Zadeh LA.Fuzzy sets.Information and Control.1965,8(3):338-353
[7]Shafer G.A mathematical theory of evidence.Princeton:Princeton University Press,1976
[8]Young V R.Fuzzy subsethood.Fuzzy Sets and Systems,1996,77(3):371-384
[9]Fan J L,Xie W X,Pei J H.Subsethood measure:new definitions.Fuzzy Sets and Systems,1999,106(2):201-209
[10]张文修,梁怡.不确定性推理原理.西安:西安交通大学出版社,1996.1-299
[11]Atanassov K.Intuitionistic fuzzy sets.Fuzzy Sets and Systems,1986,20(1):87-96
[12]Gau W L,Buehrer D J.Vague sets.IEEE Transaction on Systems,Man,and Cybernetics,1993,23(2):610-614
[13]Burillo P,Bustince H.Vague sets are intuitionistic fuzzy sets.Fuzzy Sets and Systems,1996,79(3):403-405
[14]Pawlak Z.Rough sets.International Journal of Computer and Information Science,1982,11(5):341-356
[15]Pawlak Z,Grzymala-Busse J,Slowinski R,et al.Rough sets:Communications of the ACM,1995,38(11):89-95
[16]王国胤.Rough集理论与知识获取.西安:西安交通大学出版社,2001.1-226
[17]Hu X H,Cercone N.Discovery of decision rules in relational databases:a rough set approach,in:Finin T,Labrou Y eds.Proceedings of the Third International Conference on Information and Knowledge Management(CIKM-94),Gaitherburg Maryland,USA:1994.N Y,USA:ACM Press,1994.392-400
[18]Hu X H,Cercone N.Learning in relational database:A rough set approach.International Journal of Computational Intelligence,1995,11(2):323-338
[19]侯利娟,王国胤,聂能等.粗糙集理论中的离散化问题.计算机科学,2000,27(12):89-94
[20]Nguyen S H,Skowron A.Quantization of real values attributes,rough set and boolen reasoning approaches,in:Ziarko W ed.Proceedings of the Second Joint Annual Conference on Information Science,USA:Wrightsville Beach,1995.34-37
[21]Nguyen H S.Discretization problem for rough sets methods,in:Polkwski L,Skowron A eds.Proceedings of first International Conference on Rough Sets and Current Trends in Computing(RSCTC'98).WA,Poland.1998.Berlin,Germany:Springer Verlag,1998.545-552
[22]李兴生,李德毅.一种基于云模型的决策表连续属性离散化方法.模式识别与人工智能,2003,16(1):33-38
[23]谢宏,程浩忠,牛东晓.基于信息熵的粗糙集连续属性离散化算法.计算机学报,2005,28(9):1750-1754
[24]叶明全,胡学钢.基于灰色联系度的粗糙集连续属性离散化算法.重庆邮电大学学报(自然科学版),2007,19(4):409-413
[25]Skowron A,Rauser C.The discernibility matrices and functions in information systems,in:Slowinski R ed.Intelligent Decision Support:Handbook of Applications and Advances of the Rough Sets Theory.Dordrecht:Kluwer Academic Publisher,1991.331-362
[26]Chmielewski M R,Grzymala-Busse J M.Global discretization of continuous attributes as preprocessing for machine learning.International Journal of Approximate Reasoning,1996,15(4):319-331
[27]Kim D.Data classification based on tolerant rough set.Pattern Recognition,2001,34(8):1613-1624
[28]Mssherry D.Knowledge discovery by inspection.Decision Support Systems,1997,21(1):43-37
[29]Chan C C.Rough set approach to attribute generalization in data mining.Information Science,1998,107(1-4):169-176
[30]Pawlak Z.Rough set approach to knowledge-based decision support.European Journal of Operational Research,1997,99(1):48-57
[31]Pomerol J C.Artificial intelligent and human decision making.European Journal of Operational Research,1997,99(1):3-25
[32]Pawlak Z.Rough Sets-theoretical aspects of reasoning about data.Dordrecht:Kluwer Academic Publishers,1991.1-176
[33]刘清著.Rough集及Rough推理.北京:科学出版社,2001.1-242
[34]张文修,梁怡,吴伟志著.信息系统与知识发现.北京:科学出版社,2003.1-244
[35]张文修,姚一豫,梁怡著.粗糙集与概念格.西安:西安交通大学出版社,2006.1-438
[36]梁吉业,李德玉著.信息系统中的不确定性与知识获取.北京:科学出版社,2005.1-118
[37]苗夺谦,王国胤,刘清等编著.粒计算:过去、现在与展望.北京:科学出版社.2007,1-370
[38]李道国,苗夺谦,张东星,等.粒度计算研究综述.计算机科学,2005,32(9):1-12
[39]Kryszldewicz M.Rough set approach to incomplete information systems.Information Sciences,1998,112(1-4):39-49
[40]Kryszkiewicz M.Generation of rules from incomplete information systems,in:Komorowski H J,Zytkow J M eds.Proceedings of the first European Symptom on Principles of Data Mining and Knowledge Discovery,PKDD 1997.Trondheim,Norway.1997.Berlin,Germany:Springer-Verlag,1997.156-166
[41]Stefanowski J,Tsoukias A.On the extension of rough sets under incomplete information,in:Zhong N,Skowron A,Ohsuga Seds.Proceedings of the 7~(th)International Workshop on New Directions in Rough Sets,Data Mining,and Granular-Soft Computing.Yamaguchi,Japan.1999.Berlin,Germany:Springer-Verlag,1999.73-81
