Abstract

One of the most powerful aggregation factors is the Heronian Mean (HM) factor, which is based on studying the mutual relationships between the input elements and has been applied on a wide scale by decision makers in the case of multi-criteria decision-making (MCDM) problems in uncertain environments. Despite their usefulness, HM operators face some significant limitations in expressing complex relationships between input variables and are sometimes hampered by incomplete information management. To address such limitations, this study presents a new decision-making approach bas0ed on the Shapley fuzzy metric (SFM) and an improved generalized weighted HM operator (IGWHM) in the context of α-cut neutrosophic z-numbers (α-NZNs). This improved technique combines z-number theory, neutrosophic logic, and α-cut analysis. This approach promotes a more accurate and scalable means of representing uncertainty and reliability by defining α-cut neutrosophic z-numbers across different alpha levels. This reduces information loss during reasoning and enhances the capture of complex relationships between decision criteria. Therefore, this study introduces new operator: α-cut neuromorphic z- numbers Shapley improved generalized weighted Heronian mean (α-NZN-SIGWHM). This operator introduces the Shapley fuzzy value with Shapley mean in the α-NZN environment, providing an effective solution to MCDM problems based on inaccurate data. Furthermore, the influence of k and g on the clustering results is tested, observing their significant impact on decision-making outcomes. Finally, a numerical case study is presented and fully implemented to validate the effectiveness of the proposed method. The results confirm the consistency of the classifications obtained using different parameters. Overall, the results demonstrate that the proposed approach based on α-NZN performs effectively across decision criteria, providing a more comprehensive and reliable tool for solving complex real-world MCDM problems.