## 3 Proposed Improved Particle Swarm Optimization  
This study proposes an improved PSO method, namely DGCPSO. In DGCPSO, the concept of groups and collaborations are joined to achieve the search ability of traditional PSO. PSO has fast convergence and simple implementation but also has low accuracy, excessively fast convergence, and is susceptible to local  
ptimal solutions in complex problems. Figure 2 depicts the flowchart of DGCPSO. (1) Step 1: Coding  
The parameters of the IT2 FNN are used to encode a particle; each particle is an IT2 FNN. The DGCPSO proposed in this study is used to change the parameters of each IT2 FNN, containing the uncertain mean \([m_{1}^{j},m_{2}^{j}]\), deviation \(\sigma_{i}^{j}\), and link weight in a FLNN \(\omega_{k}^{j}\). The coding format is depicted in Figure 3.  
Figure 3: Coding diagram of particles. Figure 2: Flowchart of dynamic group cooperative particle swarm optimization (DGCPSO). (2) Step 2: Sorting  
All particles are sorted from high to low according to their fitness values, and the group number 0 is the initialization of all particles, as depicted in Figure 4.  
(3) Step 3: Calculate the Similarity Threshold  
Set the current group number to 0 and the highest fitness particle as the leader of the new group; update the group number \(g\) and the initial value of \(g\) to 1, as depicted in Figure 5. Then calculate the similarity threshold of this group, including the average distance and the average fitness. The values are the average distance difference and average fitness value difference between the ungrouped particles (the \(g\) is 0) and the group leader (\(L\)). Here, \(A\)s, \(B\)s are the distance threshold and fitness value threshold of the \(g\)th group, \(L_{j}^{g}\) is the \(j\)th dimension of the \(g\)th group leader, \(F(L\delta)\) is the fitness value of the \(g\)th group leader, \(F\big{(}P^{i}\big{)}\) is the fitness value of the \(i\)th particle, \(N\) is the total number of particles with group number 0 in the current swarm, \(J\) is the dimension of the code, and \(n\) is the total number of particles. The formulas are expressed as follows. \[I^{g}=\sum_{i=1}^{n}\sum_{j=1}^{J}\sqrt{\left(I_{j}^{g}-P_{j}^{i}\right)^{2}}, \text{ if }P^{i}\text{ is ungrouped}, \tag{12}\]  
\[T^{g}=\sum_{i=1}^{n}\Big{|}F(L^{g})-F\big{(}P^{i}\big{)}\Big{|},\text{ if }P^{i}\text{ is ungrouped}, \tag{13}\]  
\[A^{g}(Average_{Distance})=\frac{I^{g}}{N}, \tag{14}\]  
\[B^{g}\left(Average_{Fitness}\right)=\frac{T^{g}}{N}. \tag{15}\]  
(4) Step 4: Particle Grouping  
Sequentially calculate the ungrouped particles using the following formulas to determine the distance difference (\(D^{i}\)) and fitness value difference (\(F^{i}\)) between the particle and the leader particle. \[D^{i}=\sum_{j=1}^{D}\sqrt{\left(I_{j}^{g}-P_{j}^{i}\right)^{2}} \tag{16}\]  
Figure 3:0  
Figure 3:1 Sorting diagram of particles. Figure 3:2 Leading diagram of the new group setting. When \(D^{i}<A^{S}\) and \(F^{i}<B^{S}\), the particles are associated with the group leader, placed in the same particle group, and the group number is updated to \(g\); otherwise, the particle is not classified to the group and no operation is performed (Figure 6). (5) Step 5: Determine Whether to End Grouping  
If ungrouped particles are present, then go back to step 4 and set the highest fitness particle among the ungrouped particles as the leader of the new group. Repeat steps 3 to 4 as depicted in Figure 3:3 If all the particles have been grouped, then the grouping step ends. (6) Step 6: Updating Particles Cooperatively  
CPSO changes the traditional PSO to a P group of one-dimensional vectors, with each group representing one dimension of the original issue. Figure 8 illustrates the flowchart of the CPSO method; instead of a group trying to detect the best P-dimensional vector, which is divided into components to P-group one-dimensional vectors, this study proposes a DGCPSO learning method combining the dynamic group and CPSO to enhance the global search ability to reduce computation time.