Risk assessment based on a new decision-making approach with fermatean fuzzy sets

Background This study presents a new approach to decision-making based on the selection of decision-makers according to evaluated criteria in multi-criteria decision-making (MCDM) methods. Therefore, sub-decision-maker groups (SDMGs) are created for each evaluated criterion. The SDMG approach, which is created according to the criteria, offers a more flexible and dynamic structure than the existing approaches. This approach aims to use the expertise and knowledge of decision-makers more effectively. The decision-making approach presented in this study offers an innovative model and adds a new dimension to decision-making processes. This decision-making approach is applied to the plastic injection moulding machine risk assessment, as it involves different criteria. In addition to classical risk parameters such as probability, severity, frequency, and detectability, new parameters such as human error, machine error, and existing safety measures are also used in the risk assessment. Methods The integration of the analytic hierarchy process (AHP) and the technique for order preference by similarity to ideal solution (TOPSIS) methods into the interval valued fermatean fuzzy set (IVFFS) environment makes an important contribution to a more comprehensive consideration of risks and uncertainties in the risk assessment process. The IVFF-AHP method is used to weight the risk parameters and determine the hazard scores, and the TOPSIS method is used to rank the hazards. A holistic and systematic approach to risk assessment has been achieved by integrating these two methods. Modelling of these methods is carried out using MATLAB_R2024a software. Results According to the evaluated criteria, it was concluded that the determination of the decision makers separately is applicable to the decision-making process. Identifying the existing safety measures parameter as the most important risk parameter emphasizes the central role of this factor in risk assessment. In addition, machine error and human error parameters are also found to be important in risk assessment. These parameters, which are used for the first time in the literature, offer a broader perspective than traditional methods and provide significant advantages in risk assessment. According to the evaluations, electricity, asphyxiating and toxic gases, and hot water use are determined as the most risky hazards. The sensitivity and comparative analysis performed in the study confirm that the proposed methodology produces consistent and reasonable results.