Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)oper...Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)operator is proposed based on the density operator theory for the decision maker(DM).Firstly,a simple TF vector clustering method is proposed,which considers the feature of TF number and the geometric distance of vectors.Secondly,the least deviation sum of squares method is used in the program model to obtain the density weight vector.Then,two TFTD operators are defined,and the MADM method based on the TFTD operator is proposed.Finally,a numerical example is given to illustrate the superiority of this method,which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.展开更多
User-transformer relations are significant to electric power marketing,power supply safety,and line loss calculations.To get accurate user-transformer relations,this paper proposes an identification method for user-tr...User-transformer relations are significant to electric power marketing,power supply safety,and line loss calculations.To get accurate user-transformer relations,this paper proposes an identification method for user-transformer relations based on improved quantum particle swarm optimization(QPSO)and Fuzzy C-Means Clustering.The main idea is:as energymeters at different transformer areas exhibit different zero-crossing shift features,we classify the zero-crossing shift data from energy meters through Fuzzy C-Means Clustering and compare it with that at the transformer end to identify user-transformer relations.The proposed method contributes in three main ways.First,based on the fuzzy C-means clustering algorithm(FCM),the quantum particle swarm optimization(PSO)is introduced to optimize the FCM clustering center and kernel parameters.The optimized FCM algorithm can improve clustering accuracy and efficiency.Since easily falls into a local optimum,an improved PSO optimization algorithm(IQPSO)is proposed.Secondly,considering that traditional FCM cannot solve the linear inseparability problem,this article uses a FCM(KFCM)that introduces kernel functions.Combinedwith the IQPSOoptimization algorithm used in the previous step,the IQPSO-KFCM algorithm is proposed.Simulation experiments verify the superiority of the proposed method.Finally,the proposed method is applied to transformer detection.The proposed method determines the class members of transformers and meters in the actual transformer area,and obtains results consistent with actual user-transformer relations.This fully shows that the proposed method has practical application value.展开更多
Intuitionistic fuzzy set (IFS) is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set (...Intuitionistic fuzzy set (IFS) is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set (IVIFS), whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clus- tering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs: the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.展开更多
In order to distinguish with effect different hesitant fuzzy elements(HFEs), we introduce the asymmetrical relative entropy between HFEs as a distance measure for higher discernment. Next,the formula of attribute weig...In order to distinguish with effect different hesitant fuzzy elements(HFEs), we introduce the asymmetrical relative entropy between HFEs as a distance measure for higher discernment. Next,the formula of attribute weights is derived via an optimal model according to TOPSIS from the relative closeness degree constructed by the discerning relative entropy. Then, we propose the concept of cocorrelation degree from the viewpoint of probability theory and develop another new formula of hesitant fuzzy correlation coeffcient, and prove their similar properties to the traditional correlation coeffcient.To make full use of the existing similarity measures including the ones presented by us, we consider aggregation of similarity measures for hesitant fuzzy sets and derive the synthetical similarity formula.Finally, the derived formula is used for netting clustering analysis under hesitant fuzzy information and the effectiveness and superiority are veri?ed through a comparison analysis of clustering results obtained by other clustering algorithms.展开更多
基金supported by the Natural Science Foundation of Hunan Province(2023JJ50047,2023JJ40306)the Research Foundation of Education Bureau of Hunan Province(23A0494,20B260)the Key R&D Projects of Hunan Province(2019SK2331)。
文摘Aiming at the triangular fuzzy(TF)multi-attribute decision making(MADM)problem with a preference for the distribution density of attribute(DDA),a decision making method with TF number two-dimensional density(TFTD)operator is proposed based on the density operator theory for the decision maker(DM).Firstly,a simple TF vector clustering method is proposed,which considers the feature of TF number and the geometric distance of vectors.Secondly,the least deviation sum of squares method is used in the program model to obtain the density weight vector.Then,two TFTD operators are defined,and the MADM method based on the TFTD operator is proposed.Finally,a numerical example is given to illustrate the superiority of this method,which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.
基金supported by the National Natural Science Foundation of China(61671208).
文摘User-transformer relations are significant to electric power marketing,power supply safety,and line loss calculations.To get accurate user-transformer relations,this paper proposes an identification method for user-transformer relations based on improved quantum particle swarm optimization(QPSO)and Fuzzy C-Means Clustering.The main idea is:as energymeters at different transformer areas exhibit different zero-crossing shift features,we classify the zero-crossing shift data from energy meters through Fuzzy C-Means Clustering and compare it with that at the transformer end to identify user-transformer relations.The proposed method contributes in three main ways.First,based on the fuzzy C-means clustering algorithm(FCM),the quantum particle swarm optimization(PSO)is introduced to optimize the FCM clustering center and kernel parameters.The optimized FCM algorithm can improve clustering accuracy and efficiency.Since easily falls into a local optimum,an improved PSO optimization algorithm(IQPSO)is proposed.Secondly,considering that traditional FCM cannot solve the linear inseparability problem,this article uses a FCM(KFCM)that introduces kernel functions.Combinedwith the IQPSOoptimization algorithm used in the previous step,the IQPSO-KFCM algorithm is proposed.Simulation experiments verify the superiority of the proposed method.Finally,the proposed method is applied to transformer detection.The proposed method determines the class members of transformers and meters in the actual transformer area,and obtains results consistent with actual user-transformer relations.This fully shows that the proposed method has practical application value.
基金supported by the National Natural Science Foundation of China (70571087)the National Science Fund for Distinguished Young Scholars of China (70625005)
文摘Intuitionistic fuzzy set (IFS) is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set (IVIFS), whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clus- tering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs: the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.
文摘In order to distinguish with effect different hesitant fuzzy elements(HFEs), we introduce the asymmetrical relative entropy between HFEs as a distance measure for higher discernment. Next,the formula of attribute weights is derived via an optimal model according to TOPSIS from the relative closeness degree constructed by the discerning relative entropy. Then, we propose the concept of cocorrelation degree from the viewpoint of probability theory and develop another new formula of hesitant fuzzy correlation coeffcient, and prove their similar properties to the traditional correlation coeffcient.To make full use of the existing similarity measures including the ones presented by us, we consider aggregation of similarity measures for hesitant fuzzy sets and derive the synthetical similarity formula.Finally, the derived formula is used for netting clustering analysis under hesitant fuzzy information and the effectiveness and superiority are veri?ed through a comparison analysis of clustering results obtained by other clustering algorithms.
