We first propose a series of similarity measures for intuitionistic fuzzy values （IFVs） based on the intuitionistic fuzzy operators （Atanassov 1995）. The parameters in the proposed similarity measures can control ...We first propose a series of similarity measures for intuitionistic fuzzy values （IFVs） based on the intuitionistic fuzzy operators （Atanassov 1995）. The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment.展开更多
The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to t...The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.展开更多
基金supported in part by the National Science Fund for Distinguished Young Scholars of China (No.70625005)the National Natural Science Foundation of China (No.71071161)the Program Sponsored for Scientific Innovation Research of College Graduate in Jiangsu Province (No.CX10B_059Z)
文摘We first propose a series of similarity measures for intuitionistic fuzzy values （IFVs） based on the intuitionistic fuzzy operators （Atanassov 1995）. The parameters in the proposed similarity measures can control the degree of membership and the degree of non-membership of an IFV, which can reflect the decision maker’s risk preference. Moreover, we can obtain some known similarity measures when some fixed values are assigned to the parameters. Furthermore, we apply the similarity measures to aggregate IFVs and develop some aggregation operators, such as the intuitionistic fuzzy dependent averaging operator and the intuitionistic fuzzy dependent geometric operator, whose prominent characteristic is that the associated weights only depend on the aggregated intuitionistic fuzzy arguments and can relieve the influence of unfair arguments on the aggregated results. Based on these aggregation operators, we develop some group decision making methods, and finally extend our results to interval-valued intuitionistic fuzzy environment.
基金supported by the National Natural Science Foundation of China(61373174)
文摘The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.
