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 clustering 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
The problem of measuring conflict in large-group decision making is examined with every decision preference expressed by multiple interval intuitionistic trapezoidal fuzzy numbers （IITFNs）. First, a distance measure...The problem of measuring conflict in large-group decision making is examined with every decision preference expressed by multiple interval intuitionistic trapezoidal fuzzy numbers （IITFNs）. First, a distance measurement between two IITFNs is given and a function of conflict between two members of the large group is proposed. Second, members of the large group are clustered. A measurement model of group conflict, which is applied to aggregating large-group preferences, is then proposed by employing the conflict measure of clusters. Finally, a simulation example is presented to validate the models. These models can deal with the preference analysis and coordination of a large-group decision, and are thus applicable to emergency group decision making.展开更多
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
提出了一种基于改进Hamming-Hausdorff距离的区间直觉模糊知识测度(interval-valued intuitionistic fuzzy knowledge measure,IVIFKM),并应用于图像阈值分割中,获得了更好的图像分割结果.最新研究成果表明,直觉模糊环境下的知识度量包...提出了一种基于改进Hamming-Hausdorff距离的区间直觉模糊知识测度(interval-valued intuitionistic fuzzy knowledge measure,IVIFKM),并应用于图像阈值分割中,获得了更好的图像分割结果.最新研究成果表明,直觉模糊环境下的知识度量包括两个重要方面,即信息量与信息清晰度.基于这种理解,提出新的区间直觉模糊知识测度公理系统.同时,改进并推广标准Hamming-Hausdorff距离,结合理想解法(technique for order preference by similarity to ideal solution,TOPSIS),建立新的满足所提公理系统要求的区间直觉模糊知识测度.随后,将所提测度模型应用于图像阈值分割中,并根据区间直觉模糊集自身结构特点,进一步提出一种精炼而高效的像素分类规则及图像区间直觉模糊化算法.最后,利用所提测度模型计算图像的区间直觉模糊知识量,确定最佳分割阈值,实现图像分割.实验结果表明,该基于知识驱动的图像阈值分割方法性能表现稳定、可靠,所生成的二值图具有更加优良的性能指标,明显优于其他同类算法.将知识测度新理论引入图像处理领域,为该理论在其他相关领域的潜在应用提供了实例.展开更多
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 clustering 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.
基金supported by a grant from the International Scholar Exchange Fellowship(2011-2012) of the Korea Foundation for Advanced StudiesNatural Science Foundation of China(71171202,71171201)+1 种基金the Science Foundation for National Innovation Research Group of China(71221061)the International Cooperation Major Project of the National Natural Science Foundation of China(71210003)
文摘The problem of measuring conflict in large-group decision making is examined with every decision preference expressed by multiple interval intuitionistic trapezoidal fuzzy numbers （IITFNs）. First, a distance measurement between two IITFNs is given and a function of conflict between two members of the large group is proposed. Second, members of the large group are clustered. A measurement model of group conflict, which is applied to aggregating large-group preferences, is then proposed by employing the conflict measure of clusters. Finally, a simulation example is presented to validate the models. These models can deal with the preference analysis and coordination of a large-group decision, and are thus applicable to emergency group decision making.
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.
文摘提出了一种基于改进Hamming-Hausdorff距离的区间直觉模糊知识测度(interval-valued intuitionistic fuzzy knowledge measure,IVIFKM),并应用于图像阈值分割中,获得了更好的图像分割结果.最新研究成果表明,直觉模糊环境下的知识度量包括两个重要方面,即信息量与信息清晰度.基于这种理解,提出新的区间直觉模糊知识测度公理系统.同时,改进并推广标准Hamming-Hausdorff距离,结合理想解法(technique for order preference by similarity to ideal solution,TOPSIS),建立新的满足所提公理系统要求的区间直觉模糊知识测度.随后,将所提测度模型应用于图像阈值分割中,并根据区间直觉模糊集自身结构特点,进一步提出一种精炼而高效的像素分类规则及图像区间直觉模糊化算法.最后,利用所提测度模型计算图像的区间直觉模糊知识量,确定最佳分割阈值,实现图像分割.实验结果表明,该基于知识驱动的图像阈值分割方法性能表现稳定、可靠,所生成的二值图具有更加优良的性能指标,明显优于其他同类算法.将知识测度新理论引入图像处理领域,为该理论在其他相关领域的潜在应用提供了实例.
