Novel distance and similarity measures on hesitant fuzzy linguistic term sets with application to pattern recognition

As two important features of hesitant fuzzy linguistic term sets (HFLTSs), distance and similarity measures have been applied widely in many fields such as pattern recognition, decision making and prediction. Through analyzing the existing distance and similarity measures on HFLTSs, we find that they are not reasonable in some cases. Therefore, we first define the hesitance degree on HFLTSs to reflect the hesitant degree among several linguistic terms. On the basis of hesitance degree on HFLTSs, we develop several novel distance measures and further discuss their properties. Afterwards, several similarity measures based on hesitance degree are proposed and applied to pattern recognition. By comparing our novel proposed distance and similarity measures with the existing methods and giving an example of pattern recognition, we prove that our proposed distance and similarity measures are more reliable than the previous method in some cases.