[42]王国胤.Rough集理论在不完备信息系统中的扩充.计算机研究与发展,2002,39(10):1238-1243
[43]黄兵,周献中.不完备信息系统中基于联系度的粗糙集模型拓展.系统工程 理论与实践,2004,24(1):88-92
[44]Ziako W.Variable precision rough set model.Journal of Computer and System Sciences,1993,46(1):39-59
[45]Pawlak Z,Wong S M,Ziako W.Rough sets:probabilistic versus deterministic approach.International Journal of Man-Machine Studies,1988,29(1):81-95
[46]Dubois D,Prade H.Rough fuzzy sets and fuzzy rough sets.International Journal of Genaral System,1990,17(2-3):191-209
[47]Dubois D,Prade H.Putting rough sets and fuzzy sets together,in:Slowinski Red.Intelligent Decision Support:Handbook of Application and Advances of the Rough Set Theory.Dordrecht:Kluwer Academic Publishers,1992.203-232
[48]Nanda S,Majumdar S.Fuzzy rough sets.Fuzzy Sets and Systems,1992,45(2):157-160
[49]Wang J,Liu S Y,Zhang J.Roughness of a Vague set.International Journal of Computional Cognition,2005,13(3):82-86
[50]朱六兵,王迪焕,杨斌.粗糙Vague集及其相似度量.模糊系统与数学,2006,20(3):130-134
[51]Zhang Q H,Wang G Y,Hu J et al.Incomplete information systems processing based on fuzzy-clustering.In:Liu Timing,Benjamin W eds.Proceedings of 2006IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology.Hongkong,China,2006.Berlin,Germany:Springer-Verlag,2006.486-489
[52]王国胤,张清华,胡军.粒计算研究综述.智能系统学报,2007,2(6):8-26
[53]吴伟志,张文修,徐宗本.粗糙模糊集构造与公理化方法.计算机学报,2004,27(2):
[54]米椐生,吴伟志,张文修.粗糙集构造与公理化方法.模式识别与人工智能,2002,15(3):
[55]Zhang W X,Mi J S,Wu W Z.Approaches to knowledge reduction in inconsistent systems.International Journal of Intelligent Systems,2003,18(4):989-1000
[56]叶东毅,陈昭炯.不兼容决策表全部属性约简计算的一个改进方法.小型微型计算机系统,2006,27(10):1909-1913
[57]刘文军,谷云东,冯艳宾等.基于可分辨矩阵和逻辑运算的属性约简算法的改进.模式识别与人工智能,2004,17(1):119-123
[58]Wong S M,Ziarko W.On optimal decision rules in decision tables.Bulletin of Polish Academy of Sciences,1985,33(11-12):693-696
[59]Jelnek J,Krawiec K,Slowinski R.Rough set reduction of attributes and their domains for neural networks.International Journal of Computional Intelligence,1995,11(2):339-347
[60]王珏,王任,苗夺谦.基于Rough Set理论的“资料浓缩”.计算机学报,1998,21(5):393-399
[61]Hu K Y Lu Y C,Shi C Y Feature ranking in rough sets.AI Communications,2003,16(1):41-50
[62]刘少辉,盛秋戬,史忠植.一种新的快速计算正区域的方法.计算机研究与发展,2003,40(5):637-642
[63]Miao D Q,Wang J.Information-based algorithm for reduction of knowledge,in:Bazan J ed.IEEE international Conference on Intelligent Processing Systems.Beijing,China.1997.Piscataway,NJ,USA:IEEE Publisher,1997.1155-1158
[64]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
[65]苗夺谦,王珏.粗糙集理论中概念与运算的信息表示.软件学报,1999,10(2):113-116
[66]王国胤,于洪,杨大春.基于条件信息熵的决策表约简.计算机学报,2002,25(7):759-766
[67]刘启和,李凡,闵帆等.一种基于新的条件信息熵的高效知识约简算法.控制与决策,2005,20(8):878-882
[68]张海云,梁吉业,梁春华.一种基于知识量的约简算法.小型微型计算机系统,2007,28(11):1968-1971
[69]梁春华,张海云.基于知识量的决策表约简算法.山西农业大学学报(自然科学版),2007,27(2):214-217
[70]苗夺谦,范世栋.知识的粒度计算及其应用.系统工程理论与实践,2002,22(1):48-56
[71]Wang Jue,Wang Ju.Reduction Algorithms Based on Discernibility Matrix:The Ordered Attributes Method.Journal of Computer Science and Technology.2001,16(6):489-504
[72]任小康,吴尚智,马如云.基于可辩识矩阵的属性频率约简算法.兰州大学学报(自然科学版),2007,43(1):138-140
[73]卢佳华.基于属性频率函数粗糙集属性约简算法.武汉大学学报(理学版),2006,52(3):331-334
[74]徐章艳,杨炳儒,宋威.基于区分对象对集的高效属性约简算法.模式识别与人工智能,2006,19(5):
[75]叶东毅,陈昭炯.一个新的差别矩阵及其求核方法.电子学报,2002,30(7):1086-108
[76]杨明,孙志挥.改进的差别矩阵及其求核方法.复旦学报(自然科学版).2004,43(10):865-868
[77]杨明.一种基于改进差别矩阵的核增量式更新算法.计算机学报,2006,29(3):407-413
[78]王国胤.决策表核属性的计算方法.计算机学报,2003,26(5):611-615
[79]赵军,王国胤,吴中福等.一种高效的属性核计算方法.小型微型计算机系统,2003,24(11):1950-1953
[80]徐章艳,刘作鹏,杨炳儒等.一个复杂度为max(O(|C‖U|),D(|C|~2|U/C|))的快速属性约简算法.计算机学报,2006,29(3):391-399
[81]Han J C,Hu X H,Lin T Y.An efficient algorithm for computing core attributes in database systems,in:Zhong N,Ras Z W,Tsumto S,et al eds.Proceedings of 14~(th)International Symposium on Methodologies for Intelligent Systems,ISMIS 2003.Maebashi,Japan.2003.Berlin,Germany:Springer Verlag,2003.663-667
[82]Hu X H,Lin T Y,Han J C.A new rough sets model based on database systems,in:Wang G Y,Liu Q,Yao Y Y,et al eds.Proceedings of 9~(th) International Conference on Rough Sets,Fuzzy sets,Data mining and Granular Computing.Chongqing,China.2003.Berlin,Germany:Springer Verlag,2003.114-121
