A novel distance measure for intuitionistic fuzzy sets with its application in pattern classification and decision-making.

A distance measure is crucial for computing the similarity or difference between two objects. Earlier studies proposed various distance measures between the two Intuitionistic Fuzzy Sets (IFSs), but measuring the distance between IFSs is a complex topic that requires substantial research. In this study, a three-dimensional distance measure for IFSs has been suggested. It is often proclaimed that for IFSs, the three-dimensional distance function is not obligatory because the two-dimensional distance function describes the distance between two IFSs in a straightforward and incisive manner. However, this research confirms that the hesitancy degree is a significant contributing element for IFSs. In addition, the difference between the membership functions and the difference between the non-membership functions are other essential factors in calculating the distance between two IFSs. The inclusion of these terms produced outperforming results, and the shortcomings of prevailing distance measures are overcome. The introduced distance measure expression satisfies the axiom definition of the distance measure. Some mathematical characteristics of the suggested distance measure have been discussed. Some numerical examples have been employed to confirm the validity and effectiveness of the proposed measure. Moreover, the suggested distance measure is suitable for medical diagnostic problems, pattern recognition, and decision-making processes. [ABSTRACT FROM AUTHOR]