# Modeling of Fuzzy Systems Based on the Competitive Neural Network
## 5 Conclusions  
In this paper, we have presented a new hybrid method based on a Competitive Neural Network and the Type-1 Fuzzy Inference Systems. The main contribution comprises automatically designing Type-1 FIS, wherein we added three variations in the design of the FIS, specifically, we made a variant in the membership functions and designed FIS with Triangular, Gaussian, and Trapezoidal membership functions, in particular, in the input variables. We also designed two types of FISs, Mamdani and Sugeno, with the three variations mentioned above. CNNT1 FL was applied in the area of data classification and the results can be summarized into three main points. (1) In the Iris dataset, the highest result was achieved by employing the Gaussian MF for both input and output variables. (2) In the Wine dataset, the best mean across all variations was obtained with Sugeno FIS using Gaussian MF; however, the best performing FIS was reached using the Triangular MF as well as Sugeno FIS. (3) The best designed FIS for the WDBC dataset is a Sugeno FIS with Trapezoidal MF. On the other hand, in the comparison we made, we achieved an improvement in the best design of the Mamdani Type-1 FIS, i.e., the three variations obtained a better percent of correct classification than IT2 FCM [6]. For the Sugeno FIS, the results were not satisfactory compared to IT2 FCM; it is important to mention two things: first, we only carried out a comparison with the Iris dataset and the best correct classification percentage because the data are not available in the paper of IT2 FCM [6], i.e., the mean and standard deviation are not documented to carry out a statistics test; second, we neither found quantitative nor qualitative features data and, as mentioned in the previous paragraphs, this results in a disadvantage to the proposed CNNT1 FL method because we are using all the features. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Membership Functions** & **Mamdani FIS** & **Sugeno FIS** \\ \hline IT2 FCM & Gaussian & 65.33 & **94.67** \\ \hline \multirow{3}{*}{CNNT1 FL} & Triangular & **86.67** & 80 \\  & Gaussian & **90** & 89.66 \\ \cline{1-1}  & Trapezoidal & **76.67** & 80 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: FIS comparison between CNNT1 FL and IT2 FCM for the Iris dataset. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**Triangular MF**} & \multicolumn{2}{c}{**Gaussian MF**} & \multicolumn{2}{c}{**Trapezoidal MF**} \\ \cline{2-7}  & **Mean** & **Best** & **Mean** & **Best** & **Mean** & **Best** \\ \hline Iris & 73.33 & 80 & **84.34** & **89.66** & 68.17 & 80 \\ \hline Wine & 49.62 & **80** & **66.46** & 75 & 52.45 & 67 \\ \hline WDBC & 73.17 & 91 & 92.44 & 94.74 & **93.91** & **96** \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Comparative results using Sugeno FIS. In general, we can conclude that the main objective of automatically designing a Type-1 FIS was achieved; according to the results, the Gaussian membership function is the best option for variables in Type-1 FIS, and the Sugeno FIS is the best option for data classification problems. We can also conclude that similarity in data features is very important for correct data classification, for example, in the Wine dataset, the percentage of correct data classification is not high because the thirteen features have a little similarity, namely, the range of data features is highly variable. Finally, as described in the previous paragraph, we have achieved the main objective of this work, highlighting the contribution with the combination of two powerful computing areas using artificial neural networks and fuzzy logic to develop robust methods that can improve results in complex classification problems. In future work, we will be designing the Interval Type-2 FIS or General Type-2 FIS and applying it to similar problems with the objective of carrying out a comparison with CNNTIFL and other state of the art methods as well as improving accuracy.