Decision-making (DMK) problems involve significant uncertainty and imprecision. Although intuitionistic fuzzy sets (IFSs) effectively model quantitative uncertainty, they are limited in representing qualitative judgments expressed by decision makers (DMs). Linguistic intuitionistic fuzzy sets (LIFSs) address this limitation by incorporating qualitative assessments; however, both the IFS and LIFS are insufficient to simultaneously handle certain and uncertain information. To overcome this drawback, set pair analysis (SPA) is integrated into the DMK framework through connection numbers (CNs) comprising identity, discrepancy, and contrary components. In this study, a VIKOR-based multiple attribute decision-making (MADM) method is developed under the LIFS environment incorporating SPA theory and a cosine distance measure. Linguistic intuitionistic fuzzy values (LIFVs) are converted into linguistic connection numbers (LCNs) using numerical scale functions (NSFs) based on linguistic semantics. Two realistic problems-coal mine safety evaluation and cyclone disaster management are used to demonstrate the strength of the proposed approach. These applications highlight the effectiveness of the method in handling complex and uncertain DMK scenarios. The results confirm its practicality and robustness in real-world settings. Comparative and sensitivity analyzes are conducted to assess robustness and the influence of different NSFs and the coefficient of the decision mechanism on the ranking results. The findings confirm that the proposed LIFS-SPA-VIKOR framework provides a stable and reliable solution to complex MADM problems that involve both qualitative and quantitative uncertainty
Kumar et al. (Tue,) studied this question.