# Modeling of Fuzzy Systems Based on the Competitive Neural Network
## 4 Experimental Results
### Mamdani FIS  
Table 5 shows the results obtained with the Mamdani FIS for the Iris dataset with the Triangular, Gaussian, and Trapezoidal MFs. The best results are shown in bold. The best results for the Iris dataset applying the Mamdani FIS were obtained using the Gaussian MF with a mean value of 81.29% and a classifier result of 90%. Figure 6 shows the results of the best classifier, correctly classifying 27 out of 30 in the test dataset. The Iris dataset has four features: Length sepals, width sepals, length, and width petals; therefore, the Mamdani FIS has four input variables, as illustrated in Figure 7.  
Figure 8 presents the output variable of the Mamdani FIS, which has three membership functions because the Iris dataset has three different classes for classification. The three fuzzy rules used in the Mamdani FIS are the following:  
1. If (Length Sepals is Cluster1) and (Width Sepals is Cluster1) and (Length Petals is Cluster1) and (Width Petals is Cluster1), then (Classification is Class 1). 2. If (Length Sepals is Cluster2) and (Width Sepals is Cluster2) and (Length Petals is Cluster2) and (Width Petals is Cluster2), then (Classification is Class 2). 3. If (Length Sepals is Cluster3) and (Width Sepals is Cluster3) and (Length Petals is Cluster3) and (Width Petals is Cluster3), then (Classification is Class 3). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Membership Functions** & **Mean** & **STD** & **Best** & **Worst** \\ \hline Triangular & 75.59 & 4.16 & 86.67 & 70 \\ Gaussian & **81.29** & 5.21 & **90** & 70 \\ Trapezoidal & 70.97 & 4.57 & 76.67 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mamdani FIS results for the Iris dataset. Figure 6: Test data for the Iris dataset with Mamdani FIS. The results obtained for the Wine dataset is using the Gaussian membership function with 74.29% based on 26 out of 35 correct classifications in the test dataset, as shown in Figure 9. Figures 10-13 illustrate the input variables which represent the 13 features of the Wine dataset, these are divided into parts 1, 2, 3, and 4, respectively and Figure 14 presents the output variable with two classes. Similarly, in the Iris dataset, the Wine dataset has three classes; therefore, in Mamdani FIS, three fuzzy rules are used, which are presented below:  
1. If (Alcohol is Cluster1) and (Malic acid is Cluster1) and (Ash is Cluster1) and (Alcalinity of ash is Cluster1) and (Magnesium is Cluster1) and (Total phenols is Cluster1) and (Flavanoids is Cluster1) and (Nonflavanoid phenols is Cluster1) and (Proanthocyanins is Cluster1) and (Color intensity is Cluster1) and (Hue is Cluster1) and (OD280/OD315 of diluted wines is Cluster1) and (Proline is Cluster1), then (Classification is Class 1). 2. If (Alcohol is Cluster2) and (Malic acid is Cluster2) and (Ash is Cluster2) and (Alcalinity of ash is Cluster2) and (Magnesium is Cluster2) and (Total phenols is Cluster2) and (Flavanoids is Cluster2) and (Nonflavanoid phenols is Cluster2) and (Proanthocyanins is Cluster2) and (Color intensity is Cluster2) and (Hue is Cluster2) and (OD280/OD315 of diluted wines is Cluster2) and (Proline is Cluster2), then (Classification is Class 2). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Membership Functions** & **Mean** & **STD** & **Best** & **Worst** \\ \hline Triangular & 48.53 & 14.46 & 72.22 & 33.33 \\ Gaussian & 63.21 & 9.16 & 74.29 & 36.11 \\ Trapezoidal & 51.76 & 10.35 & 68.57 & 44.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Mamdani FIS results for the Wine dataset. Figure 8: Output variable of the Mamdani FIS. Figure 7: Input variables of the Mamdani FIS. 3. If (Alcohol is Cluster3) and (Malic acid is Cluster3) and (Ash is Cluster3) and (Alcalinity of ash is Cluster3) and (Magnesium is Cluster3) and (Total phenols is Cluster3) and (Flavanoids is Cluster3) and (Nonflavanoid phenols is Cluster3) and (Proanthocyanins is Cluster3) and (Color intensity is Cluster3) and (Hue is Cluster3) and (OD280/OD315 of diluted wines is Cluster3) and (Proline is Cluster3), then (Classification is Class 3).