区间直觉模糊集相似性测度及其在模式识别中的应用(英文)

On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions

定义了区间直觉模糊集相似度的概念,并且基于Hamming距离、标准化的Hamming距离、加权的Hamming Euclidean距离、Euclidean距离、标准化的Euclidean距离、加权的Euclidean距离等,定义了一些区间直觉模糊集距离测度.然后,通过把Hamming距离和Euclidean距离以及它们的加权形式与Hausdorff度量相结合,给出了2种组合的区间直觉模糊集距离测度,即基于Hausdorff度量的加权Hamming距离和基于Hausdorff度量的加权Euclidean距离,并且研究了它们的性质.最后,基于上述距离测度,给出了区间直觉模糊集相似性测度,并且把它们应用于模式识别领域.

The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.