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. The practical relevance of the proposed measure is demonstrated through its application in medical diagnosis and decision-making processes. A comparative analysis between the newly introduced distance measure denoted as chi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi$$\end{document}, and an existing measure, chi 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi _1$$\end{document} is performed to underscore the superiority and potential advantages of the new approach in real-world scenarios.