Novel complex fuzzy distance measures with hesitance values and their applications in complex decision-making problems.

A complex fuzzy distance measure (CFDMs) plays a significant role in applications involving complex or high-dimensional data where traditional distance measures may not adequately capture the nuances of the data relationships. The significance of CFDMs lies in their ability to handle uncertainty, imprecision, and complexity in various domains. Numerous researchers introduced different concepts of CFDMs, yet these CFDMs fails to convey any information regarding the hesitancy degree associated with an element. The main objective of this paper is to introduce some new distance measures based on complex fuzzy sets, called complex fuzzy hesitance distance measure and complex fuzzy Euclidean Hesitance distance measure, which is the generalization of complex fuzzy normalized Hamming distance measure and complex fuzzy Euclidean distance measure. Some new operations and primay results are discussed in the environment of proposed CFDMs and complex fuzzy operations. Moreover, we discussed the applications of the proposed CFDMs in addressing decision-making problems. We introduced a new decision-making algorithm that integrates CFDMs into decision-making processes, providing a robust methodology for handling real-world complexities. Further, the comparative study of the proposed CFDMs is discussed with some existing CFDMs.