Approach to Multi-Attribute Decision Making Based on Spherical Fuzzy Einstein Z-Number Aggregation Information

Spherical fuzzy sets are an enhanced framework of the fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PyFS), and picture fuzzy set (PFS) with the restriction that the total square sum of the membership, indeterminacy, and non-membership degrees must be in 0 and 1. In contrast, the Z-number, a revolutionary idea that captures both the restriction and the reliability of evaluation, is more significant than fuzzy numbers in the fields of decision-making (DM), risk assessment, etc. However, there are still few and insufficient discussions of how to effectively deal with the limitations and reliability of the literature currently in existence. To address this, we first introduced the spherical fuzzy Einstein Z-numbers (SFEZNs), those elements are pairwise comparisons of the decision-makers options. It can be used effectively to make truly ambiguous judgments, reflecting the fuzzy nature, flexibility, and applicability of decision-making data. We present the spherical fuzzy Einstein Z-number weighted aggregation operators and the spherical fuzzy Einstein Z-number weighted geometric operators. We develop a model for spherical fuzzy Einstein Z-number aggregation operators. The main focus of this study is on a technique for handling the issue of multi-attribute decision-making (MADM) effectively and based on one's preferences. We also developed the algorithms for ranking the best options. Finally, we developed the relative comparison and discussion analysis to show the practicability and efficacy of the suggested operators and approaches. The study's findings and implications are discussed.