Fully Completed Spherical Fuzzy Approach-Based Z Numbers (PHI Model) for Enhanced Group Expert Consensus

This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets (SFSs) and Z-Numbers (SFZs). A novel group expert consensus technique, the PHI model, is developed to address the inherent limitations of both SFSs and the traditional Delphi technique, particularly in uncertain, complex scenarios. In such contexts, the accuracy of expert knowledge and the confidence in their judgments are pivotal considerations. This study provides the fundamental operational principles and aggregation operators associated with SFSs and Z-numbers, encompassing weighted geometric and arithmetic operators alongside fully developed operators tailored for SFZs numbers. Subsequently, a case study and comparative analysis are conducted to illustrate the practicality and effectiveness of the proposed operators and methodologies. Integrating the PHI model with SFZs numbers represents a significant advancement in decision-making frameworks reliant on expert input. Further, this combination serves as a comprehensive tool for decision-makers, enabling them to achieve heightened levels of consensus while concurrently assessing the reliability of expert contributions. The case study results demonstrate the PHI model’s utility in resolving complex decision-making scenarios, showcasing its ability to improve consensus-building processes and enhance decision outcomes. Additionally, the comparative analysis highlights the superiority of the integrated approach over traditional methodologies, underscoring its potential to revolutionize decision-making practices in uncertain environments.