[83]Hu X H,Lin T Y,Han J C.A new rough sets model based on database systems.Fundamenta Informaticae,2004,59(2-3):135-152
[84]徐章艳,杨炳儒,宋威等.一个新的基于数据库技术的快速求核算法.小型微型计算机系统,2007,28(7):1302-1305
[85]刘启和,陈雷霆,闵帆等.基于数据库系统的Rough集模型扩展.控制与决策,2006,21(12):1374-1378
[86]乔梅,韩文秀.基于Rough集和数据库技术的属性约简算法.计算机工程,2005,31(6):18-20
[87]黄国顺.基于数据库系统的决策表核和属性约简算法.计算机应用,2008,28(5):1180-1182
[88]苗夺谦,王珏.粗糙集理论中知识粗糙性与信息熵关系讨论.模式识别与人工智能,1998,11(1):34-40
[89]李玉榕,乔斌,蒋静坪.粗糙集理论中不确定性的粗糙信息熵表示.计算机科学,2002,29(5):101-103
[90]Shannon C E.The mathematica theory of communication.The Bell System Technical Journal,1948,27(3-4):283-297
[91]Wierman M J.Measuring uncertainty in rough set theory.International Journal of General Systems,1999,28(4):283-297
[92]Beaubouef T,Petry F E,Arora G.Information-theoretic measures of uncertainty for rough sets and rough relational databases.Information Sciences,1998,109(1-4):185-195
[93]Beaubouef T,Petry F E.Fuzzy rough set techniques for uncertainty processing in a relational database.International Journal of Intelligent Systems,2000,15(5):389-424
[94]Zhao Jun,Wang Guoyin.Research on system uncertainty measures based on rough set.Proceeding of the RSKT2006,Chongqing,2006:227-232
[95]Wang G Y,Zhao J,An J J,et al.A comparative study of algebra viewpoint and information viewpoint in attribute reduction.Fundamenta Informaticae,2005,68(6):289-301
[96]王向阳,蔡念,杨杰等.基于近似精度和条件信息熵的粗糙集不确定性度量方法.上海交通大学学报,2006,40(7):1130-1134
[97]Liang Jiye,Wang Junhong,Qian Yuhua.A new measure of uncertainty based on knowledge granulation for rough sets.Information Sciences,2008,179:458-470
[98]何亚群,胡寿松,朱江.粗糙集中不确定性度量的修正粗糙熵方法.海军工程大学学报,2006,18(4):26-29
[99]Liang J Y,Dang C Y,Chin K S,et al.A new method for measurinf uncertainty and fuzziness in rough set theory.International Journal of General Systems,2002,31 (4):331-342
[100]徐章艳,杨炳儒,宋威等.差别矩阵属性约简的信息观解释.计算机科学,2007,34(9):191-193
[101]Liang J Y,Shi Z Z.The information entropy,rough entropy and knowledge granulation in rough set theory.International Journal of Uncertainty,Fuzziness and Knowledge-based Systems,2004,19(1):37-46
[102]梁吉业,李德玉.信息系统中的不确定性与知识获取.北京:科学出版社,2005.1-118
[103]Liu X C.Entropy,distance measure and similarity measure of fuzzy sets and their relations.Fuzzy Sets and Systems,1992,52(3):305-318
[104]王国胤,张清华.不同知识粒度下粗糙集的不确定性研究.计算机学报,2008,30(9):1587-1598
[105]徐燕,怀进鹏,王兆其.基于区分能力大小的启发式约简算法及其应用.计算机学报,2003,26(1):97-103
[106]陈堂敏.基于区分能力大小的启发式约简算法的研究.计算机学报,2006,29(3):480-487
[107]梁吉业,徐宗本,李月香.包含度与粗糙集资料分析中的度量.计算机学报,2001,24(5):544-547
[108]Liang J Y,Shi Z Z,Li D Y.Application of inclusion degree in rough set theory.International Journal of Computional Cognition,2003,1(2):67-78
[109]Xu Z B,Liang J Y.Dang C Y,et al.Inclusion degree:a perspective on measures for rough set data analysis.Information Sciences,2002,141(3-4):227-236
[110]Qiu G F,Li H Z,Xu L D,et al.A knowledge processing method for intelligent systems based on inclusion degree.Expert Systems,2003,20(4):187-195
[111]Zhang M,Xu L D,Zhang W X,et al.A rough approach to knowledge reduction based on inclusion degree and evidence reasoning theory.Expert Systems,2003,20(5):298-304
[112]张文修,米据生,吴伟志.不协调目标信息系统的知识约简.计算机学报,2003,26(1):12-18
[113]Kryszkiewicz M.Comparative study of alternative types of knowledge reduction in inconsistent systems.International Journal of Intelligent Systems,2001,16(1):105-120
[114]Wang G Y.Rough reduction in algebra view and information view.International Journal of Intelligent Systems,2003,18(6):679-688
[115]Wang G Y.Algebra view and information view of rough sets theory,in:Dasarthy ed.Proceedings of Data Mining and Knowledge Discovery:Theory,Tools and Technology Ⅲ,Orlando,USA.2001.Bellingham WA:SPIE,2001.200-207
[116]袁修久,张文修.决策表的分布约简和严凸函数下约简的等价性.系统工程,2003,21(5):5-7
[117]王国胤,安久江,吴渝.Rough集理论代数观与信息观的差异量化分析.小型微型计算机系统,2005,26(7):1187-1190
[118]黄国顺,刘云生.不一致决策表信息熵约简与代数约简的核计算与转化.小型微型计算机系统,2008,29(2):308-312
[119]黄国顺,刘云生.不一致决策表各种属性约简的不一致性分析与转化.小型微型计算机系统,2008,29(4):703-708
[120]徐章艳,杨炳儒,宋威,等.几种不同属性约简的比较研究.小型微型计算机系统,2008,299(5):848-853
