基于直觉模糊熵的群组聚类决策方法
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摘要
针对直觉模糊群决策问题,依据专家的直觉模糊评价信息,利用直觉模糊相似度和相异度构造直觉模糊相似矩阵,为了得到合理的专家聚类结果,设计风险参数并提出聚类阈值变化率分析方法,综合聚类结果和直觉模糊熵对各专家进行组合赋权。提出基于离散正态分布的位置权重确定方法,构造直觉模糊集混合加权集结算子对各专家关于方案集的直觉模糊评价信息进行综合集成。结合算例验证了方法的可行性和有效性。
Aiming at intutionistic fuzzy group decision-making problem,according to experts' intuitionistic fuzzy evaluation information,we use intuitionistic fuzzy similarity and dissimilarity to construct the intutionistic fuzzy similarity matrix.In order to obtain reasonable expert clustering results,we design risk parameters and a clustering threshold rate analysis method.The weights of expert combinations are determined according to the classification result and the entropy of intuitionistic fuzzy vectors.We also propose a method for determining position weight based on discrete normal distribution.We construct intuitionistic fuzzy sets and mix them with weighted aggregation operators to integrate intutionistic fuzzy evaluation information of each expert on the solution set.The feasibility and effectiveness of this method is verified through examples.
Aiming at intutionistic fuzzy group decision-making problem,according to experts' intuitionistic fuzzy evaluation information,we use intuitionistic fuzzy similarity and dissimilarity to construct the intutionistic fuzzy similarity matrix.In order to obtain reasonable expert clustering results,we design risk parameters and a clustering threshold rate analysis method.The weights of expert combinations are determined according to the classification result and the entropy of intuitionistic fuzzy vectors.We also propose a method for determining position weight based on discrete normal distribution.We construct intuitionistic fuzzy sets and mix them with weighted aggregation operators to integrate intutionistic fuzzy evaluation information of each expert on the solution set.The feasibility and effectiveness of this method is verified through examples.
引文
[1]Li Deng-feng.Intuitionistic fuzzy set decision and game analysis methodologies[M].Beijing:National Defense Industry Press,2012.(in Chinese)
[2]Atanassov K T.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
[3]Li Peng,Liu Si-feng,Zhu Jian-jun.Clustering method based on new intuitionistic fuzzy similarity degree[J].Control and Decision,2013,28(5):758-762.(in Chinese)
[4]He Zheng-hong,Lei Ying-jie,Wang Gang.Target recognition based on intuitionistic fuzzy clustering[J].Systems Engineering and Electronics,2011,33(6):1283-1286.(in Chinese)
[5]Zhou Wei,He Jian-min,Yu De-jian.Accurate method of obtaining decision expert weights in intuitionistic fuzzy group decision making[J].Control and Decision,2013,28(5):716-721.(in Chinese)
[6]Shi Chao,Cheng Yong-mei,Pan Quan.Method to aggregate hybrid preference information based on intuitionistic fuzzy and evidence theory[J].Control and Decision,2012,27(8):1163-1168.(in Chinese)
[7]Zhou S M,Chiclana F C,John R I,et al.Fuzzification of the OWA operators for aggregating uncertain information with uncertain weights[J].Studies in Fuzziness and Soft Computing,2011,265:91-109.
[8]Garcia-Cascales M S,Lamata M T,Verdegay J L.The TOP-SIS method and its application to linguistic variables[M]∥Preference and Decisions.Heidelberg:Springer,2010:383-395.
[9]Zhang Hong-mei,Xu Ze-shui,Chen Qi.On clustering approach to intuitionistic fuzzy sets[J].Control and Decision,2007,22(8):882-888.(in Chinese)
[10]Liu Hua-wen.New similarity measures between intuitionistic fuzzy sets and between elements[J].Mathematical and Computer Modelling,2005,42(1-2):61-70.
[11]Li Deng-feng.Some measures of dissimilarity in intuitionistic fuzzy structures[J].Journal of Computer and System Sciences,2004,68(1):115-122.
[12]Li Peng,Liu Si-feng,Zhu Jian-jun.Clustering method based on new intuitionistic fuzzy similarity degree[J].Control and Decision,2013,28(5):758-762.(in Chinese)
[13]Szmidt E,Kacprzyk J.Entropy for intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,2001,118(3):467-477.
[14]Li D F.The GOWA operator based approah to multiattribute decision making using intuitionistic fuzzy sets[J].Mathematical and Computer Modelling,2011,53(5-6):1182-1196.
[15]Xu Ze-shui.An overview of methods for determining OWAweights[J].International Journal of Intelligent Systems,2005,20(8):843-865.
