Spherical Picture Fuzzy Sets: Enhancing Decision-Making with Geometric Bonferroni Methods

The representation of a spherical picture fuzzy set (SPFS) employs a spherical framework to depict uncertainty across positive, negative, and neutral membership functions, effectively capturing the vagueness inherent in these degrees. Through this structure, SPFS enable nuanced decision-making, supported by novel ranking mechanisms, parametric distance measures and Euclidean distance evaluations. Additionally, an extended version of the spherical picture fuzzy Bonferroni method is introduced, tailored to MCDM scenarios. Applied to diverse stakeholder contexts, this approach overcomes the limitations of traditional averaging methods, offering a comprehensive representation of collective opinions within a spherical framework. In contrast to conventional picture fuzz set theories, our research introduces the SPFS, revolutionizing decision-making paradigms with its geometric model.