Applications of distance measure between dual hesitant fuzzy sets in medical diagnosis and weighted dual hesitant fuzzy sets in making decision.

This paper introduces a novel distance measure for dual hesitant fuzzy sets (DHFS) and weighted dual hesitant fuzzy sets (WDHFS), with a rigorous proof of the triangular inequality to ensure its mathematical validity. The proposed measure extends the normalized Hamming, generalized, and Euclidean distance measures to dual hesitant fuzzy elements (DHFE), offering a broader framework for handling uncertainty in fuzzy environments. Additionally, the utilization of a score function is shown to simplify the computation of these distance measures.