## 6 Problem Statement
With the goal of realizing a comparison, the three variants of BCO algorithm were used: Original BCO, which is the original method by [PERSON]; BCO + T1 FS, which is the BCO algorithm with type-1 fuzzy system with dynamic adaptation parameters; and BCO + IT2 FS, which is the BCO algorithm with interval type-2 fuzzy system with dynamic adaptation parameters. Results for the BCO and Fuzzy BCO algorithms are presented in Tables 8 and 9. For comparison purposes, there are three variations of PSO, which are described below. All of these variations use the parameters described in Table 5.  
**Original PSO** is the original PSO method with linear decreasing inertia weight. **PSO + T1 FS** is the PSO method with parameter adaptation using the type-1 fuzzy system illustrated in Figure 3.  
**PSO + IT2 FS** is the PSO method with parameter adaptation using the interval type-2 fuzzy system illustrated in Figure 4. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Original BA** & **Proposed BA** \\ \hline Population & 30 & 30 \\ Iterations & 100 & 100 \\ Frequency min & 0 & 0 \\ Frequency max & 2 & 2 \\ Loudness & 0.5 & 0.5 \\ Beta & Random [0, 1] & Dynamic \\ Pulse rate & 0.5 & Dynamic \\ \hline \end{tabular}
\end{table} 
Table 6: Parameters for the BA method original/proposed. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Original BCO** & **Proposed BCO** \\ \hline Population & 30 & 30 \\ Iterations & 100 & 100 \\ Alpha & Random [0, 1] & Dynamic \\ Beta & Random [2, 4] & Dynamic \\ Food Number & 20 & 20 \\ Limit & 100 & 100 \\ \hline \end{tabular}
\end{table} 
Table 7: Parameters for the BCO method original/proposed. Table 10 contains the results of applying the variations of PSO to the optimization of the membership functions from the fuzzy controller illustrated in Figure 9, using the plant without noise shown in Figure 8. In this case, results in bold are the best from all methods on each category. From results in Table 10, the proposed PSO + IT2 FS method obtains the best results on average, best, worst and standard deviation, when compared with the original PSO and PSO + T1 FS. In addition, the PSO + T1 FS obtains better results than the original PSO. Table 11 contains the results of applying the variations of PSO to the optimization of the membership functions from the fuzzy controller illustrated in Figure 9, using the plant with noise shown in Figure 11. Results highlighted in bold are the best from all methods on each category. From the results in Table 11 the proposed PSO + IT2 FS method obtains better results than the other two methods, also PSO + T1 FS obtains better results than original PSO. For comparison, there are three variants of the bat algorithm: Original BA, which is the original method by [PERSON]; BA + T1 FS, which is the bat algorithm with type-1 fuzzy system for dynamical parameter adaptation; and BA + IT2 FS, which is the bat algorithm with interval type-2 fuzzy system for dynamical parameter adaptation. Table 12 contains the results of applying the variations of the BA to the optimization of the membership functions from the fuzzy controller illustrated in Figure 9, using the plant without noise shown in Figure 8.  
Table 13 contains the results of applying the variations of the BA algorithm to the optimization of the membership functions from the fuzzy controller illustrated in Figure 9, using the plant with noise shown in Figure 11.  
After presenting each method separately, we now present two tables to compare the best results from each of the BA, BCO and PSO methods, applied to the optimization of fuzzy controllers for a plant with and without noise. Table 14 contains a comparison of the best methods with the plant without noise. In this case, the best method from Bat Algorithm is the original BA; from Bee Colony Optimization, it is BCO + IT2 FS; and, from Particle Swarm Optimization, it is PSO + IT2 FS.