New distance measures of complex Fermatean fuzzy sets with applications in decision making and clustering problems

Complex Fermatean fuzzy sets (CFFSs) integrate the ideas of complex fuzzy sets and Fermatean fuzzy sets, where the membership, non-membership, and hesitancy degrees are all complex numbers, allowing the express uncertain information more flexibly and comprehensively. However, how to reasonably measure the discrepancies between CFFSs in decision-making remains an open task. This paper presents a series of new distance measures of CFFSs and their weighted versions based on Hamming, Euclidean, Hausdorff, and Hellinger distances. On this basis, we explore some outstanding properties that the proposed measures satisfy (i.e., boundedness, nondegeneracy, symmetry, and triangular inequality) and demonstrate their effectiveness through several examples. Furthermore, we design a decision-making algorithm as well as a clustering algorithm based on the proposed measures and verify the performance of the proposed measures through several applications.