Uncertainty Decision Modeling Approach for Control Engineering Tools to Support Industrial Cyber-Physical Metaverse Smart Manufacturing Systems

The uncertainty decision modeling of control engineering tools to support industrial cyber-physical metaverse smart manufacturing systems (ICPMSMSs) falls under the multicriteria decision-making problem for three reasons: the presence of multiple industry cyber-physical system (ICPS) components, the importance degree of these components, and the variation in data. It is unfortunate that none of the control engineering tools developed to support ICPMSMS have been able to satisfy all ICPS components, despite the tremendous effort expended. Consequently, selecting the best control engineering tool to support ICPMSMS is a challenging task. Although literature reviews have evaluated control engineering tools, informational ambiguity and uncertainty remain open issues. This study extends fuzzy weighted with zero inconsistency (FWZIC) with interval-valued spherical fuzzy rough sets (IvSFRSs) to weight the components of the ICPS. Then, the developed IvSFRS-FWZIC method is integrated with the PROMETHEE II method to uncertain the modeling of control engineering tools. Results of the IvSFRS-FWZIC revealed that cybersecurity was the most influential component, whereas the digital twin component was the least influential. According to PROMETHEE II results, tool_1, tool_3, and tool_2 achieved the first model among the ten tools. Finally, the robustness of the proposed methods is evaluated by conducting sensitivity and comparative analysis.