[121]蒋思宇,卢炎生.两种新的决策表属性约简概念.小型微型计算机系统,2006,27(3):512-515
[122]徐章艳,宋威,杨炳儒,等.关于“两种新的决策表属性约简概念”的注记.小型微型计算机系统,2007,28(9):1686-1689
[123]徐久成,孙林,马媛媛.决策强度的决策表约简设计与比较.微计算机应用,2007,28(8):791-796
[124]Qian Yuhua,Liang Jiye,Li Deyu et al.Measures for evaluating the decision performance of a decision table in rough set theory.Information Sciences,2008,178:181-202
[125]Wu W Z,Zhang M,Li H Z,et al.Knowledge reduction in random information systems via Dempster-Shafer theory of evidence.Information Sciences,2005,174(3-4):143-164
[126]Golan R,Ziako W.Methodology for stock market analysis utilizing rough set theory,in:Anon ed.Proceedings of IEEE/IAFE Conference on Computational Intelligence for Financial Engineering,New Work,NY,USA.1995.Piscataway,NJ,USA:IEEE Press,1995.32-40
[127]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
[128]Tsumoto S.Modeling medical diagnostic rules based on rough sets.in:Polkowski L,Skowron A eds.Proceedings of The First International Conference on Rough Sets and Current Trends in Computing.Warsaw,Poland.1998.Berlin,Germany:Springer-Vedag,1998.475-482
[129]Chen Y Q,Gao W,Zhu T S.Learning prosodic patterns for mandarin speech synthesis.Journal of Intelligent Information Systems,2002,19(1):95-109
[130]Kim D J,Bang S Y.A handwritten numeral character classification using tolerant rough set.IEEE Transactions on Pattem Analysis and Machine Intelligence,2000,22(9):923-937
[131]Pawlak Z,Slowinski R.Rough set approach to multi-attribute decision analysis.European Journal of Operational Reasearch.1994,72(3):443-459
[132]Xu Y T,Wang L S.Fault diagnosis system based on rough set theory and support vector machine,in:Wang L P,Jin Y C eds.Proceedings of Second International Conference on Fuzzy Systems and Knowledge Discovery,FSKD 2005,Changsa,China.2005.Berlin,Germany:Springer-Vedag,2005.980-988
[133]Peters J F,Skowron A,Suraj Z.Application of rough set methods in control design.Fundamenta Informaticae,2000,43(1):269-290
[134]He M,Feng B Q.Intelligent information retrieval based on the variable precision rough set model and fuzzy sets.in:Slezak D,Wang G Y,Szczuka M S,et al eds.Proceedings of 10~(th) International Conference on Rough Sets,Fuzzy Sets,Data Mining and Granular Computing(RSFDGrC2005),Regina,Canada.2005.Berlin,Germany:Springer-Vedag,2005.184-192
[135]Komorowski J.ROSETTA:A rough set toolkit for analysis of data.in:Wang P.ed.Proceedings of the Third International Joint Conference on Informationa Sciences.San Jose,California,USA.1997.North Carolina,USA:Durham,1997.403-407
[136]Grzymal-Busse J.New version of the rule induction system LERS.Fundamenta informaticae,1997,31(1):27-39
[137]Ziarko W,Shan N.KDD-R:A comprehensive system for knowledge discovery in database using rough set.in:Lin T Y,Wildberger A Meds.Proceedings of the International Workshop on Rough sets and Soft Computing.San Jose,CA,USA.1995.San Diego,CA,USA:Simulation Counciles,1995.298-301
[138]BlakeC L,Merz C J.UCI Repository of Machine Learning Databases,University of Califonia at Irvine,1998,http://www.ics.uci.edu/～mleam/MLRepositioy.html
[139]王彪.粗糙集与模糊集的应用研究.北京:电子工业出版社,2008.1-199
[140]刘映杰,马德义,夏春水.粗糙集理论及其在图像处理中的应用.计算机应用研究,2007(04):201-205
[141]孙秋野,黎明.粗糙集理论及其电力行业应用.北京:机械工业出版社,2009.1-258
[142]苗守谦,李道国.粗糙集理论、算法与应用.北京:清华大学出版社,2008.205-326
[143]李凡,刘启和,叶茂等.不一致决策表的知识约简方法研究.控制与决策,2006,21(8):857-862
[144]刘少辉,盛秋戬,吴斌等.Rough集高效算法的研究.计算机学报,2003,26(5):524-529
[145]刘启和,李凡,颜俊华等.三种差别矩阵的比较.计算机科学,2005,32(11):166-169
[146]徐章艳,杨炳儒,宋威等.一种快速计算HU差别矩阵的属性约简算法,小型微型计算机系统,2008,29(10):1820-1827
[147]李龙星,运士伟,杨炳儒.粗糙集概念与运算的布尔矩阵表示.计算机工程,2005,31(14):16-17
[148]李龙星,运士伟,杨炳儒.基于布尔矩阵表示的粗集属性约简启发式算法.计算机工程,2007,33(10):205-206
[149]赵敏,罗可,秦哲.基于粒计算的属性约简算法.计算机工程与应用,2008,44(30):157-159
[150]胡清华,于达仁,谢宗霞.基于邻域粒化和粗糙逼近的数值属性约简.软件学报,2008,19(3):640-649
[151]任志刚,冯祖仁,柯良军.蚁群优化属性约简算法.西安交通大学学报,2008,42(4):440-444
[2]Fayyad U M,Piatestsky-Shapiro G,Smyth P.Knowledge discovery and data mining:towards a unifying framework,in:Simoudis E,Han J W,Fayyad U M.eds.Proceedings of Second International Conference on Knowledge Discovery and DataMining(KDD-96).Menlo Park,California:AAAI Press,1996.82-88
