# Hybrid Learning for General Type-2 TSK Fuzzy Logic Systems
## 4 Experimentation and Results Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{1}{c}{**Proposed Hybrid Learning Technique**} & \multirow{2}{*}{**FCM**} & \multirow{2}{*}{**Subtractive**} & \multirow{2}{*}{**Decision**} & \multirow{2}{*}{**SVM**} & \multirow{2}{*}{**KNN**} & \multirow{2}{*}{**Naive**} \\  & \multicolumn{2}{c}{**Hybrid Learning**} & & & & & \\  & \multicolumn{2}{c}{**Technique**} & & & & & \\ \hline \multirow{2}{*}{Iris} & 95.7880 & 85.5004 & 96.1394 & 95.0559 & - & 94.8267 & 94.8515 \\  & (1.4738) & (4.4088) & (1.7889) & (3.1016) & - & (1.8996) & (2.4019) \\ \hline \multirow{2}{*}{Wine} & 87.5556 & 67.2222 & 74.2222 & 88.2963 & - & 70.2593 & 96.5926 \\  & (8.0889) & (6.2489) & (13.09) & (5.5401) & - & (4.4034) & (2.1084) \\ \hline \multirow{2}{*}{Breast} & 95.5861 & 93.2998 & 94.1186 & 91.6426 & 94.9867 & 93.4189 & 94.7079 \\  & (1.1888) & (1.6142) & (1.121) & (2.4014) & (1.2044) & (1.5414) & (1.3952) \\ \hline \multirow{2}{*}{Glass chemical} & 90.6983 & 89.5373 & 90.6164 & 90.7540 & 91.3606 & 93.0778 & 89.8460 \\  & (1.9856) & (2.9519) & (2.9945) & (2.3476) & (3.165) & (2.8169) & (3.055) \\ \hline \multirow{2}{*}{Crab gender} & 95.5000 & 50.3000 & 90.7667 & 79.1333 & 94.1000 & 83.7000 & 63.4667 \\  & (1.6132) & (3.2641) & (3.3211) & (4.3366) & (2.1804) & (3.8411) & (10.7027) \\ \hline \multirow{2}{*}{Huberman survival} & 74.4116 & 72.4723 & 71.0549 In Table 4, an experiment to demonstrate that the value of \(\rho\) has no effect whatsoever in the classification performance of the proposed hybrid learning technique is shown. Two datasets were chosen at random with 60% training data and 40% testing data, with \(\rho=[0,\ 0.5,\ 1,\ 2]\). To achieve a truer experiment when comparing chosen \(\rho\) values, the exact same training data and testing data was used, i.e., with each execution run, data was not randomly separated into a 60/40 partition; instead, the partition was fixed with exact data in each experiment, and only the value of \(\rho\) was changed. As a visual example, the input partition for the iris dataset modeled by a GT2 TSK FLS which obtained the given result in Table 2, is shown in Figures 7-10, where a top and orthogonal view can be seen; in all accounts, the amount of uncertainty within each membership function is quite contrasting, as there are membership functions with barely any uncertainty and also membership functions with quite a lot of uncertainty. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{4}{c}{\(\rho\)} \\ \cline{2-5}  & **0** & **0.5** & **1** & **2** \\ \hline Breast cancer & 94.6939 & 94.6939 & 94.6939 & 94.6939 \\ Qualitative bankruptcy & 98.7342 & 98.7342 & 98.7342 & 98.7342 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Demonstration that varying \(\rho\) values have no effect on classification performance. Figure 8: Input partition of the GT2 TSK FLS for the second input of the iris dataset, where (**a**) shows a top view of the GT2 membership functions; and (**b**) shows an orthogonal view of the same GT2 membership functions. Figure 7: Input partition of the GT2 TSK fuzzy logic system (FLS) for the first input of the iris dataset, where (**a**) shows a top view of the GT2 membership functions; and (**b**) shows an orthogonal view of the same GT2 membership functions. It must also be noted that there are a couple of variables where classification performance could be improved. First, as the initial hybrid learning technique requires prototype centers to begin constructing the GT2 FSs around them, if better prototypes are found, then the classification performance is also bound to improve; for the included experimentation in this paper, a FCM clustering algorithm was used to obtain the initial prototypes, yet other techniques could be used to improve the final classification performance by providing better quality initial prototypes. As is known, different techniques perform differently with each dataset, therefore by changing this part of the proposed hybrid algorithm, better results could be expected.