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

Abstract

Abstract 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 $$\chi$$ χ , and an existing measure, $$\chi _1$$ χ 1 is performed to underscore the superiority and potential advantages of the new approach in real-world scenarios.

Keywords

• Metric axioms
• Dual hesitant fuzzy sets
• Hesitancy degree
• Fuzzy logic
• Decision making
• Medical diagnosis