## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **System Linguistic Variable** & **Variables** & **Linguistic Values** & **Fuzzy Interval** \\ \hline  & & Low & 0.2 3 0 \\
1. & GRC for MT & Medium & 0.2 3 0.5 \\  & & High & 0.2 3 1 \\
2. & GRC for DA & Medium & 0.2 3 0.5 \\  & Input & High & 0.2 3 1 \\
3. & GRC for KW & Medium & 0.2 3 0.5 \\  & & High & 0.2 3 1 \\
4. & & GRC for SR & Medium & 0.2 3 0.5 \\  & & High & 0.2 3 1 \\ \hline  & & Very low & 0.2 3 0 \\
5. & Output & Grey fuzzy relation grade—GFRG & Low & 0.2 3 0.5 \\  & & Medium & 0.2 3 1 \\ \hline \end{tabular}
\end{table} 
Table 6: Inputs, outputs, linguistic values, and fuzzy intervals. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline  & \multicolumn{4}{c}{**Machining Time [s]**} & \multicolumn{4}{c}{**Dimensional Accuracy [mm]**} & \multicolumn{4}{c}{**Kert Width [mm]**} & \multicolumn{4}{c}{**Surface Roughness [mm]**} & \multicolumn{4}{c}{**Relational Grade**} \\ \cline{3-14}
**No. ** & \multicolumn{2}{c}{**Smaller the Better**} & \multicolumn{4}{c}{**Smaller the Better**} & \multicolumn{4}{c}{**Smaller the Better**} & \multicolumn{4}{c}{**Smaller the Better**} & \multicolumn{4}{c}{**Smaller the Better**} & \multicolumn{4}{c}{**Smaller the Better**} \\ \cline{2-14}  & **Norm. ** & **Dev. ** & **GRC** & **Norm. ** & **Dev. ** & **GRC** & **Norm. ** & **Dev. ** & **GRC** & **Norm. ** & **Dev. ** & **GRC** & **GFRG** & **Rank** \\ \hline
1. & 0.9690 & 0.0310 & 0.7259 & 0.3709 & 0.6291 & 0.1153 & 0.3036 & 0.6964 & 0.1054 & 0.8184 & 0.1816 & 0.4671 & 0.218 & 7 \\
2. & 0.9971 & 0.0209 & 0.7972 & 0.1962 & 0.8038 & 0.0926 & 0.1458 & 0.8542 & 0.0876 & 1.0000 & 0.0000 & 0.1000 & 0.498 & 3 \\
3. & 0.9970 & 0.0203 & 0.9643 & 0.0000 & 1.0000 & 0.0758 & 0.0000 & 1.0000 & 0.0758 & 0.6924 & 0.3076 & 0.3410 & 0.142 & 6 \\
4. & 0.9760 & 0.0204 & 0.7775 & 0.9798 & 0.0202 & 0.8024 & 1.0000 & 0.0000 & 1.0000 & 0.6993 & 0.3007 & 0.3470 & 0.728 & 1 \\
5. & 0.9818 & 0.0169 & 0.8288 & 0.9177 & 0.0823 & 0.4993 & 0.9345 & 0.0655 & 0.5561 & 0.5314 & 0.4686 & 0.2535 & 0.501 & 2 \\
6. & 1.0000 & 0.0000 & 1.0000 & 0.8139 & 0.1861 & 0.3058 & 0.8631 & 0.1369 & 0.3746 & 0.0000 & 1.0000 & 0.1373 & 0.497 & 4  
parameters are used for the other input parameters. Figure 6 shows the output membership functions for GFRG. The third phase of the grey fuzzy relationship analysis involves the creation of fuzzy rules according to the experimental design. After determining the fuzzification, the input data with the conditions of the rules are determined and evaluated. The essential part of the fuzzy rule inference system is a set of IF-THEN linguistic rules that have the form  
Figure 5: Example of Gbell membership function of GRC for MT. Figure 6: Example of Gbell membership function of GFRG. \"If (GRC_MT is HIGH) and (GRC_DA is LOW) and (GRC_KW is LOW) and (GRC_SR is MEDIUM) then (GFRG is LOW)\", where the first four terms in parentheses (antecedents) are grey relational coefficients containing linguistic variables. The fifth parenthesis represents the consequence. Starting from a larger grey relational coefficient indicating better performance characteristics, nine fuzzy rules are formed as shown in Table 7.  
Between antecedents, the AND operator is used. Two built-in AND methods are supported in the fuzzy logic toolbox: MIN (minimum) and PROD (product). When building the fuzzy model, both methods were tried, but the MIN operator resulted in a higher GFRG coefficient. Moreover, better results were obtained by using PROD implication method and SUM aggregation. Finally, the area centroid defuzzification technique is applied to convert the fuzzy numbers into crisp real numbers. The value of the fuzzy numbers can be found in the penultimate column of Table 6. Table 8 shows the characteristics of the fuzzy inference system used to calculate the GFRG. One of the advantages of the fuzzy model is the 3D representation, which can also be used for easier decision making, especially when a large amount of data are involved.