[3]Fayyad U M,Piatestsky-Shapiro G,Smyth P.The KDD process for extracting useful knowledge from volumes of data.Communition of the ACM,1996,39(11):27-34
[4]Han J W,Kamber M.Data Mining:Concepts and Techniques.New York:Morgan Kaufmann Publisher,2000,1-14
[5]史忠植.知识发现.北京:清华大学出版社,2002.1-416
[6]Zadeh LA.Fuzzy sets.Information and Control.1965,8(3):338-353
[7]Shafer G.A mathematical theory of evidence.Princeton:Princeton University Press,1976
[8]Young V R.Fuzzy subsethood.Fuzzy Sets and Systems,1996,77(3):371-384
[9]Fan J L,Xie W X,Pei J H.Subsethood measure:new definitions.Fuzzy Sets and Systems,1999,106(2):201-209
[10]张文修,梁怡.不确定性推理原理.西安:西安交通大学出版社,1996.1-299
[11]Atanassov K.Intuitionistic fuzzy sets.Fuzzy Sets and Systems,1986,20(1):87-96
[12]Gau W L,Buehrer D J.Vague sets.IEEE Transaction on Systems,Man,and Cybernetics,1993,23(2):610-614
[13]Burillo P,Bustince H.Vague sets are intuitionistic fuzzy sets.Fuzzy Sets and Systems,1996,79(3):403-405
[14]Pawlak Z.Rough sets.International Journal of Computer and Information Science,1982,11(5):341-356
[15]Pawlak Z,Grzymala-Busse J,Slowinski R,et al.Rough sets:Communications of the ACM,1995,38(11):89-95
[16]王国胤.Rough集理论与知识获取.西安:西安交通大学出版社,2001.1-226
[17]Hu X H,Cercone N.Discovery of decision rules in relational databases:a rough set approach,in:Finin T,Labrou Y eds.Proceedings of the Third International Conference on Information and Knowledge Management(CIKM-94),Gaitherburg Maryland,USA:1994.N Y,USA:ACM Press,1994.392-400
[18]Hu X H,Cercone N.Learning in relational database:A rough set approach.International Journal of Computational Intelligence,1995,11(2):323-338
[19]侯利娟,王国胤,聂能等.粗糙集理论中的离散化问题.计算机科学,2000,27(12):89-94
[20]Nguyen S H,Skowron A.Quantization of real values attributes,rough set and boolen reasoning approaches,in:Ziarko W ed.Proceedings of the Second Joint Annual Conference on Information Science,USA:Wrightsville Beach,1995.34-37
[21]Nguyen H S.Discretization problem for rough sets methods,in:Polkwski L,Skowron A eds.Proceedings of first International Conference on Rough Sets and Current Trends in Computing(RSCTC'98).WA,Poland.1998.Berlin,Germany:Springer Verlag,1998.545-552
[22]李兴生,李德毅.一种基于云模型的决策表连续属性离散化方法.模式识别与人工智能,2003,16(1):33-38
[23]谢宏,程浩忠,牛东晓.基于信息熵的粗糙集连续属性离散化算法.计算机学报,2005,28(9):1750-1754
[24]叶明全,胡学钢.基于灰色联系度的粗糙集连续属性离散化算法.重庆邮电大学学报(自然科学版),2007,19(4):409-413
[25]Skowron A,Rauser C.The discernibility matrices and functions in information systems,in:Slowinski R ed.Intelligent Decision Support:Handbook of Applications and Advances of the Rough Sets Theory.Dordrecht:Kluwer Academic Publisher,1991.331-362
[26]Chmielewski M R,Grzymala-Busse J M.Global discretization of continuous attributes as preprocessing for machine learning.International Journal of Approximate Reasoning,1996,15(4):319-331
[27]Kim D.Data classification based on tolerant rough set.Pattern Recognition,2001,34(8):1613-1624
[28]Mssherry D.Knowledge discovery by inspection.Decision Support Systems,1997,21(1):43-37
[29]Chan C C.Rough set approach to attribute generalization in data mining.Information Science,1998,107(1-4):169-176
[30]Pawlak Z.Rough set approach to knowledge-based decision support.European Journal of Operational Research,1997,99(1):48-57
[31]Pomerol J C.Artificial intelligent and human decision making.European Journal of Operational Research,1997,99(1):3-25
[32]Pawlak Z.Rough Sets-theoretical aspects of reasoning about data.Dordrecht:Kluwer Academic Publishers,1991.1-176
[33]刘清著.Rough集及Rough推理.北京:科学出版社,2001.1-242
[34]张文修,梁怡,吴伟志著.信息系统与知识发现.北京:科学出版社,2003.1-244
[35]张文修,姚一豫,梁怡著.粗糙集与概念格.西安:西安交通大学出版社,2006.1-438
[36]梁吉业,李德玉著.信息系统中的不确定性与知识获取.北京:科学出版社,2005.1-118
[37]苗夺谦,王国胤,刘清等编著.粒计算:过去、现在与展望.北京:科学出版社.2007,1-370
[38]李道国,苗夺谦,张东星,等.粒度计算研究综述.计算机科学,2005,32(9):1-12
[39]Kryszldewicz M.Rough set approach to incomplete information systems.Information Sciences,1998,112(1-4):39-49
[40]Kryszkiewicz M.Generation of rules from incomplete information systems,in:Komorowski H J,Zytkow J M eds.Proceedings of the first European Symptom on Principles of Data Mining and Knowledge Discovery,PKDD 1997.Trondheim,Norway.1997.Berlin,Germany:Springer-Verlag,1997.156-166
