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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>χ</mml:mi></mml:math> , and an existing measure, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>χ</mml:mi> <mml:mn>1</mml:mn></mml:msub> </mml:math> is performed to underscore the superiority and potential advantages of the new approach in real-world scenarios.