基于多元异构不确定性案例学习的广义区间灰数熵权聚类模型
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摘要
现实生活中多数聚类对象具有多元异构不确定性特征,表现为对象聚类指标体系异构化以及对象信息具有多元不确定性特点,而现有的不确定性多属性聚类决策方法对此类对象的聚类研究具有局限性.为此,针对聚类问题,首先,根据聚类对象多元不确定性信息的特点,提出广义区间灰数的概念,证明多元不确定性信息可统一用广义区间灰数进行表征;然后,结合极大熵思想,构建基于多元异构不确定性案例学习的广义区间灰数熵权配置模型,通过对对象相关的历史案例进行充分学习,测算各层指标的广义区间灰数熵权,以此确定各指标的聚类权重,再结合广义区间灰数的白化权函数对对象的新案例进行聚类分析;最后,通过案例研究验证所提出聚类模型的合理性和可行性.
Most of the clustering objects have the characteristic of multiple heterogeneous uncertainty in real life, which is presented via the heterogeneity of the clustering indicator system of objects and multi-uncertainty of the objects information. However, the present uncertainty multiple attribute clustering decision methods have limitations to research the clustering of these kinds of objects. Therefore, firstly the concept of generalized interval grey number is proposed according to the characteristics of multi-uncertainty information. It is proved that multi-uncertainty information can be all represented with generalized interval grey number in some specific conditions. Then, the rule of maximum entropy is introduced, the generalized interval grey entropy-weight allocation model based on multiple heterogeneous uncertainty cases study is built. The entropy-weight of multiple level is calculated through studying the cases about the objects, and then the weight of every indexes is got. Furthermore, the white function of generalized interval grey is used to analyze the clustering for the new cases of objects. Finally, the case study verifies the rationality and feasibility of the proposed clustering model.
Most of the clustering objects have the characteristic of multiple heterogeneous uncertainty in real life, which is presented via the heterogeneity of the clustering indicator system of objects and multi-uncertainty of the objects information. However, the present uncertainty multiple attribute clustering decision methods have limitations to research the clustering of these kinds of objects. Therefore, firstly the concept of generalized interval grey number is proposed according to the characteristics of multi-uncertainty information. It is proved that multi-uncertainty information can be all represented with generalized interval grey number in some specific conditions. Then, the rule of maximum entropy is introduced, the generalized interval grey entropy-weight allocation model based on multiple heterogeneous uncertainty cases study is built. The entropy-weight of multiple level is calculated through studying the cases about the objects, and then the weight of every indexes is got. Furthermore, the white function of generalized interval grey is used to analyze the clustering for the new cases of objects. Finally, the case study verifies the rationality and feasibility of the proposed clustering model.
引文
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[17]高志扬,雒赵飞,景国勋,等.综采工作面环境状况灰色熵权聚类分析[J].煤炭技术,2016,35(6):145-147.(Gao Z Y,Luo Z F,Jing G X,et al.Grey entropy weight clustering analysis of environment state of fully mechanized mining faces[J].Coal Technology,2016,35(6):145-147.)
[18]Yang Y,John R.Grey sets and greyness[J].Information Sciences,2012,185(1):249-264.
[19]刘思峰,党耀国,方志耕.灰色系统理论及其应用[M].北京:科学出版社,2004:14-25.(Liu S F,Dang Y G,Fang Z G.The theory of grey system and its application[M].Beijing:Science Press,2004:14-25.)
[20]Halberstam H,Elliott P D.Probabilistic number theory I and II[J].Mathematical Gazette,1982,66(435):92.
[21]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[22]Zhang H,Shu L.Generalized interval-valued fuzzy rough set and its application in decision making[J].Int J of Fuzzy Systems,2015,17(2):279-291.
[23]周伟杰,党耀国,熊萍萍,等.区间灰数的灰色变权与定权聚类模型[J].系统工程理论与实践,2013,33(10):2590-2595.(Zhou W J,Dang Y G,Xiong P P,et al.Grey clustering model for interval grey number with variable and fixed weights[J].Systems Engineering—–Theory&Practice,2013,33(10):2590-2595.)
[24]邱菀华.管理决策与应用熵学[M].北京:机械工业出版社,2002:79-96.(Qiu W H.Management decision making and application of entropy[M].Beijing:Mechanical Industry Press,2002:79-96.)
[25]刘思峰,方志耕,谢乃明.基于核和灰度的区间灰数运算法则[J].系统工程与电子技术,2010,32(2):313-316.(Liu S F,Fang Z G,Xie N M.Algorithm rules of interval grey numbers based on the kernel and the degree of greyness of grey numbers[J].Systems Engineering and Electronic,2010,32(2):313-316.)
[2]Wu Y,Xu H,Xu C,et al.Uncertain multi-attributesdecision making method based on interval number with probability distribution weighted operators and stochastic dominance degree[J].Knowledge-Based Systems,2016,113(1):199-209.
[3]陆亿红,夏聪.不确定数据的最优k近邻和局部密度聚类算法[J].控制与决策,2016,31(3):541-546.(Lu Y H,Xia C.Optimal k-nearest neighbors and local density-based clustering algorithm for uncertain data[J].Control and Decision,2016,31(3):541-546.)
