基于正态云相似度的语言型多属性群决策方法
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摘要
在分析已有正态云模型相似性度量的不足的基础上,综合考虑正态云的形状相似度和位置相似度,提出了一种新的正态云相似性度量方法,并对其性质进行了证明。与已有方法相比,该方法具有很强的区分性。将提出的正态云相似性度量方法应用于语言型多属性群决策中,首先依据正态分布规律将语言变量转化为正态云;其次通过云加权算术平均算子CWAA实现信息集结;最后依据VIKOR排序方法,计算方案属性与最优云、最差云的综合相似度,以实现方案排序。通过算例分析了所提方法的可行性和有效性。
On the basis of analyzing the inadequacies of existed similarity measures between normal clouds,through synthetically considering the shape similarity and position similarity of normal clouds,this paper proposed a new similarity measure between normal clouds,and proved its characteristics.The comparison results with other methods demonstrate the stronger discrimination of the proposed method.The proposed normal cloud similarity measurement method was applied to the linguistic multi-attribute group decision.Firstly,the linguistic variables is transformed into a normal cloud according to the normal distribution law.Secondly,information aggregation is realized by means of cloud weighted arithmetic mean operator.Finally,according to the VIKOR method,the scheme is ranked by the comprehensive similarity of the optimal cloud and the worst cloud.The feasibility and validity of this method were analyzed through an example in this paper.
On the basis of analyzing the inadequacies of existed similarity measures between normal clouds,through synthetically considering the shape similarity and position similarity of normal clouds,this paper proposed a new similarity measure between normal clouds,and proved its characteristics.The comparison results with other methods demonstrate the stronger discrimination of the proposed method.The proposed normal cloud similarity measurement method was applied to the linguistic multi-attribute group decision.Firstly,the linguistic variables is transformed into a normal cloud according to the normal distribution law.Secondly,information aggregation is realized by means of cloud weighted arithmetic mean operator.Finally,according to the VIKOR method,the scheme is ranked by the comprehensive similarity of the optimal cloud and the worst cloud.The feasibility and validity of this method were analyzed through an example in this paper.
引文
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[2] FAN Z P,XIAO S H.The consistency and ranking method for comparison matrix with linguistic assessment [J].Systems Engineering Theory&Practice,2002,22(5):87-91.(in Chinese)樊治平,肖四汉.基于自然语言符号表示的比较矩阵的一致性及排序方法 [J].系统工程理论与实践,2002,22(5):87-91.
[3] CHEN S M,HONG J A.Multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets[J].Information Sciences,2014,286:63-74.
[4] DONG Y C,LI C C,HERRERA,et al.Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information [J].Information Sciences,2016,367:259-278.
[5] LIU P,CHEN S M.Multiattribute group decision making based on intuitionistic 2-tuple linguistic information [J].Information Sciences,2018,430:599-619.
[6] 李德毅,杜鹢.不确定性人工智能(第2版)[M].北京:国防工业出版社,2014:50-51.
[7] ZHANG Y,ZHAO D N,LI D Y.The similar cloud andthe measurement method[J].Information and Control,2004,33(2):129-132.(in Chinese)张勇,赵东宁,李德毅.相似云及其度量分析方法[J].信息与控制,2004,33(2):129-132.
[8] LI T Z,YANG X L.Risk Assessment Model for Water and Mud Inrush in Deep andLongTunnels Based on Normal Grey Cloud Clustering Method[J].Korean Society of Civil Engineers,2018,22(5):1991-2001.
[9] PENG B,ZHOU J M,PENG D H.Cloud model based approach to groupdecision making with uncertain purelinguistic information[J].Journal of Intelligent & Fuzzy Systems,2017,32(3):1959-1968.
[10] PENG H G,WANG J Q.Cloud decision model for selecting sustainable energy crop based on linguisticintuitionistic information[J].International Journal of Systems Science,2017,48(15):3316-3333.
[11] LIU P D,LIU X.Multi-attribute Group Decision-Making Method Based on Cloud Distance Operators With Linguistic Information[J].International Journal of Fuzzy Systems,2017,19(4):1011-1024.
[12] CAI S B,FANG W,ZHAO J,et al.Research of interval-based cloud similaritycomparison algorithm[J].Journal of Chinese ComputerSystems,2011,32(12):2456-2460.(in Chinese)蔡绍滨,方伟,赵靖,等.基于区间的云相似度比较算法的研究[J].小型微型计算机系统,2011,32(12):2456-2460.
[13] XU X H,WANG P,CAI C G.Linguistic multiattributelarge group decision-making method based on similarity measurement of cloud model [J].Control and Decision,2017,32(3):459-466.(in Chinese)徐选华,王佩,蔡晨光.基于云相似度的语言偏好信息多属性大群体决策方法[J].控制与决策,2017,32(3):459-466.
[14] ZHANG G W,LI D Y,LI P,et al.A collaborative filtering recommendation algorithm based on cloud model [J].Journal of Software,2007,18(10):2403-2411.(in Chinese)张光卫,李德毅,李鹏,等.基于云模型的协同过滤推荐算法[J].软件学报,2007,18(10):2403-2411.
[15] LI H L,GUO C H,QIU W R.Similarity meraurement between normal cloud models [J].Acta Electronica Sinica,2011,39(11):2561-2567.(in Chinese)李海林,郭崇慧,邱望仁.正态云模型相似度计算方法[J].电子学报,2011,39(11):2561-2567.
[16] GONG Y B,JIANG Y D,LIANG X C.Similarity measurement for normal cloud models based on fuzzysimilarity measure[J].Systems Engineering,2015,33(9):133-137.(in Chinese)龚艳冰,蒋亚东,梁雪春.基于模糊贴近度的正态云模型相似度度量[J].系统工程,2015,33(9):133-137.
[17] YAN Y,TANG Z M.Pertinencemeasurement of cloud model by using expectation-entropycurves[J].Journal of Huazhong University of Science and Technology(Natural Science Edition),2012,40(10):95-100.(in Chinese)阎岩,唐振民.基于含熵期望曲线的云模型相关性度量方法[J].华中科技大学学报(自然科学版),2012,40(10):95-100.
[18] LI D Y,LIU C Y.Study on the universality of the normalcloud model[J].Engineering Science,2004,6(8):28-34.(in Chinese)李德毅,刘常昱.论正态云模型的普适性[J].中国工程科学,2004,6(8):28-34.
[19] WANG J Q,LU P,ZHANG H Y,et al.Method of multi-crriteria group decision-making based on Cloud aggregation operators with linguistic information[J].Information Sciences,2014,274:177-191.
[20] LIAO H C,XU Z S,ZENG X J.Hesitant fuzzy linguistic VIKOR method and itsapplication in qualitative multiple criteria decision making[J].IEEE Transactions on Fuzzy Systems.2015,23:1343-1355.