In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fu...In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fuzzy numbers are presented. Meantime, some important properties of them and relationships between them are studied.展开更多
Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squ...Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given.展开更多
The aggregation of fuzzy opinions is an important component of group decision analysis with fuzzy information. This paper proposes two new approaches for the assessment of the weights to be associated with fuzzy opini...The aggregation of fuzzy opinions is an important component of group decision analysis with fuzzy information. This paper proposes two new approaches for the assessment of the weights to be associated with fuzzy opinions. These approaches involve,respectively,the minimization of the sum of squared differences between the individual weighted fuzzy opinion and the weighted mean value of all fuzzy opinions,which is called the weighted minimum variance method (WMVM),and the minimax difference of any two adjacent individual weighted fuzzy opinions,which is called the mean value minimax differences method (MVMDM). The two approaches are developed and numerical examples are presented to illustrate their simplicity and effectiveness in aggregating fuzzy opinions.展开更多
基金The NSF (10971232,60673191,60873055) of Chinathe NSF (8151042001000005,9151026005000002) of Guangdong Province+1 种基金the Guangdong Province Planning Project of Philosophy and Social Sciences (09O-19)the Guangdong Universities Subject Construction Special Foundation
文摘In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fuzzy numbers are presented. Meantime, some important properties of them and relationships between them are studied.
基金The research was supported by the National Natural Science Foundation of China(41204003)Scientific Research Foundation of ECIT(DHBK201113)Scientific Research Foundation of Jiangxi Province Key Laboratory for Digital Land(DLLJ201207)
文摘Through theoretical derivation, some properties of the total least squares estimation are found. The total least squares estimation is the linear transformation of the least squares estimation, and the total least squares estimation is unbiased. The condition number of the total least squares estimation is greater than the least squares estimation, so the total least squares estimation is easier to be affected by the data error than the least squares estimation. Then through the further derivation, the relationships of solutions, residuals and unit weight variance estimations between the total least squares and the least squares are given.
文摘The aggregation of fuzzy opinions is an important component of group decision analysis with fuzzy information. This paper proposes two new approaches for the assessment of the weights to be associated with fuzzy opinions. These approaches involve,respectively,the minimization of the sum of squared differences between the individual weighted fuzzy opinion and the weighted mean value of all fuzzy opinions,which is called the weighted minimum variance method (WMVM),and the minimax difference of any two adjacent individual weighted fuzzy opinions,which is called the mean value minimax differences method (MVMDM). The two approaches are developed and numerical examples are presented to illustrate their simplicity and effectiveness in aggregating fuzzy opinions.
