基于覆盖的区间值信息系统的属性约简
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摘要
区间值信息系统是单值信息系统的泛化模型.基于区间值相似程度的相容类形成整个论域的覆盖,而这种覆盖独具特征.提出了相容类覆盖率和覆盖稠密度的概念,对变精度相容关系下形成的覆盖进行数字表征,并探究其性质;其次基于相容类覆盖率和覆盖稠密度,讨论了相容类覆盖约简、最大相容类覆盖约简和覆盖稠密约简;最后进行了实例分析.
The interval-valued information system is a generalized model of single-valued information system.Tolerant classes which are based on interval value similarity degree form the covering of the entire universe of discourse,and such covering is of unique characteristics.The concepts of tolerant classes coverage rate and covering density are proposed.Then the covering formed under the variable precision tolerance relation is numerically characterized and its properties are explored.Furthermore,the tolerant classes covering reduction,the maximum tolerant classes covering reduction and covering dense reduction based on tolerant classes coverage and covering density are discussed.Lastly,a case analysis is performed.
The interval-valued information system is a generalized model of single-valued information system.Tolerant classes which are based on interval value similarity degree form the covering of the entire universe of discourse,and such covering is of unique characteristics.The concepts of tolerant classes coverage rate and covering density are proposed.Then the covering formed under the variable precision tolerance relation is numerically characterized and its properties are explored.Furthermore,the tolerant classes covering reduction,the maximum tolerant classes covering reduction and covering dense reduction based on tolerant classes coverage and covering density are discussed.Lastly,a case analysis is performed.
引文
[1]SLOWINSKI R,VANDERPOOTEN D.A Generalized Definition of Rough Approximations Based on Similarity[J].IEEE Transactions on Knowledge &Data Engineering,2000,12(2):331-336.
[2]SKOWRON A,STEPANIUK J.Tolerance Approximation Spaces[J].Fundamenta Informaticae,1996,27(2/3):245-253.
[3]ABU-DONIA H M.Comparison Between Different Kinds of Approximations by using a Family of Binary Relations[J].Knowledge-Based Systems,2008,21(8):911-919.
[4]DEMBCZYNSKI K,GRECO S,SLOWINSKI R.Methodology of Rough-set-based Classification and Sorting with Hierarchical Structure of Attributes and Criteria[J].Control &Cybernetics,2002,31(4):891-920.
[5]ZAKOWSKI W.Approximations in the Space(U,Π)[J].Demonstratio Mathematica,1983,16(3):761-769.
[6]钟纯真.基于集值信息系统的扩充粗糙集模型[J].内江师范学院学报,2013,28(2):19-21.
[7]GONZáLEZ-RIVERA G,LIN W.Constrained Regression for Interval-Valued Data[J].Journal of Business &Economic Statistics,2013,31(4):473-490.
[8]SHU B M,KUNG J Y,SHU M H.Interval-valued Process Data Monitoring and Controlling[J].Artificial Intelligence Research,2013,2(3):90-101.
[9]LIU X Y,ZHOU Z H.Learning with cost intervals[C]//Acm Sigkdd International Conference on Knowledge Discovery &Data Mining.2010.
[10]YANG X,QI Y,YU D J,et al.α-Dominance Relation and Rough Sets in Interval-valued Information Systems[J].Information Sciences,2015,294(5):334-347.
[11]DAI J,WANG W,MI J S.Uncertainty Measurement for Interval-valued Information Systems[J].Information Sciences,2013,251(4):63-78.
[12]陈子春,秦克云.区间值信息系统在变精度相容关系下的属性约简[J].计算机科学,2009,36(3):163-166.
[13]彭家寅.区间值模糊推理的CRI方法[J].内江师范学院学报,2018,33(6):46-50.
[14]LEUNG Y,FISCHER M M,WU W Z,et al.A Rough Set Approach for the Discovery of Classification Rules in Interval-valued Information Systems[J].International Journal of Approximate Reasoning,2008,47(2):233-246.
[15]CHENG Y,MIAO D,FENG Q.Positive Approximation and Converse Approximation in Interval-valued Fuzzy Rough sets[J].Information Sciences,2011,181(11):2086-2110.
[16]张转转.相容关系下的覆盖粗糙集[J].电脑与信息技术,2012,20(5):16-19.
[17]汤建国,佘堃,祝峰.一种新的覆盖粗糙模糊集模型[J].控制与决策,2012,27(11):1653-1662.
