A novel distance and similarity measures on hesitant fuzzy sets with applications in pattern recognition

Distance and similarity measures are considered useful tools in a variety of scientific fields such as decision-making, pattern recognition, clustering analysis, medical diagnosis, etc. In this paper, we review the existing distance and similarity measures between hesitant fuzzy sets (HFSs) and show that in some cases they are not logical or efficient. So, we propose some improved distance and similarity measures for HFSs, considering the deviation degree as a hesitancy index for these sets. Comparing our novel measures with some existing distance measures shows that our proposed measures are reasonable and valid.

Keywords:

Hesitant fuzzy set , distance measure , similarity measure , hesitancy index , pattern recognition