A Novel Optimized Ranking Function Method of Spherical Fuzzy Multi-Attribute Decision-Making and Application

Compared to intuitive fuzzy sets (IFSs) and Pythagorean fuzzy sets, spherical fuzzy sets (SFSs) more accurately capture the fuzziness and uncertainty inherent in complex problems. SFSs have found extensive applications across numerous fields. To address the common shortcomings of insufficient ranking capabilities and unknown attribute weights in existing ranking methods under spherical fuzzy (SF) environments. By integrating the principles of technique for order preference by similarity to an ideal solution (TOPSIS) method into the ranking function design, an innovative spherical fuzzy number (SFN) ranking function is developed that combines the characteristics of a ranking function while retaining the advantages of the TOPSIS method. Secondly, for scenarios where attribute weight information is completely unknown, this paper develops a weigh calculation method based on the newly proposed ranking function combined with the criteria importance through the intercriteria correlation (CRITIC) method. Using the Lagrange multiplier method to construct an optimization model, a specific formula for determining attribute weights is derived. For scenarios with partially known attribute weights, an optimization model is constructed where the optimal solution corresponds to the desired attribute weight values. Finally, two case studies validate the feasibility and effectiveness of the new ranking function for SFNs, providing theoretical support for addressing multi-attribute decision-making (DM) problems in complex uncertain environments.