[41]Stefanowski J,Tsoukias A.On the extension of rough sets under incomplete information,in:Zhong N,Skowron A,Ohsuga Seds.Proceedings of the 7~(th)International Workshop on New Directions in Rough Sets,Data Mining,and Granular-Soft Computing.Yamaguchi,Japan.1999.Berlin,Germany:Springer-Verlag,1999.73-81
[42]王国胤.Rough集理论在不完备信息系统中的扩充.计算机研究与发展,2002,39(10):1238-1243
[43]黄兵,周献中.不完备信息系统中基于联系度的粗糙集模型拓展.系统工程 理论与实践,2004,24(1):88-92
[44]Ziako W.Variable precision rough set model.Journal of Computer and System Sciences,1993,46(1):39-59
[45]Pawlak Z,Wong S M,Ziako W.Rough sets:probabilistic versus deterministic approach.International Journal of Man-Machine Studies,1988,29(1):81-95
[46]Dubois D,Prade H.Rough fuzzy sets and fuzzy rough sets.International Journal of Genaral System,1990,17(2-3):191-209
[47]Dubois D,Prade H.Putting rough sets and fuzzy sets together,in:Slowinski Red.Intelligent Decision Support:Handbook of Application and Advances of the Rough Set Theory.Dordrecht:Kluwer Academic Publishers,1992.203-232
[48]Nanda S,Majumdar S.Fuzzy rough sets.Fuzzy Sets and Systems,1992,45(2):157-160
[49]Wang J,Liu S Y,Zhang J.Roughness of a Vague set.International Journal of Computional Cognition,2005,13(3):82-86
[50]朱六兵,王迪焕,杨斌.粗糙Vague集及其相似度量.模糊系统与数学,2006,20(3):130-134
[51]Zhang Q H,Wang G Y,Hu J et al.Incomplete information systems processing based on fuzzy-clustering.In:Liu Timing,Benjamin W eds.Proceedings of 2006IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology.Hongkong,China,2006.Berlin,Germany:Springer-Verlag,2006.486-489
[52]王国胤,张清华,胡军.粒计算研究综述.智能系统学报,2007,2(6):8-26
[53]吴伟志,张文修,徐宗本.粗糙模糊集构造与公理化方法.计算机学报,2004,27(2):
[54]米椐生,吴伟志,张文修.粗糙集构造与公理化方法.模式识别与人工智能,2002,15(3):
[55]Zhang W X,Mi J S,Wu W Z.Approaches to knowledge reduction in inconsistent systems.International Journal of Intelligent Systems,2003,18(4):989-1000
[56]叶东毅,陈昭炯.不兼容决策表全部属性约简计算的一个改进方法.小型微型计算机系统,2006,27(10):1909-1913
[57]刘文军,谷云东,冯艳宾等.基于可分辨矩阵和逻辑运算的属性约简算法的改进.模式识别与人工智能,2004,17(1):119-123
[58]Wong S M,Ziarko W.On optimal decision rules in decision tables.Bulletin of Polish Academy of Sciences,1985,33(11-12):693-696
[59]Jelnek J,Krawiec K,Slowinski R.Rough set reduction of attributes and their domains for neural networks.International Journal of Computional Intelligence,1995,11(2):339-347
[60]王珏,王任,苗夺谦.基于Rough Set理论的“资料浓缩”.计算机学报,1998,21(5):393-399
[61]Hu K Y Lu Y C,Shi C Y Feature ranking in rough sets.AI Communications,2003,16(1):41-50
[62]刘少辉,盛秋戬,史忠植.一种新的快速计算正区域的方法.计算机研究与发展,2003,40(5):637-642
[63]Miao D Q,Wang J.Information-based algorithm for reduction of knowledge,in:Bazan J ed.IEEE international Conference on Intelligent Processing Systems.Beijing,China.1997.Piscataway,NJ,USA:IEEE Publisher,1997.1155-1158
[64]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
[65]苗夺谦,王珏.粗糙集理论中概念与运算的信息表示.软件学报,1999,10(2):113-116
[66]王国胤,于洪,杨大春.基于条件信息熵的决策表约简.计算机学报,2002,25(7):759-766
[67]刘启和,李凡,闵帆等.一种基于新的条件信息熵的高效知识约简算法.控制与决策,2005,20(8):878-882
[68]张海云,梁吉业,梁春华.一种基于知识量的约简算法.小型微型计算机系统,2007,28(11):1968-1971
[69]梁春华,张海云.基于知识量的决策表约简算法.山西农业大学学报(自然科学版),2007,27(2):214-217
[70]苗夺谦,范世栋.知识的粒度计算及其应用.系统工程理论与实践,2002,22(1):48-56
[71]Wang Jue,Wang Ju.Reduction Algorithms Based on Discernibility Matrix:The Ordered Attributes Method.Journal of Computer Science and Technology.2001,16(6):489-504
[72]任小康,吴尚智,马如云.基于可辩识矩阵的属性频率约简算法.兰州大学学报(自然科学版),2007,43(1):138-140
[73]卢佳华.基于属性频率函数粗糙集属性约简算法.武汉大学学报(理学版),2006,52(3):331-334
[74]徐章艳,杨炳儒,宋威.基于区分对象对集的高效属性约简算法.模式识别与人工智能,2006,19(5):
[75]叶东毅,陈昭炯.一个新的差别矩阵及其求核方法.电子学报,2002,30(7):1086-108
[76]杨明,孙志挥.改进的差别矩阵及其求核方法.复旦学报(自然科学版).2004,43(10):865-868
[77]杨明.一种基于改进差别矩阵的核增量式更新算法.计算机学报,2006,29(3):407-413
[78]王国胤.决策表核属性的计算方法.计算机学报,2003,26(5):611-615
[79]赵军,王国胤,吴中福等.一种高效的属性核计算方法.小型微型计算机系统,2003,24(11):1950-1953
[80]徐章艳,刘作鹏,杨炳儒等.一个复杂度为max(O(|C‖U|),D(|C|~2|U/C|))的快速属性约简算法.计算机学报,2006,29(3):391-399
[81]Han J C,Hu X H,Lin T Y.An efficient algorithm for computing core attributes in database systems,in:Zhong N,Ras Z W,Tsumto S,et al eds.Proceedings of 14~(th)International Symposium on Methodologies for Intelligent Systems,ISMIS 2003.Maebashi,Japan.2003.Berlin,Germany:Springer Verlag,2003.663-667
