一种面向缺失数据的信息熵和知识粒度
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摘要
针对含有缺失数据的数据集的不确定性度量问题,分别给出了信息熵和知识粒度的公理化定义,并提出了该环境下的粗糙集的两种不确定性度量,证明了精度是一种信息熵,粗糙度是一种知识粒度,并得出了几个较好的性质,进一步克服了已有缺失数据集不确定性度量的部分局限性,实例验证了不确定性度量的有效性,且适合度量含缺失数据的粗糙集的模糊性和精确性。
For the uncertainty measurement problem with missing data,an axiomatic definition of information entropy and knowledge granularity is given,and two ancertainty measwres ment approaehes are presented.It is proved that the precision is a kind of information entropy,and then some properties of entropy measurement are deduced.The new measurements are validated that they can overcome the limitations of existing uncertainty measurement,and they can be used to measure the accuracy and roughness of the rough set in incomplete information system.
For the uncertainty measurement problem with missing data,an axiomatic definition of information entropy and knowledge granularity is given,and two ancertainty measwres ment approaehes are presented.It is proved that the precision is a kind of information entropy,and then some properties of entropy measurement are deduced.The new measurements are validated that they can overcome the limitations of existing uncertainty measurement,and they can be used to measure the accuracy and roughness of the rough set in incomplete information system.
引文
[1]Shannon C E.The Mathematical Theory of Communication[J].The Bell System Technical Journal,1948,27(3-4):373-423.
[2]Wierman M J.Measuring Uncertainty in Rough Set Theory[J].International Journal of General Systems,1999,28(4):283-297.
[3]Hartley R V L.Transmission of Information[J].The Bell Systems Technical Journal,1928,7(3):535-563.
[4]苗夺谦,王珏.粗糙集理论中概念与运算的信息表示[J].软件学报,1999,10(2):113-116.
[5]Yao Y Y.Information Granulation and Rough Set Approximation[J].Internation Journal of Intelligent Systems,2001,16(1):87-104.DOI:10.1002/1098-111X.
[6]王国胤,于洪,杨大春.基于条件信息熵的决策表约简[J].计算机学报,2002,25(7):759-766.
[7]Liang J Y,Chin K S,Dang C Y,et al.A New Method for Measuring Uncertainty and Fuzziness in Rough Set Rheory[J].International Journal of General Systems,2002,31(4):331-342.DOI:http:∥dx.doi.org/10.108010308107021000013635.
[8]Liang J Y,Shi Z Z.The Information Entropy,Rough Entropy and Knowledge Granulation in Rough Set Theory[J].International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems,2004,12(1):37-46.DOI:10.1142/S0218488504002631.
[9]Liang J Y,Li D Y.Uncertainty and Knowledge Acquisition in Information System[M].Beijing:Science Press(in Chinese),2005.
[10]Beaubouef T,Petry F E,Arora G.Information-theoretic Measures of Uncertainty for Rough Sets and Rough Relational Databases[J].Information Sciences,1998,109(48):185-195.
[11]Pawlak Z.Rough Sets[J].International Journal of Computer and Information Sciences,1982,11(5):341-356.
[12]梁吉业,李德玉.信息系统中的不确定性与知识获取[M].北京:科学出版社,2005.
[13]GU S M,WU W Z.Knowledge Acquisition in Inconsistent Multi-scale Decision Systems[C]∥YAO J T,RAMANNA S,WANG G Y,et al.eds.Lecture Notes in Computer Science.Berlin,Germany:Springer,2011,6954:669-678.DOI:10.1007/978-3-642-24425-4_84.
[14]GU S M,WU W Z.On Knowledge Acquisition in Multi-scale Decision Systems[J].International Journal of Machine Learning and Cybernetics,2013,4(5):477-486.DOI:10.1007/s13042-012-0115-7.
[15]解滨,米据生,张军鹏.粗糙集不确定性度量的矩阵运算[J].计算机工程与应用,2011,47(29):42-45.
[16]刘财辉,苗夺谦,岳晓冬,等.知识不确定性度量及其关系研究[J].计算机科学,2014,41(3):66-70.DOI:1002-137X.2014.03.013.
[17]滕书华,卢敏,杨阿锋,等.基于一般二元关系的粗糙集加权不确定性度量[J].计算机学报,2014,37(3):649-665.
[18]吴伟志,陈颖,徐优红,等.协调的非完备多粒度标记决策系统的最优粒度选择[J].模式识别与人工智能,2016,29(2):108-115.
[19]Zadeh L A.Fuzzy Sets and Information Granularity[J].Advances in Fuzzy Set Theory and Application.Amsterdam:North-Holland,1979:3-18.DOI:10.1142/9789814261302_0022.
[20]Liang J Y,Shi Z Z.Information Entropy,Rough Entropy and Knowledge Granulation in Incomplete Information Systems[J].International Journal of General systems,2006,35(6):641-654.DOI:10.1080/03081070600687668.
[21]钱宇华,梁吉业,王锋.面向非完备决策表的正向近似特征选择加速算法[J].计算机学报,2011,34(3):435-442.DOI:10.3724/SP.J.1016.2011.00435.
[22]王锋,魏巍.缺失数据数据集的组增量式特征选择[J].计算机科学,2015,42(7):285-290.DOI:10.11896/j.issn.1002-137X.2015.07.061.
[23]Wang J H,Liang J Y,Qian Y H,et al.Uncertainty Measure of Rough Sets Based on Aknowledge Granulation for Incomplete Information Systems[J].International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems,2008,16(2):233-244.DOI:10.1142/S0218488508005157.
