# Expert System Based on Integrated Fuzzy AHP for Automatic Cutting Tool Selection
## 3 Case Study on Cutting Tool Type Selection  
For a clear explanation, one case study for shoulder milling is given. Suppose that rough milling through a step 120 mm long, 12.3 mm wide, and 10.2 mm deep under the condition of a thin wall (2 mm wall thickness) is required. The initial selection is for a low aspect ratio, small width, top side, light stability, and rough quality. The hierarchy tree is shown in Figure 5. The pair-wise comparison matrix for the main criteria is shown in Table 3. It is obvious that the three selection criteria, including the shape characteristics, workpiece, and feature quality, are key factors in optimal cutting tool type selection. Thus, they have higher importance than others. The workpiece stability and feature quality have the same and highest weights in comparison with the other criteria. The consistency checking process is done using Equations (4) and (5). The \(CR\) value is equal to 0.07, which means the comparison matrix is expected to be consistent. Equations (6) and (7) are applied to determine the geometric means, fuzzy weights, and the normalized weights or priorities for the main criteria, as shown in Table 4. According to the table, the feature quality has the highest weight among the three selection criteria. The power requirement has the lowest weight among all evaluation criteria. The process to obtain the results is shown in Tables 3 and 4. All weights of the selection criteria, evaluation criteria, and alternatives of the developed hierarchy are shown in Table 5. _WS1_, _WS2_, and _WS3_ represent the weights for the main selection criteria, sub-criteria, and sub-sub-criteria, respectively. For example, in the first row, the last five columns represent the weights of five alternatives (SFM, IEM, LEM, SEM, and SAFM) with respect to the shape characteristics (presented in _WS1_) for the aspect ratio (presented in WS2) at a low level (presented in _WS3_). The underlined numbers mean the initial selection, and the bold numbers represent the highest weight of a specific criterion for the case study. Although the solid end mill has the highest weight for five criteria and sub-sub-criteria, the indexable end mill is the best choice for three sub-sub criteria. The indexable end mill, which still has the highest total weight, is the optimal alternative, while the second tool type choice is the solid flat end mill, as shown in Table 6. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Main Criteria** & \multicolumn{2}{c}{\(\widetilde{\mathbf{r_{i}}}\)} & \multicolumn{2}{c}{\(\widetilde{\mathbf{fw_{i}}}\)} & \multicolumn{2}{c}{\(\widetilde{\mathbf{N_{i}}}\)} \\ \hline _SC_ & 1.27 & 1.723 & 2.416 & 0.103 & 0.188 & 0.365 & 0.193 \\ _WS_ & 1.795 & 2.416 & 3.161 & 0.146 & 0.264 & 0.478 & 0.261 \\ _FQ_ & 1.902 & 2.737 & 3.489 & 0.155 & 0.299 & 0.528 & 0.289 \\ _MRC_ & 0.557 & 0.795 & 1.06 & 0.045 & 0.087 & 0.16 & 0.086 \\ _PR_ & 0.266 & 0.334 & 0.469 & 0.022 & 0.036 & 0.071 & 0.038 \\ _TC_ & 0.367 & 0.5 & 0.731 & 0.03 & 0.055 & 0.11 & 0.057 \\ _FE_ & 0.457 & 0.662 & 0.96 & 0.037 & 0.072 & 0.145 & 0.075 \\ \hline \hline \end{tabular} \(\widetilde{\mathbf{r_{i}}}\): geometric mean; \(\widetilde{\mathbf{fw_{i}}}\): fuzzy weight; \(\widetilde{N_{i}}\): normalized weight.  
\end{table} 
Table 4: Geometric means, fuzzy weights, and normalized weights for the main criteria.