[82]Hu X H,Lin T Y,Han J C.A new rough sets model based on database systems,in:Wang G Y,Liu Q,Yao Y Y,et al eds.Proceedings of 9~(th) International Conference on Rough Sets,Fuzzy sets,Data mining and Granular Computing.Chongqing,China.2003.Berlin,Germany:Springer Verlag,2003.114-121
[83]Hu X H,Lin T Y,Han J C.A new rough sets model based on database systems.Fundamenta Informaticae,2004,59(2-3):135-152
[84]徐章艳,杨炳儒,宋威等.一个新的基于数据库技术的快速求核算法.小型微型计算机系统,2007,28(7):1302-1305
[85]刘启和,陈雷霆,闵帆等.基于数据库系统的Rough集模型扩展.控制与决策,2006,21(12):1374-1378
[86]乔梅,韩文秀.基于Rough集和数据库技术的属性约简算法.计算机工程,2005,31(6):18-20
[87]黄国顺.基于数据库系统的决策表核和属性约简算法.计算机应用,2008,28(5):1180-1182
[88]苗夺谦,王珏.粗糙集理论中知识粗糙性与信息熵关系讨论.模式识别与人工智能,1998,11(1):34-40
[89]李玉榕,乔斌,蒋静坪.粗糙集理论中不确定性的粗糙信息熵表示.计算机科学,2002,29(5):101-103
[90]Shannon C E.The mathematica theory of communication.The Bell System Technical Journal,1948,27(3-4):283-297
[91]Wierman M J.Measuring uncertainty in rough set theory.International Journal of General Systems,1999,28(4):283-297
[92]Beaubouef T,Petry F E,Arora G.Information-theoretic measures of uncertainty for rough sets and rough relational databases.Information Sciences,1998,109(1-4):185-195
[93]Beaubouef T,Petry F E.Fuzzy rough set techniques for uncertainty processing in a relational database.International Journal of Intelligent Systems,2000,15(5):389-424
[94]Zhao Jun,Wang Guoyin.Research on system uncertainty measures based on rough set.Proceeding of the RSKT2006,Chongqing,2006:227-232
[95]Wang G Y,Zhao J,An J J,et al.A comparative study of algebra viewpoint and information viewpoint in attribute reduction.Fundamenta Informaticae,2005,68(6):289-301
[96]王向阳,蔡念,杨杰等.基于近似精度和条件信息熵的粗糙集不确定性度量方法.上海交通大学学报,2006,40(7):1130-1134
[97]Liang Jiye,Wang Junhong,Qian Yuhua.A new measure of uncertainty based on knowledge granulation for rough sets.Information Sciences,2008,179:458-470
[98]何亚群,胡寿松,朱江.粗糙集中不确定性度量的修正粗糙熵方法.海军工程大学学报,2006,18(4):26-29
[99]Liang J Y,Dang C Y,Chin K S,et al.A new method for measurinf uncertainty and fuzziness in rough set theory.International Journal of General Systems,2002,31 (4):331-342
[100]徐章艳,杨炳儒,宋威等.差别矩阵属性约简的信息观解释.计算机科学,2007,34(9):191-193
[101]Liang J Y,Shi Z Z.The information entropy,rough entropy and knowledge granulation in rough set theory.International Journal of Uncertainty,Fuzziness and Knowledge-based Systems,2004,19(1):37-46
[102]梁吉业,李德玉.信息系统中的不确定性与知识获取.北京:科学出版社,2005.1-118
[103]Liu X C.Entropy,distance measure and similarity measure of fuzzy sets and their relations.Fuzzy Sets and Systems,1992,52(3):305-318
[104]王国胤,张清华.不同知识粒度下粗糙集的不确定性研究.计算机学报,2008,30(9):1587-1598
[105]徐燕,怀进鹏,王兆其.基于区分能力大小的启发式约简算法及其应用.计算机学报,2003,26(1):97-103
[106]陈堂敏.基于区分能力大小的启发式约简算法的研究.计算机学报,2006,29(3):480-487
[107]梁吉业,徐宗本,李月香.包含度与粗糙集资料分析中的度量.计算机学报,2001,24(5):544-547
[108]Liang J Y,Shi Z Z,Li D Y.Application of inclusion degree in rough set theory.International Journal of Computional Cognition,2003,1(2):67-78
[109]Xu Z B,Liang J Y.Dang C Y,et al.Inclusion degree:a perspective on measures for rough set data analysis.Information Sciences,2002,141(3-4):227-236
[110]Qiu G F,Li H Z,Xu L D,et al.A knowledge processing method for intelligent systems based on inclusion degree.Expert Systems,2003,20(4):187-195
[111]Zhang M,Xu L D,Zhang W X,et al.A rough approach to knowledge reduction based on inclusion degree and evidence reasoning theory.Expert Systems,2003,20(5):298-304
[112]张文修,米据生,吴伟志.不协调目标信息系统的知识约简.计算机学报,2003,26(1):12-18
[113]Kryszkiewicz M.Comparative study of alternative types of knowledge reduction in inconsistent systems.International Journal of Intelligent Systems,2001,16(1):105-120
[114]Wang G Y.Rough reduction in algebra view and information view.International Journal of Intelligent Systems,2003,18(6):679-688
[115]Wang G Y.Algebra view and information view of rough sets theory,in:Dasarthy ed.Proceedings of Data Mining and Knowledge Discovery:Theory,Tools and Technology Ⅲ,Orlando,USA.2001.Bellingham WA:SPIE,2001.200-207
[116]袁修久,张文修.决策表的分布约简和严凸函数下约简的等价性.系统工程,2003,21(5):5-7
