An Intuitionistic Fuzzy Metric and its Application in Varied Decision Making Approaches

Distance measures for Intuitionistic Fuzzy Sets (IFSs) have been extensively studied from a theoretical perspective and successfully applied in various fields, such as pattern recognition, medical diagnosis, and multi-criteria decision-making. However, the literature highlights several shortcomings in these intuitionistic fuzzy distance measures. This paper proposes a novel distance measure for IFSs to address these limitations and fill the identified gaps. The proposed measure is tested through numerical examples to ensure its robustness and reliability. Furthermore, its metric properties are validated using geometric visualization. To demonstrate its practical utility, the measure is applied to problems in pattern classification, medical diagnosis, and multi-criteria group decision-making (MCGDM). A case study related to MCGDM is presented to illustrate the applicability of the proposed method and to compare it with alternative approaches, thus validating its effectiveness.