# Determining the Best Dressing Parameters for External Cylindrical Grinding Using MABAC Method
## 3 Determining the Best Alternative in Dressing Process for External Grinding
### Finding the Best Alternative by Using MABAC Method  
The following are the steps to perform MCDM using the MABAC method (see Section 2.1): The initial matrix is generated using Equation (1); after that, the normalized values of \(r_{ij}^{*}\) are determined using formula (2) if the criterion \(j\) is \"the wheel life\"and formula (3) if the criterion \(j\) is\"the surface roughness\" or \"the roundness\". Next, the normalized weighted values \(v_{\bar{y}}\) are calculated using a formula (4). The border approximation area matrix is then computed using Equation (5). After that, using the formula (6), the distance between the alternatives and the border approximation area \(q_{\bar{y}}\) is computed. Finally, the total distances between each alternative and the approximate border area S are then determined using a formula (7). S is maximized to determine the ranking of alternatives. Several calculated parameters and ranking of alternatives are presented in Table 4 when using the MABAC and entropy methods and in Table 5 when using the MABAC and MEREC methods.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Trial.**} & \multicolumn{2}{c}{\(v_{ij}\)} & \multicolumn{3}{c}{\(g_{ij}\)} & \multicolumn{3}{c}{\(q_{ij}\)} & \multirow{2}{*}{**Si**} & \multirow{2}{*}{**Rank**} \\ \cline{2-2} \cline{5-10}  & **Ra** & **T** & **R** & **Ra** & **T** & **R** & **Ra** & **T** & **R** \\ \hline
1 & 0.437 & 0.363 & 0.242 & 0.601 & 0.390 & 0.360 & 0.164 & 0.027 & 0.119 & \(-\)0.310 & 16 \\
2 & 0.505 & 0.351 & 0.336 & 0.601 & 0.390 & 0.360 & 0.096 & 0.039 & 0.025 & \(-\)0.160 & 15 \\
3 & 0.677 & 0.642 & 0.453 & 0.601 & 0.390 & 0.360 & 0.076 & 0.253 & 0.092 & 0.421 & 1 \\
4 & 0.578 & 0.333 & 0.421 & 0.601 & 0.390 & 0.360 & 0.023 & 0.057 & 0.061 & \(-\)0.019 & 9 \\
5 & 0.656 & 0.385 & 0.328 & 0.601 & 0.390 & 0.360 & 0.055 & 0.005 & 0.033 & 0.017 & 8 \\
6 & 0.594 & 0.373 & 0.328 & 0.601 & 0.390 & 0.360 & 0.007 & 0.017 & 0.033 & \(-\)0.057 & 11 \\
7 & 0.694 & 0.353 & 0.484 & 0.601 & 0.390 & 0.360 & 0.094 & 0.037 & 0.123 & 0.180 & 3 \\
8 & 0.621 & 0.366 & 0.437 & 0.601 & 0.390 & 0.360 & 0.020 & 0.024 & 0.077 & 0.072 & 5 \\
9 & 0.595 & 0.500 & 0.320 & 0.601 & 0.390 & 0.360 & 0.005 & 0.110 & 0.040 & 0.064 & 6 \\
10 & 0.677 & 0.422 & 0.406 & 0.601 & 0.390 & 0.360 & 0.077 & 0.032 & 0.045 & 0.154 & 4 \\
11 & 0.592 & 0.376 & 0.351 & 0.601 & 0.390 & 0.360 & 0.009 & 0.014 & 0.009 & \(-\)0.033 & 10 \\
12 & 0.621 & 0.359 & 0.421 & 0.601 & 0.390 & 0.360 & 0.020 & 0.031 & 0.061 & 0.050 & 7 \\
13 & 0.591 & 0.352 & 0.289 & 0.601 & 0.390 & 0.360 & 0.010 & 0.038 & 0.072 & \(-\)0.120 & 14 \\
14 & 0.566 & 0.403 & 0.281 & 0.601 & 0.390 & 0.360 & 0.035 & 0.013 & 0.079 & \(-\)0.101 & 13 \\
15 & 0.679 & 0.438 & 0.421 & 0.601 & 0.390 & 0.360 & 0.078 & 0.048 & 0.061 & 0.187 & 2 \\
16 & 0.591 & 0.321 & 0.351 & 0.601 & 0.390 & 0.360 & 0.010 & 0.069 & 0.009 & \(-\)0.088 & 12 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Calculated results when using MABAC and entropy methods.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Trial.**} & \multicolumn{2}{c}{\(v_{ij}\)} & \multicolumn{3}{c}{\(g_{ij}\)} & \multicolumn{3}{c}{\(q_{ij}\)} & \multirow{2}{*}{**Si**} & \multirow{2}{*}{**Rank**} \\ \cline{2-2} \cline{5-10}  & **Ra** & **T** & **R** & **Ra** & **T** & **R** & **Ra** & **T** & **R** \\ \hline
1 & 0.306 & 0.497 & 0.254 & 0.421 & 0.534 & 0.378 & 0.115 & 0.037 & 0.124 & \(-\)0.276 & 16 \\
2 & 0.354 & 0.481 & 0.352 & 0.421 & 0.534 & 0.378 & 0.067 &