An enhancement of smartphone selection process based on a new 3D Pythagorean fuzzy distance metric via TOPSIS technique

The idea of Pythagorean fuzzy distance metrics (PFDMs) has been used to discuss sundry selection problems. Existing PFDMs often fail to incorporate all three essential parameters of a Pythagorean fuzzy set (PFS), namely; membership degree (MD), non-membership degree (NMD), and hesitation degree (HD), thereby limiting their precision and effectiveness in real-world decision-making situations. To explore this gap, this research presents a novel three-dimensional (3D) weighted distance metric under the Pythagorean fuzzy framework, which integrates MD, NMD, and HD for a more comprehensive representation of imprecision. The proposed PFDM is theoretically validated and it is shown to fulfill the axioms of a distance function. It is then embedded into the technique for order of preference by similarity to ideal solution (TOPSIS) to enhance multi-criteria decision-making (MCDM), particularly in the context of smartphone selection. A comparative analysis against existing PFDMs demonstrates the superior precision and stability of the new approach. Furthermore, a sensitivity analysis of the novel 3D distance model confirms its robustness with respect to changes in criteria weights. This enhanced 3D distance metric provides a more reliable and interpretable tool for decision-makers in decision making fields.