基于改进Gini-Simpson指数的指标及权重均为混合属性的广义灰靶决策方法
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摘要
提出了一种新的以改进的Gini-Simpson指数为决策依据的指标及权重均为混合属性值的广义灰靶决策方法。该方法构造权重函数将不确定性混合指标权重确定化,并以改进的综合加权Gini-Simpson指数作为方案决策的依据。首先将各方案的混合属性指标值转化为二元联系数,并分解为确定项和不确定项以组成(确定,不确定)二元组数;其次,分别获得各属性下靶心指标的(确定,不确定)二元组数;然后,构造权重函数将不确定性权重确定化,继而求得各方案的综合加权Gini-Simpson指数;最后以综合加权的Gini-Simpson指数为依据对各方案进行决策,以其值越小方案越优。案例分析的结果验证了该法的可行性。
A novel improved Gini-Simpson index based generalised grey target decision method with index and weight both containing mixed attribute values is proposed.This method builds the weight function to transform the mixed attribute-based weights into the certain number-based weights and takes the improved comprehensive weighted Gini-Simpson indices to rank the alternatives.This method first transforms all alternatives' indices into binary connection numbers and divides them into the deterministic terms and uncertain terms to compose the two-tuple(determinacy,uncertainty)numbers.Then the target centre indices of two-tuple(determinacy,uncertainty)number are determined.Next the certain numberbased weights can be determined by the weight function.Following this,the comprehensive weighted GiniSimpson index of all alternatives can be obtained.Finally,the alternatives ranking is easy to be made with the Gini-Simpson index the smaller the better.A case study illustrates the proposed approach.
A novel improved Gini-Simpson index based generalised grey target decision method with index and weight both containing mixed attribute values is proposed.This method builds the weight function to transform the mixed attribute-based weights into the certain number-based weights and takes the improved comprehensive weighted Gini-Simpson indices to rank the alternatives.This method first transforms all alternatives' indices into binary connection numbers and divides them into the deterministic terms and uncertain terms to compose the two-tuple(determinacy,uncertainty)numbers.Then the target centre indices of two-tuple(determinacy,uncertainty)number are determined.Next the certain numberbased weights can be determined by the weight function.Following this,the comprehensive weighted GiniSimpson index of all alternatives can be obtained.Finally,the alternatives ranking is easy to be made with the Gini-Simpson index the smaller the better.A case study illustrates the proposed approach.
引文
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[2]王正新,党耀国,杨虎.改进的多目标灰靶决策方法[J].系统工程与电子技术,2009,31(11).
[3]Song J,Dang Y,Wang Z,et al.The Decision-making Model of Harden Grey Target Based on Interval Number with Preference Information on Alternatives[J].Journal of Grey System,2009,21(3).
[4]Luo D,Wang X.The Multi-attribute Grey Target Decision Method for Attribute Value within Three-parameter Interval Grey Number[J].Applied Mathematical Modelling,2012,36(5).
[5]Zeng B,Li C,Liu S.A Novel Grey Target Decision-making Model Based on Cobweb Area and Its Application for Choosing the Software Development Pattern[J].Scientia Iranica,2016,23(1).
[6]关欣,孙贵东,衣晓,等.基于关联系数靶心距的混合多属性识别[J].航空学报,2015,36(7).
[7]Ma J,Ji C.Generalized Grey Target Decision Method for Mixed Attributes Based on Connection Number[J/OL].Journal of Applied Mathematics,2014(ID 763543).
[8]Ma J.Generalised Grey Target Decision Method for Mixed Attributes with Index Weights Wontaining Uncertain Numbers[J].Journal of Intelligent and Fuzzy Systems,2018,34(1).
[9]Ma J.Grey Target Decision Method for a Variable Target Centre Based on the Decision Maker's Preferences[J/OL].Journal of Applied Mathematics,2014(ID 572529).
[10]Fabrizi E,Trivisano C.Small Area Estimation of the Gini Concentration Coefficient[J].Computational Statistics and Data Analysis,2016(99).
[11]Pesenti N,Quatto P,Ripamonti E.Bootstrap Confidence Intervals for Biodiversity Measures based on Gini Index and Entropy[J].Quality&Quantity,2017,51(2).
[12]Guiasu R C,Guiasu S.The Weighted Gini-Simpson Index:Revitalizing an Old Index of Biodiversity[J/OL].International Journal of Ecology,2012(ID:478728).
[13]Casquilho J P.A Methodology to Determine the Maximum Value of Weighted Gini-Simpson index[J].Casquilho Springer Plus,2016(5).
[14]Gregori J,Perales C,Rodriguez-Frias F,et al.Viral Quasispecies Complexity Measures[J].Virology,2016(493).
[15]Eliazar I,Sokolov I M.Maximization of Statistical Heterogeneity:From Shannon's Entropy to Gini's Index[J].Physica A:Statistical Mechanics and Its Applications,2010(389).
[16]Petry F,Elmore P,Yager R.Combining Uncertain Information of Differing Modalities[J].Information Sciences,2015(322).
[17]Jiang J,Shang P,Zhang Z,et al.Permutation Entropy Analysis based on Gini-Simpson Index for Financial Time Series[J].Physica A:Statistical Mechanics and its Applications,2017(486).
[18]赵克勤.二元联系数A+Bi的理论基础与基本算法及在人工智能中的应用[J].智能系统学报,2008,3(6).
[19]赵克勤.基于集对分析的不确定性多属性决策模型与算法[J].智能系统学报,2010,5(1).
[20]刘中侠,刘思峰,蒋诗泉,等.基于区间灰数相离度的灰色关联决策模型[J].统计与信息论坛,2017,32(9).