# Machine Selection for Inventory Tracking with a Continuous Intuitionistic Fuzzy Approach
## 5 Case Study
### Stage 2: Determine Criteria Weights with CINFU-AHP
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** \\ \hline C1 & (0, 0) & (0.222, 0.264) & (0.34, 0.454) & (0.317, 0.344) & (0.127, 0.21) & (0.502, 0.578) \\ C2 & (\(-\)0.264, \(-\)0.222) & (0, 0) & (0.023, 0.139) & (0.4, 0.411) & (\(-\)0.373, \(-\)0.203) & (0.142, 0.284) \\ C3 & (\(-\)0.428, \(-\)0.315) & (\(-\)0.13, \(-\)0.003) & (0, 0) & (0.094, 0.238) & (\(-\)0.326, \(-\)0.305) & (0.053, 0.118) \\ C4 & (\(-\)0.329, \(-\)0.3) & (\(-\)0.394, \(-\)0.384) & (\(-\)0.23, \(-\)0.074) & (0, 0) & (\(-\)0.558, \(-\)0.194) & (\(-\)0.327, \(-\)0.093) \\ C5 & (\(-\)0.192, \(-\)0.119) & (0.238, 0.388) & (0.318, 0.342) & (0.228, 0.568) & (0, 0) & (0.237, 0.361) \\ C6 & (\(-\)0.517, \(-\)0.459) & (\(-\)0.277, \(-\)0.135) & (\(-\)0.102, \(-\)0.027) & (0.094, 0.329) & (\(-\)0.337, \(-\)0.221) & (0, 0) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Score judgment matrix. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** \\ \hline C1 & (1, 1) & (1.666, 1.836) & (2.19, 2.847) & (1.99, 2.207) & (1.32, 1.555) & (3.175, 3.782) \\ C2 & (0.545, 0.6) & (1, 1) & (1.055, 1.348) & (2.421, 2.578) & (0.409, 0.578) & (1.387, 1.923) \\ C3 & (0.373, 0.484) & (0.726, 0.948) & (1, 1) & (1.187, 1.728) & (0.455, 0.481) & (1.129, 1.313) \\ C4 & (0.469, 0.502) & (0.388, 0.398) & (0.589, 0.805) & (1, 1) & (0.271, 0.591) & (0.471, 0.807) \\ C5 & (0.643, 0.761) & (1.594, 2.363) & (2.08, 2.116) & (1.562, 3.696) & (1, 1) & (1.725, 2.296) \\ C6 & (0.304, 0.348) & (0.520, 0.721) & (0.79, 0.886) & (1.239, 2.124) & (0.436, 0.601) & (1, 1) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Interval multiplicative matrix. Table 8 shows the priority vector, calculating the interval \(\bar{\omega}_{j}\) of the criteria based on Table 7 by utilizing Equation (25). This equation aggregates the multiplicative relationships produced from the interval multiplicative matrix (Table 7) to calculate the interval weights for each criterion. Table 9 gives the possibility degree matrix obtained by comparing the priority vector for each criterion based on Table 8 using Equation (26). This matrix seeks to determine the possible overlapping and uncertainty inherent in the interval weights. For example, the priority vector for criterion C1 (Speed) is (0.229, 0.330). This interval indicates that the weight assigned to Speed in the machine selection process could fall between 0.229 and 0.330. For instance, the cell corresponding to C1 (Speed) and C2 (Setup Time) with a value of 1 suggests that Speed can be considered to be 100% more important than Setup Time based on the priority vectors. Then, the prioritized possibility degrees were originated by employing Equation (27), and the normalized criteria weights were obtained by Equation (28), which yields the crisp numerical weights to each criterion from the possibility degree matrix, as shown in Table 10. For example, the normalized weight for C1 (Speed) is 0.25, which indicates that Speed has a 25% weight in the overall machine selection decision.