# Soil Classification from Piezoone Penetration Test Using Fuzzy Clustering and Neuro-Fuzzy Theory
## 3 Fuzzy Clustering and Neuro-Fuzzy Modeling
### Neuro-Fuzzy Algorithm
Among the results, the maximum success rate was 79.09% when the triangular membership function, Gaussian membership function, and sigmoidal membership  
Figure 7: Shapes of fuzzy membership functions for input parameters. function were selected as the membership functions for \(q_{t}\), \(R_{f}\), and \(B_{q}\) respectively. The optimized shapes of each membership function after training are shown in Figure 8. \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{**Selected Fuzzy Membership Functions**} & \multicolumn{4}{c}{**Success Rate (\%)**} \\ \hline \(q_{t}\) (MPa) & \(R_{f}\) & \(B_{q}\) & **Clay** & **Silt** & **Sand** & **Average** \\ \hline Triangular & Triangular & 99.88 & 60.31 & 75.61 & 78.60 \\ \hline Triangular & Gaussian & 99.43 & 57.19 & 72.76 & 76.46 \\ \hline Triangular & Bell & 99.58 & 55.31 & 76.83 & 77.24 \\ \hline Triangular & Sigmoidal & 99.63 & 57.81 & 75.61 & 77.68 \\ \hline Gaussian & Triangular & 99.85 & 55.06 & 80.49 & 78.80 \\ \hline Gaussian & Gaussian & 99.43 & 57.19 & 73.58 & 76.73 \\ \hline Gaussian & Bell & 99.63 & 54.38 & 77.24 & 77.08 \\ \hline Gaussian & Sigmoidal & **99.58** & **57.19** & **80.49** & **79.09** \\ \hline Bell & Triangular & 99.38 & 58.44 & 73.98 & 77.27 \\ \hline Bell & Gaussian & 99.48 & 55.94 & 75.61 & 77.01 \\ \hline Bell & Bell & 99.63 & 54.06 & 78.46 & 77.38 \\ \hline Bell & Sigmoidal & 99.60 & 55.94 & 80.89 & 78.81 \\ \hline Sigmoidal & Triangular & 99.43 & 57.5 & 73.98 & 76.97 \\ \hline Sigmoidal & Gaussian & 99.48 & 56.25 & 75.61 & 77.11 \\ \hline Sigmoidal & Bell & 99.58 & 53.13 & 77.24 & 76.65 \\ \hline Sigmoidal & Sigmoidal & 99.58 & 55.31 & 80.89 & 78.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Success rate when using a triangular membership function for \(q_{t}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{2}{c}{**Selected Fuzzy Membership Functions**} & \multicolumn{4}{c}{**Success Rate (\%)**} \\ \hline \(q_{t}\) (MPa) & \(R_{f}\) & \(B_{q}\) & **Clay** & **Silt** & **Sand** & **Average** \\ \hline Triangular & Triangular & 99.60 & 57.19 & 73.98 & 76.92 \\ \hline Triangular & Gaussian & 99.65 & 56.25 & 73.98 & 76.63 \\ \hline Triangular & Bell & 99.43 & 51.25 & 72.36 & 74.35 \\ \hline Triangular & Sigmoidal & 99.48 & 57.19 & 71.95 & 76.21 \\ \hline Gaussian & Triangular & Bad & Bad & Bad & Bad \\ \hline Gaussian & Gaussian & 99.65 & 57.50 & 76.42 & 77.86 \\ \hline Gaussian & Bell & 99.43 & 52.50 & 76.02 & 75.98 \\ \hline Gaussian & Sigmoidal & 99.48 & 55.63 & 78.05 & 77.72 \\ \hline Bell & Triangular & 99.13 & 54.69 & 72.36 & 75.39 \\ \hline Bell & Gaussian & 99.65 & 57.50 & 76.83 & 77.99 \\ \hline Bell & Bell & 99.43 & 52.50 & 74.80 & 75.58 \\ \hline Bell & Sigmoidal & 99.50 & 55.63 & 78.05 & 77.73 \\ \hline Sigmoidal & Triangular & 99.13 & 55.63 & 67.07 & 73.94 \\ \hline Sigmoidal & Gaussian & 99.58 & 55.63 & 76.02 & 77.08 \\ \hline Sigmoidal & Bell & 99.48 & 51.88 & 72.76 & 74.71 \\ \hline Sigmoidal & Sigmoidal & 99.50 & 55.31 & 76.42 & 77.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Success rate when using a Gaussian membership function for \(q_{t}\).