[18]魏莱,苗夺谦,徐菲菲,等.基于覆盖的粗糙模糊集模型研究[J].计算机研究与发展,2006,43(10):1719-1723.
[19]徐忠印,廖家奇.基于覆盖的模糊粗糙集模型[J].模糊系统与数学,2006,20(3):141-144.
[20]HU J,WANG G Y,ZHANG Q H.Covering Based Generalized Rough Fuzzy Set Model[J].Journal of Software,2010,21(5):968-977.
[21] WANG P,LI Q.The rough membership function based on C 10-and its applications[J].Journal of Intelligent &Fuzzy Systems,2017,32(1):279-289.
[22]D'EER L,CORNELIS C.A Comprehensive Study of Fuzzy Covering-based Rough Set Models:Definitions,properties and interrelationships[J].Fuzzy Sets &Systems,2017,336:1-26.
[2]SKOWRON A,STEPANIUK J.Tolerance Approximation Spaces[J].Fundamenta Informaticae,1996,27(2/3):245-253.
[3]ABU-DONIA H M.Comparison Between Different Kinds of Approximations by using a Family of Binary Relations[J].Knowledge-Based Systems,2008,21(8):911-919.
[4]DEMBCZYNSKI K,GRECO S,SLOWINSKI R.Methodology of Rough-set-based Classification and Sorting with Hierarchical Structure of Attributes and Criteria[J].Control &Cybernetics,2002,31(4):891-920.
[5]ZAKOWSKI W.Approximations in the Space(U,Π)[J].Demonstratio Mathematica,1983,16(3):761-769.
[6]钟纯真.基于集值信息系统的扩充粗糙集模型[J].内江师范学院学报,2013,28(2):19-21.
[7]GONZáLEZ-RIVERA G,LIN W.Constrained Regression for Interval-Valued Data[J].Journal of Business &Economic Statistics,2013,31(4):473-490.
[8]SHU B M,KUNG J Y,SHU M H.Interval-valued Process Data Monitoring and Controlling[J].Artificial Intelligence Research,2013,2(3):90-101.
[9]LIU X Y,ZHOU Z H.Learning with cost intervals[C]//Acm Sigkdd International Conference on Knowledge Discovery &Data Mining.2010.
[10]YANG X,QI Y,YU D J,et al.α-Dominance Relation and Rough Sets in Interval-valued Information Systems[J].Information Sciences,2015,294(5):334-347.
[11]DAI J,WANG W,MI J S.Uncertainty Measurement for Interval-valued Information Systems[J].Information Sciences,2013,251(4):63-78.
[12]陈子春,秦克云.区间值信息系统在变精度相容关系下的属性约简[J].计算机科学,2009,36(3):163-166.
[13]彭家寅.区间值模糊推理的CRI方法[J].内江师范学院学报,2018,33(6):46-50.
[14]LEUNG Y,FISCHER M M,WU W Z,et al.A Rough Set Approach for the Discovery of Classification Rules in Interval-valued Information Systems[J].International Journal of Approximate Reasoning,2008,47(2):233-246.
[15]CHENG Y,MIAO D,FENG Q.Positive Approximation and Converse Approximation in Interval-valued Fuzzy Rough sets[J].Information Sciences,2011,181(11):2086-2110.
[16]张转转.相容关系下的覆盖粗糙集[J].电脑与信息技术,2012,20(5):16-19.
[17]汤建国,佘堃,祝峰.一种新的覆盖粗糙模糊集模型[J].控制与决策,2012,27(11):1653-1662.
[18]魏莱,苗夺谦,徐菲菲,等.基于覆盖的粗糙模糊集模型研究[J].计算机研究与发展,2006,43(10):1719-1723.
[19]徐忠印,廖家奇.基于覆盖的模糊粗糙集模型[J].模糊系统与数学,2006,20(3):141-144.
[20]HU J,WANG G Y,ZHANG Q H.Covering Based Generalized Rough Fuzzy Set Model[J].Journal of Software,2010,21(5):968-977.
[21] WANG P,LI Q.The rough membership function based on C 10-and its applications[J].Journal of Intelligent &Fuzzy Systems,2017,32(1):279-289.
[22]D'EER L,CORNELIS C.A Comprehensive Study of Fuzzy Covering-based Rough Set Models:Definitions,properties and interrelationships[J].Fuzzy Sets &Systems,2017,336:1-26.