Distance Measure of Hesitant Fuzzy Sets and its Application in Image Segmentation

Hesitant fuzzy set (HFS) is an important tool to describe uncertainty, and many scholars have proposed some different distance measures which are applied in decision-making. In this paper, based on the feature vector introduced by Zeng et al. (in: 2019 15th International Conference on Computational Intelligence and Security (CIS), 2019), we propose the distance measure of hesitant fuzzy elements (sets), investigate its related properties, develop some novel similarity measures of HFSs, and do comparison analysis with the existing similarity measures of HFSs. Finally, we apply them in image segmentation to illustrate that our distance measures and similarity measures are effective.

Automated summary

In this paper, a distance measure for hesitant fuzzy elements is proposed, and its related properties are investigated. Additionally, some novel similarity measures for hesitant fuzzy sets are developed and compared with existing measures. Finally, these measures are applied to image segmentation to demonstrate their effectiveness.