## 1 Introduction  
Neural networks (NNs) and fuzzy NNs (FNNs) have been widely applied in various applications involving system identification prediction and control. For example, artificial NNs can be used to accurately predict cemented paste backfill strength [1]. Nonlinear autoregressive functions with an external input NN are combined with Simscape electronic systems to achieve high-accuracy identification in DC motors [2]. In autonomous robot control, fuzzy logic exhibits high toughness and noise-suppressing ability [3]. Reinforcement learning has been used in autonomous driving technology to provide convenience and to avoid crashes caused by driver errors. However, this approach has limited accuracy, and adaptive control is absent [4]. [PERSON] and [PERSON] [5] connected infrared sensors to an adaptive neuro-fuzzy inference system to realize obstacle detection. The steering angle and speed were appropriately adjusted to achieve navigation and collision safety. In intelligent omnidirectional robots, a proportional-integral controller was designed for adjusting the steering angle to a predetermined final desired position to achieve satisfactory navigation and obstacle avoidance [6]. The traditional type-1 fuzzy system (T1 FS) comprises two conceptual components: a set of rules and a reasoning mechanism. The rules contain fuzzy rule definitions; the variable provides a degree of membership for each fuzzy rule. The reasoning mechanism involves counting the degree of membership obtained by each rule to obtain the firing strength [7; 8; 9]. A neural fuzzy system combined with approximation exhibits superior chaotic time-series prediction and is considerably compact when compared with a traditional FNN [10]. However, noise from the environment can adversely affect T1 FS performance [11]. An interval type-2 fuzzy system (IT2 FS) was developed to overcome drawbacks of T1 FS [12]. However, the computational complexity of this system is high. To overcome the computational complexity problem of the IT2 FS, the type-reducer method was used [13]. A type-2 FNN (TZFNN) was applied to an actual wind farm, and the results were simulated to verify the validity and applicability of the approach for accurate wind energy prediction of the power system control center [14]. [PERSON] and [PERSON] [15] and [PERSON] [16] have adopted the IT2 FS for solving control and prediction problems, improving the flexible of the type-2 fuzzy system and the error tolerance of the controller [17]. Furthermore, to reduce the uncertainty caused by large differences between patient parameters, the interval type-2 FNN (IT2 FNN) was used as the controller for surgical anesthesia stimulation, and the backpropagation (BP) algorithm trained the parameters of the IT2 FNN controller online [18]. The BP algorithm exhibits fast convergence and local optimum susceptibility; the steepest descent technique obtains an error function for adjusting the parameters in the network model. Therefore, this process is typically used in the parameter learning process of the FNN [19]. Although the BP algorithm has fast convergence, it is susceptible to the local optimum problem. Therefore, some researchers have adopted evolutionary computation methods to solve the parameter optimization problem [20; 21; 22]. Evolutionary algorithms based on various biological behavior models, such as artificial bee colony (ABC), ant colony optimization (ACO), differential evolution (DE), the whale optimization algorithm (WOA), and particle swarm optimization (PSO), have been derived by observing nature [23; 24; 25]. In this study, PSO was used because of its fast convergence and relatively few parameter settings. These advantages are offset by instability and susceptibility to the local optimum problem. Quantum-based particle swarm optimization (QPSO) can improve on PSO performance. However, the QPSO method is susceptible to premature convergence [26]. Cooperative PSO (CPSO) can obtain a solution set with strong diversity and excellent convergence.