2D and 3D Jensen–Shannon Divergence Measures of Complex Fermatean Fuzzy Sets: Applications of Pattern Classification, Medical Diagnosis, and CAEM Problems

Complex Fermatean fuzzy sets effectively handle two-dimensional periodic uncertain information through complex-valued membership and nonmembership functions. The role of distance measures becomes pivotal when analyzing such sets, yet existing methodologies, despite extensive research, frequently generate illogical outcomes in various scenarios. However, existing distance measures of complex Fermatean fuzzy sets exhibit counterintuitive results and fail to satisfy fundamental axiomatic properties. Addressing this gap, this study introduces a novel distance measure of complex Fermatean fuzzy sets that incorporates membership, nonmembership, and hesitancy grades while considering both amplitude and phase terms. We rigorously prove that the proposed measures satisfy the properties of a distance function. Besides, based on 2D and 3D Jensen–Shannon divergence measures, we further present a normalized distance measure of complex Fermatean fuzzy sets. Moreover, numerical examples verify that normalized distance measures can obtain more reasonable and superior results. A multiattribute decision-making (MADM) framework is developed to demonstrate practical applicability. Based on the proposed algorithms, a comprehensive methodology involving these proposed measures has been illustrated, along with their implementation in solving different problems in pattern classification and decision-making under uncertainty with periodic characteristics. Additionally, a comparative analysis has been conducted to provide better clarity and understanding of the effectiveness of these measures. The results indicate that the proposed distance measures offer significant advantages and improved accuracy for pattern classification, the computer-aided engineering market, and medical diagnostic problems.