# Machine Selection for Inventory Tracking with a Continuous Intuitionistic Fuzzy Approach
## 5 Case Study
### Stage 3: Rank Alternatives with CINFU-CODAS
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline  & & **A1** & & **A2** & & **A3** & & **A4** & \\ \hline \multirow{4}{*}{C1} & & \(\xi\) & \(\mu\) & \(v\) & \(\mu\) & \(v\) & \(\mu\) & \(v\) & \(\mu\) & \(v\) \\ \cline{2-10}  & 0.1 & 0.254 & 0.101 & 0.285 & 0.073 & 0.249 & 0.109 & 0.203 & 0.154 \\  & 0.2 & 0.452 & 0.182 & 0.506 & 0.131 & 0.442 & 0.195 & 0.361 & 0.275 \\  & 0.3 & 0.593 & 0.243 & 0.664 & 0.174 & 0.581 & 0.258 & 0.474 & 0.364 \\  & 0.4 & 0.678 & 0.281 & 0.759 & 0.2 & 0.664 & 0.296 & 0.542 & 0.417 \\  & 0.5 & 0.706 & 0.294 & 0.791 & 0.209 & 0.691 & 0.309 & 0.565 & 0.435 \\  & 0.6 & 0.678 & 0.281 & 0.759 & 0.2 & 0.664 & 0.296 & 0.542 & 0.417 \\  & 0.7 & 0.593 & 0.243 & 0.664 & 0.174 & 0.581 & 0.258 & 0.474 & 0.364 \\  & 0.8 & 0.452 & 0.182 & 0.506 & 0.131 & 0.442 & 0.195 & 0.361 & 0.275 \\  & 0.9 & 0.254 & 0.101 & 0.285 & 0.073 & 0.249 & 0.109 & 0.203 & 0.154 \\ \hline \multirow{4}{*}{C2} & & 0.1 & 0.315 & 0.045 & 0.27 & 0.09 & 0.225 & 0.135 & 0.18 & 0.18 \\  & 0.2 & 0.56 & 0.08 & 0.48 & 0.16 & 0.4 & 0.24 & 0.32 & 0.32 \\  & 0.3 & 0.735 & 0.105 & 0.63 & 0.21 & 0.525 & 0.315 & 0.42 & 0.42 \\  & 0.4 & 0.84 & 0.12 & 0.72 & 0.24 & 0.6 & 0.36 & 0.48 & 0.48 \\  & 0.5 & 0.875 & 0.125 & 0.75 & 0.25 & 0.625 & 0.375 & 0.5 & 0.5 \\  & 0.6 & 0.84 & 0.12 & 0.72 & 0.24 & 0.6 & 0.36 & 0.48 & 0.48 \\  & 0.7 & 0.735 & 0.105 & 0.63 & 0.21 & 0.525 & 0.315 & 0.42 & 0.42 \\  & 0.8 & 0.56 & 0.08 & 0.48 & 0.16 & 0.4 & 0.24 & 0.32 & 0.32 \\  & 0.9 & 0.315 & 0.045 & 0.27 & 0.09 & 0.225 & 0.135 & 0.18 & 0.18 \\ \hline \end{tabular}
\end{table} 
Table 12: Aggregated normalized CINFU decision matrix. Then, the weighted normalized CINFU decision matrix was formed from the weights obtained from CINFU AHP. Multiplying the normalized CINFUNs with their respective weights guarantees that criteria with higher weights are a high proportion, showing a more significant influence on the final ranking. The CINFU negative ideal solution (NIS CINFU) represents a theoretical machine that is the worst alternative for all criteria. It was determined by specifying the minimum score values among the weighted normalized alternative evaluations for each criterion using Equation (33) in Table 13. For criterion C1 (Speed) at \(\zeta=0.3\), the NIS CINFU is (\(\mu=0.146\), \(v=0.78\)). This signifies that the worst possible performance in the Speed criterion would have a very low membership degree (0.146) and a very high non-membership degree (0.78), indicating a strong consensus that a machine with such an evaluation would be highly undesirable. Table 14 shows the Taxicab and Euclidean distances of the alternatives of the CINFU negative ideal solution calculated by Equations (34) and (35). A shorter distance, whether Euclidean or Taxicab, implies that the alternative machine is nearer to the ideal solution and away from the NIS, meaning a better overall performance. Experts can evaluate their relative performance by comparing the distances of different alternatives. The expert's optimism level \(\zeta\) is a crucial factor significantly affecting the computed distances. A higher \(\zeta\) value might result in larger distances, representing a more pessimistic perspective where