[24]Pawlak Z,Skowron A.Rudiments of Rough Sets[J].Information Sciences,2007,177(1):3-27.DOI:10.1016/j.ins.2006.06.003.
[25]Qian Y H,Liang J Y.Combination Entropy and Combination Granulation in Incomplete Information System[J].Lect Notes Artif Intel,2006,4062:184-190.DOI:10.1007/11795131_27.
[26]Liang J Y,Xu Z B.The Algorithm on Knowledge Reduction in Incomplete Information Systems[J].Int J Uncertain Fuzz,2002,24(1):95-103.DOI:10.1142/S021848850200134X.
[2]Wierman M J.Measuring Uncertainty in Rough Set Theory[J].International Journal of General Systems,1999,28(4):283-297.
[3]Hartley R V L.Transmission of Information[J].The Bell Systems Technical Journal,1928,7(3):535-563.
[4]苗夺谦,王珏.粗糙集理论中概念与运算的信息表示[J].软件学报,1999,10(2):113-116.
[5]Yao Y Y.Information Granulation and Rough Set Approximation[J].Internation Journal of Intelligent Systems,2001,16(1):87-104.DOI:10.1002/1098-111X.
[6]王国胤,于洪,杨大春.基于条件信息熵的决策表约简[J].计算机学报,2002,25(7):759-766.
[7]Liang J Y,Chin K S,Dang C Y,et al.A New Method for Measuring Uncertainty and Fuzziness in Rough Set Rheory[J].International Journal of General Systems,2002,31(4):331-342.DOI:http:∥dx.doi.org/10.108010308107021000013635.
[8]Liang J Y,Shi Z Z.The Information Entropy,Rough Entropy and Knowledge Granulation in Rough Set Theory[J].International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems,2004,12(1):37-46.DOI:10.1142/S0218488504002631.
[9]Liang J Y,Li D Y.Uncertainty and Knowledge Acquisition in Information System[M].Beijing:Science Press(in Chinese),2005.
[10]Beaubouef T,Petry F E,Arora G.Information-theoretic Measures of Uncertainty for Rough Sets and Rough Relational Databases[J].Information Sciences,1998,109(48):185-195.
[11]Pawlak Z.Rough Sets[J].International Journal of Computer and Information Sciences,1982,11(5):341-356.
[12]梁吉业,李德玉.信息系统中的不确定性与知识获取[M].北京:科学出版社,2005.
[13]GU S M,WU W Z.Knowledge Acquisition in Inconsistent Multi-scale Decision Systems[C]∥YAO J T,RAMANNA S,WANG G Y,et al.eds.Lecture Notes in Computer Science.Berlin,Germany:Springer,2011,6954:669-678.DOI:10.1007/978-3-642-24425-4_84.
[14]GU S M,WU W Z.On Knowledge Acquisition in Multi-scale Decision Systems[J].International Journal of Machine Learning and Cybernetics,2013,4(5):477-486.DOI:10.1007/s13042-012-0115-7.
[15]解滨,米据生,张军鹏.粗糙集不确定性度量的矩阵运算[J].计算机工程与应用,2011,47(29):42-45.
[16]刘财辉,苗夺谦,岳晓冬,等.知识不确定性度量及其关系研究[J].计算机科学,2014,41(3):66-70.DOI:1002-137X.2014.03.013.
[17]滕书华,卢敏,杨阿锋,等.基于一般二元关系的粗糙集加权不确定性度量[J].计算机学报,2014,37(3):649-665.
[18]吴伟志,陈颖,徐优红,等.协调的非完备多粒度标记决策系统的最优粒度选择[J].模式识别与人工智能,2016,29(2):108-115.
[19]Zadeh L A.Fuzzy Sets and Information Granularity[J].Advances in Fuzzy Set Theory and Application.Amsterdam:North-Holland,1979:3-18.DOI:10.1142/9789814261302_0022.
[20]Liang J Y,Shi Z Z.Information Entropy,Rough Entropy and Knowledge Granulation in Incomplete Information Systems[J].International Journal of General systems,2006,35(6):641-654.DOI:10.1080/03081070600687668.
[21]钱宇华,梁吉业,王锋.面向非完备决策表的正向近似特征选择加速算法[J].计算机学报,2011,34(3):435-442.DOI:10.3724/SP.J.1016.2011.00435.
[22]王锋,魏巍.缺失数据数据集的组增量式特征选择[J].计算机科学,2015,42(7):285-290.DOI:10.11896/j.issn.1002-137X.2015.07.061.
[23]Wang J H,Liang J Y,Qian Y H,et al.Uncertainty Measure of Rough Sets Based on Aknowledge Granulation for Incomplete Information Systems[J].International Journal of Uncertainty,Fuzziness and Knowledge-Based Systems,2008,16(2):233-244.DOI:10.1142/S0218488508005157.
[24]Pawlak Z,Skowron A.Rudiments of Rough Sets[J].Information Sciences,2007,177(1):3-27.DOI:10.1016/j.ins.2006.06.003.
[25]Qian Y H,Liang J Y.Combination Entropy and Combination Granulation in Incomplete Information System[J].Lect Notes Artif Intel,2006,4062:184-190.DOI:10.1007/11795131_27.
[26]Liang J Y,Xu Z B.The Algorithm on Knowledge Reduction in Incomplete Information Systems[J].Int J Uncertain Fuzz,2002,24(1):95-103.DOI:10.1142/S021848850200134X.