[4]陈健美,陆虎,宋余庆,等.一种隶属关系不确定的可能性模糊聚类方法[J].计算机研究与发展,2008,45(9):1486-1492.(Chen J M,Lu H,Song Y Q,et al.A possibility fuzzy clustering algorithm based on the uncertainty membership[J].J of Computer Research and Development,2008,45(9):1486-1492.)
[5]郑爱武.基于模糊k-均值聚类模型的移动终端业务故障诊断[J].统计与决策,2014,3(11):83-85.(Zhen A W.Fault diagnosis of mobile terminal based on fuzzy k-means clustering model[J].Statistics and Decision,2014,3(11):83-85.)
[6]Jian H,Shu-bin S,Yi-min M,et al.High dimensional uncertain data efficient clustering algorithm[J].Computer Knowledge&Technology,2014,10(4):673-676.
[7]李慧,张庆范,段培永,等.一种基于聚类的超闭球模糊神经网络[J].控制与决策,2011,26(12):1803-1807.(Li H,Zhang Q F,Duan P Y,et al.Hyperball fuzzy neural network based on clustering[J].Control and Decision,2011,26(12):1803-1807.)
[8]何云斌,张志超,万静,等.不确定数据聚类的U-PAM算法和UM-PAM算法的研究[J].计算机科学,2016,43(6):263-269.(He Y B,Zhang Z C,Wan J,et al.Research for uncertain data clustering algorithm:U-PAM and UM-PAM algorithm[J].Computer Science,2016,43(6):263-269.)
[9]Deng J L.Control problem of grey system[J].Systems and Control Letters,1982,1(5):288-294.
[10]Liu H Q,Fang Z G,Li W D,et al.Object-oriented multi-attribute differences matrix grey clustering method and its application[J].Control and Decision,2015,30(2):366-370.
[11]王翯华,朱建军,方志耕.基于灰色聚类的大规模群体语言评价信息集结研究[J].控制与决策,2012,27(2):271-275.(Wang H H,Zhu J J,Fang Z G.Group aggregation method on large-scale linguistic evaluation information based on grey cluster[J].Control and Decision,2012,27(2):271-275.)
[12]Yuan C Q,Liu S F.Core of grey cluster and its application in evaluation of scientific and technological strength[J].J of Grey System,2012,24(4):327-336.
[13]Pei L L,Wang Z X.An optimized grey cluster model for evaluating quality of labor force[J].J of Software,2013,8(10):2489-2494.
[14]Li S Z,Zhang Z D,He R S.Application of grey clustering evaluations in coal railway transportation[J].Kybernetes,2012,41(5/6):714-725.
[15]钱丽丽,刘思峰,谢乃明.基于熵权和区间灰数信息的灰色聚类模型[J].系统工程与电子技术,2016,38(2):352-356.(Qian L L,Liu S F,Xie N M.Grey clustering model based on entropy-weight and grey numbers[J].Systems Engineering and Electronics,2016,38(2):352-356.)
[16]王斐,梁晓庚,郭超,等.灰云熵权聚类的制导仿真系统可信度评估[J].系统仿真学报,2015,27(8):1703-1707.(Wang F,Liang X G,Guo C,et al.Guidances simulation credibility evaluation based on clustering with grey cloud and entropy weight[J].J of System Simulation,2015,27(8):1703-1707.)
[17]高志扬,雒赵飞,景国勋,等.综采工作面环境状况灰色熵权聚类分析[J].煤炭技术,2016,35(6):145-147.(Gao Z Y,Luo Z F,Jing G X,et al.Grey entropy weight clustering analysis of environment state of fully mechanized mining faces[J].Coal Technology,2016,35(6):145-147.)
[18]Yang Y,John R.Grey sets and greyness[J].Information Sciences,2012,185(1):249-264.
[19]刘思峰,党耀国,方志耕.灰色系统理论及其应用[M].北京:科学出版社,2004:14-25.(Liu S F,Dang Y G,Fang Z G.The theory of grey system and its application[M].Beijing:Science Press,2004:14-25.)
[20]Halberstam H,Elliott P D.Probabilistic number theory I and II[J].Mathematical Gazette,1982,66(435):92.
[21]Zadeh L A.Fuzzy sets[J].Information and Control,1965,8(3):338-353.
[22]Zhang H,Shu L.Generalized interval-valued fuzzy rough set and its application in decision making[J].Int J of Fuzzy Systems,2015,17(2):279-291.
[23]周伟杰,党耀国,熊萍萍,等.区间灰数的灰色变权与定权聚类模型[J].系统工程理论与实践,2013,33(10):2590-2595.(Zhou W J,Dang Y G,Xiong P P,et al.Grey clustering model for interval grey number with variable and fixed weights[J].Systems Engineering—–Theory&Practice,2013,33(10):2590-2595.)
[24]邱菀华.管理决策与应用熵学[M].北京:机械工业出版社,2002:79-96.(Qiu W H.Management decision making and application of entropy[M].Beijing:Mechanical Industry Press,2002:79-96.)
[25]刘思峰,方志耕,谢乃明.基于核和灰度的区间灰数运算法则[J].系统工程与电子技术,2010,32(2):313-316.(Liu S F,Fang Z G,Xie N M.Algorithm rules of interval grey numbers based on the kernel and the degree of greyness of grey numbers[J].Systems Engineering and Electronic,2010,32(2):313-316.)