A robust multi-criteria supplier selection framework based on linguistic cubic interval-valued intuitionistic fuzzy aggregation operators.

Decision-making (DM) problems in real-world environments are frequently described by ambiguity, expert hesitation, linguistic assessments, and incomplete information, which limit the effectiveness of traditional fuzzy set (FS) and intuitionistic fuzzy set (IFS) frameworks. To deal with such problems, this paper demonstrates an innovative and more expressive model, called linguistic cubic interval-valued intuitionistic fuzzy sets (LCuIVIFSs), which combines interval-valued intuitionistic fuzzy uncertainty, linguistic information, and cubic structures into a single framework. Some traditional operations of the newly defined LCuIVIFS model, such as union, intersection, and complement, are systematically introduced to ensure operational consistency and mathematical soundness. Within the framework of LCuIVIFSs, several aggregation operators (AOs), including arithmetic AO, geometric AO, weighted arithmetic AO, and weighted geometric AO, is presented to significantly combine complex and uncertain information. The key features of the proposed AOs are investigated. Moreover, a novel multi-criteria decision-making (MCDM) technique is developed using the newly defined AOs. To discuss the significance of the proposed approach, it is implemented to a case study of supplier selection problem in smart manufacturing, where both quantitative and qualitative criteria under uncertainty are considered. The final results ensure that the newly defined approach contributes reliable, flexible, and robust decision outcomes compared with existing FS-based models. The proposed study thus provides a valuable decision-support framework for complex DM problems under linguistic and cubic uncertainty.