[117]王国胤,安久江,吴渝.Rough集理论代数观与信息观的差异量化分析.小型微型计算机系统,2005,26(7):1187-1190
[118]黄国顺,刘云生.不一致决策表信息熵约简与代数约简的核计算与转化.小型微型计算机系统,2008,29(2):308-312
[119]黄国顺,刘云生.不一致决策表各种属性约简的不一致性分析与转化.小型微型计算机系统,2008,29(4):703-708
[120]徐章艳,杨炳儒,宋威,等.几种不同属性约简的比较研究.小型微型计算机系统,2008,299(5):848-853
[121]蒋思宇,卢炎生.两种新的决策表属性约简概念.小型微型计算机系统,2006,27(3):512-515
[122]徐章艳,宋威,杨炳儒,等.关于“两种新的决策表属性约简概念”的注记.小型微型计算机系统,2007,28(9):1686-1689
[123]徐久成,孙林,马媛媛.决策强度的决策表约简设计与比较.微计算机应用,2007,28(8):791-796
[124]Qian Yuhua,Liang Jiye,Li Deyu et al.Measures for evaluating the decision performance of a decision table in rough set theory.Information Sciences,2008,178:181-202
[125]Wu W Z,Zhang M,Li H Z,et al.Knowledge reduction in random information systems via Dempster-Shafer theory of evidence.Information Sciences,2005,174(3-4):143-164
[126]Golan R,Ziako W.Methodology for stock market analysis utilizing rough set theory,in:Anon ed.Proceedings of IEEE/IAFE Conference on Computational Intelligence for Financial Engineering,New Work,NY,USA.1995.Piscataway,NJ,USA:IEEE Press,1995.32-40
[127]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
[128]Tsumoto S.Modeling medical diagnostic rules based on rough sets.in:Polkowski L,Skowron A eds.Proceedings of The First International Conference on Rough Sets and Current Trends in Computing.Warsaw,Poland.1998.Berlin,Germany:Springer-Vedag,1998.475-482
[129]Chen Y Q,Gao W,Zhu T S.Learning prosodic patterns for mandarin speech synthesis.Journal of Intelligent Information Systems,2002,19(1):95-109
[130]Kim D J,Bang S Y.A handwritten numeral character classification using tolerant rough set.IEEE Transactions on Pattem Analysis and Machine Intelligence,2000,22(9):923-937
[131]Pawlak Z,Slowinski R.Rough set approach to multi-attribute decision analysis.European Journal of Operational Reasearch.1994,72(3):443-459
[132]Xu Y T,Wang L S.Fault diagnosis system based on rough set theory and support vector machine,in:Wang L P,Jin Y C eds.Proceedings of Second International Conference on Fuzzy Systems and Knowledge Discovery,FSKD 2005,Changsa,China.2005.Berlin,Germany:Springer-Vedag,2005.980-988
[133]Peters J F,Skowron A,Suraj Z.Application of rough set methods in control design.Fundamenta Informaticae,2000,43(1):269-290
[134]He M,Feng B Q.Intelligent information retrieval based on the variable precision rough set model and fuzzy sets.in:Slezak D,Wang G Y,Szczuka M S,et al eds.Proceedings of 10~(th) International Conference on Rough Sets,Fuzzy Sets,Data Mining and Granular Computing(RSFDGrC2005),Regina,Canada.2005.Berlin,Germany:Springer-Vedag,2005.184-192
[135]Komorowski J.ROSETTA:A rough set toolkit for analysis of data.in:Wang P.ed.Proceedings of the Third International Joint Conference on Informationa Sciences.San Jose,California,USA.1997.North Carolina,USA:Durham,1997.403-407
[136]Grzymal-Busse J.New version of the rule induction system LERS.Fundamenta informaticae,1997,31(1):27-39
[137]Ziarko W,Shan N.KDD-R:A comprehensive system for knowledge discovery in database using rough set.in:Lin T Y,Wildberger A Meds.Proceedings of the International Workshop on Rough sets and Soft Computing.San Jose,CA,USA.1995.San Diego,CA,USA:Simulation Counciles,1995.298-301
[138]BlakeC L,Merz C J.UCI Repository of Machine Learning Databases,University of Califonia at Irvine,1998,http://www.ics.uci.edu/～mleam/MLRepositioy.html
[139]王彪.粗糙集与模糊集的应用研究.北京:电子工业出版社,2008.1-199
[140]刘映杰,马德义,夏春水.粗糙集理论及其在图像处理中的应用.计算机应用研究,2007(04):201-205
[141]孙秋野,黎明.粗糙集理论及其电力行业应用.北京:机械工业出版社,2009.1-258
[142]苗守谦,李道国.粗糙集理论、算法与应用.北京:清华大学出版社,2008.205-326
[143]李凡,刘启和,叶茂等.不一致决策表的知识约简方法研究.控制与决策,2006,21(8):857-862
[144]刘少辉,盛秋戬,吴斌等.Rough集高效算法的研究.计算机学报,2003,26(5):524-529
[145]刘启和,李凡,颜俊华等.三种差别矩阵的比较.计算机科学,2005,32(11):166-169
[146]徐章艳,杨炳儒,宋威等.一种快速计算HU差别矩阵的属性约简算法,小型微型计算机系统,2008,29(10):1820-1827
[147]李龙星,运士伟,杨炳儒.粗糙集概念与运算的布尔矩阵表示.计算机工程,2005,31(14):16-17
[148]李龙星,运士伟,杨炳儒.基于布尔矩阵表示的粗集属性约简启发式算法.计算机工程,2007,33(10):205-206
[149]赵敏,罗可,秦哲.基于粒计算的属性约简算法.计算机工程与应用,2008,44(30):157-159
[150]胡清华,于达仁,谢宗霞.基于邻域粒化和粗糙逼近的数值属性约简.软件学报,2008,19(3):640-649
[151]任志刚,冯祖仁,柯良军.蚁群优化属性约简算法.西安交通大学学报,2008,42(4):440-444