[1]李登峰.直觉模糊集决策与对策分析方法[M].北京:国防工业出版社,2012.
[3]李鹏,刘思峰,朱建军.基于新直觉模糊相似度的聚类方法[J].控制与决策,2013,28(3):758-762.
[4]贺正洪,雷英杰,王刚.基于直觉模糊聚类的目标识别[J].系统工程与电子技术,2011,33(6):1283-1286.
[5]周伟,何建敏,余德建.直觉模糊群决策中专家权重确定的一种精确方法[J].控制与决策,2013,28(5):716-721.
[6]史超,程咏梅,潘泉.基于直觉模糊和证据理论的混合型偏好信息集结方法[J].控制与决策,2012,27(8):1163-1168.
[9]张洪美,徐泽水,陈琦.直觉模糊集的聚类方法研究[J].控制与决策,2007,22(8):882-888.
[12]李鹏,刘思峰,朱建军.基于新直觉模糊相似度的聚类方法[J].控制与决策,2013,28(5):758-762.
[2]Atanassov K T.Intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,1986,20(1):87-96.
[3]Li Peng,Liu Si-feng,Zhu Jian-jun.Clustering method based on new intuitionistic fuzzy similarity degree[J].Control and Decision,2013,28(5):758-762.(in Chinese)
[4]He Zheng-hong,Lei Ying-jie,Wang Gang.Target recognition based on intuitionistic fuzzy clustering[J].Systems Engineering and Electronics,2011,33(6):1283-1286.(in Chinese)
[5]Zhou Wei,He Jian-min,Yu De-jian.Accurate method of obtaining decision expert weights in intuitionistic fuzzy group decision making[J].Control and Decision,2013,28(5):716-721.(in Chinese)
[6]Shi Chao,Cheng Yong-mei,Pan Quan.Method to aggregate hybrid preference information based on intuitionistic fuzzy and evidence theory[J].Control and Decision,2012,27(8):1163-1168.(in Chinese)
[7]Zhou S M,Chiclana F C,John R I,et al.Fuzzification of the OWA operators for aggregating uncertain information with uncertain weights[J].Studies in Fuzziness and Soft Computing,2011,265:91-109.
[8]Garcia-Cascales M S,Lamata M T,Verdegay J L.The TOP-SIS method and its application to linguistic variables[M]∥Preference and Decisions.Heidelberg:Springer,2010:383-395.
[9]Zhang Hong-mei,Xu Ze-shui,Chen Qi.On clustering approach to intuitionistic fuzzy sets[J].Control and Decision,2007,22(8):882-888.(in Chinese)
[10]Liu Hua-wen.New similarity measures between intuitionistic fuzzy sets and between elements[J].Mathematical and Computer Modelling,2005,42(1-2):61-70.
[11]Li Deng-feng.Some measures of dissimilarity in intuitionistic fuzzy structures[J].Journal of Computer and System Sciences,2004,68(1):115-122.
[12]Li Peng,Liu Si-feng,Zhu Jian-jun.Clustering method based on new intuitionistic fuzzy similarity degree[J].Control and Decision,2013,28(5):758-762.(in Chinese)
[13]Szmidt E,Kacprzyk J.Entropy for intuitionistic fuzzy sets[J].Fuzzy Sets and Systems,2001,118(3):467-477.
[14]Li D F.The GOWA operator based approah to multiattribute decision making using intuitionistic fuzzy sets[J].Mathematical and Computer Modelling,2011,53(5-6):1182-1196.
[15]Xu Ze-shui.An overview of methods for determining OWAweights[J].International Journal of Intelligent Systems,2005,20(8):843-865.
[1]李登峰.直觉模糊集决策与对策分析方法[M].北京:国防工业出版社,2012.
[3]李鹏,刘思峰,朱建军.基于新直觉模糊相似度的聚类方法[J].控制与决策,2013,28(3):758-762.
[4]贺正洪,雷英杰,王刚.基于直觉模糊聚类的目标识别[J].系统工程与电子技术,2011,33(6):1283-1286.
[5]周伟,何建敏,余德建.直觉模糊群决策中专家权重确定的一种精确方法[J].控制与决策,2013,28(5):716-721.
[6]史超,程咏梅,潘泉.基于直觉模糊和证据理论的混合型偏好信息集结方法[J].控制与决策,2012,27(8):1163-1168.
[9]张洪美,徐泽水,陈琦.直觉模糊集的聚类方法研究[J].控制与决策,2007,22(8):882-888.
[12]李鹏,刘思峰,朱建军.基于新直觉模糊相似度的聚类方法[J].控制与决策,2013,28(5):758-762.