Establishment of distance measures on Fermatean fuzzy sets and their applications in pattern classification and multi-attribute decision-making

As an advanced extension of intuitionistic fuzzy sets (IFSs), Fermatean fuzzy sets (FFSs) serve as powerful methods for managing uncertainties in complicated problem-solving contexts. When working with Fermatean fuzzy information, distance measures are fundamental in measuring the differences between two FFSs. These measures are essential to accurately assess and compare the variations in fuzzy data. However, accurately measuring the distance between two FFSs is still challenging and requires further exploration. We propose two novel distance measures for FFSs. Moreover, we demonstrate that the proposed distance measures meet the necessary axiomatic conditions. Afterwards, we present numerical examples to highlight the superiority of the proposed measures compared to those already available. Finally, we apply the proposed distance measures to pattern classification and multi-attribute decision-making (MADM) problems. Experimental results show that the proposed measures improve classification performance and decision-making efficiency. Specifically, they enhance pattern recognition in autonomous driving systems and improve strategic investment decision-making in sustainable transportation.