On Similarity Measures of interval-valued Intuitionistic Fuzzy Sets and Their Application to Pattern Recognitions

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 IVIESs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.