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
Round method is the common method for discrete variable optimization in optimal design of complex mechanical structures;however,it has some disadvantages such as poor precision,simple model and lacking of working cond...Round method is the common method for discrete variable optimization in optimal design of complex mechanical structures;however,it has some disadvantages such as poor precision,simple model and lacking of working conditions＇ description,etc.To solve these problems,a new model is constructed by defining parameterized fuzzy entropy,and the rationality of parameterized fuzzy entropy is verified.And a new multidirectional searching algorithm is further put forward,which takes information of actual working conditions into consideration and has a powerful local searching capability.Then this new algorithm is combined with the GA by the fuzzy clustering algorithm（FCA）.With the application of FCA,the optimal solution can be effectively filtered so as to retain the diversity and the elite of the optimal solution,and avoid the structural re-analysis phenomenon between the two algorithms.The structure design of a high pressure bypass-valve body is used as an example to make a structural optimization by the proposed HGA and finite element method（FEM）,respectively.The comparison result shows that the improved HGA fully considers the characteristic of discrete variable and information of working conditions,and is more suitable to the optimal problems with complex working conditions.Meanwhile,the research provides a new approach for discrete variable structure optimization problems.展开更多
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.
基金supported by Key Program for International S&T Cooperation Projects of China (Grant No. 2009DFA71860)Program for New Century Excellent Talents in Heilongjiang Provincial University of China(Grant No. 1153-NCET-005)
文摘Round method is the common method for discrete variable optimization in optimal design of complex mechanical structures;however,it has some disadvantages such as poor precision,simple model and lacking of working conditions＇ description,etc.To solve these problems,a new model is constructed by defining parameterized fuzzy entropy,and the rationality of parameterized fuzzy entropy is verified.And a new multidirectional searching algorithm is further put forward,which takes information of actual working conditions into consideration and has a powerful local searching capability.Then this new algorithm is combined with the GA by the fuzzy clustering algorithm（FCA）.With the application of FCA,the optimal solution can be effectively filtered so as to retain the diversity and the elite of the optimal solution,and avoid the structural re-analysis phenomenon between the two algorithms.The structure design of a high pressure bypass-valve body is used as an example to make a structural optimization by the proposed HGA and finite element method（FEM）,respectively.The comparison result shows that the improved HGA fully considers the characteristic of discrete variable and information of working conditions,and is more suitable to the optimal problems with complex working conditions.Meanwhile,the research provides a new approach for discrete variable structure optimization problems.
