Gamified approach towards optimizing supplier selection through Pythagorean Fuzzy soft-max aggregation operators for healthcare applications

The soft-max function, a well-known extension of the logistic function, has been extensively utilized in numerous stochastic classification methodologies, such as linear differential analysis, soft-max extrapolation, naive Bayes detectors, and neural networks. The focus of this study is the development of soft-max based fuzzy aggregation operators (AOs) for Pythagorean fuzzy sets (PyFS), capitalizing on the benefits provided by the soft-max function. In addition to introducing these novel AOs, we also present a comprehensive approach to multi-attribute decision-making (MADM) that employs the proposed operators. To demonstrate the efficacy and applicability of our MADM method, we applied it to a real-world problem involving Pythagorean fuzzy data. The analysis of supplier selection has been extensively examined in many academic works as a crucial component of supply chain management (SCM), recognised as a significant MADM challenge. The process of choosing healthcare suppliers is a pivotal element that has the potential to greatly influence the efficacy and calibre of healthcare provisions. In addition, we given a numerical example to rigorously evaluate the accuracy and dependability of the proposed procedures. This examination demonstrates the effectiveness and potential of our proposed soft-max based AOs and their applicability in Pythagorean fuzzy environments.