Interval Type-2 Fuzzy Neural Network Research Articles

Application of self-learning interval type-2 fuzzy neural network in PM2.5 concentration prediction

Abstract The change of PM2.5 concentration in air quality is nonlinear and difficult to predict. Therefore, a self-learning interval type-2 fuzzy neural network (SLIT2FNN) is proposed. SLIT2FNN has two parts: online structure learning and parameter learning. In structure learning, to improve the training accuracy and speed of the model, the Possibilistic Fuzzy C-Means (PFCM) algorithm is used to process the input data and obtain the number of initial rules before model training. The PFCM algorithm introduces the concept of possibility P to Fuzzy C-Means (FCM), allowing PFCM to overcome the shortcomings of FCM that cannot accurately cluster a large number of nonlinear problems. SLIT2FNN can establish an appropriate number of rules in the preparation stage, and then use the firing strength of the antecedents of the rules to judge whether to generate fuzzy rules for online self-learning, thereby optimizing its network structure. Then, the improved Levenberg–Marquardt (ILM) algorithm is used to modify the relevant parameters of SLIT2FNN. The ILM algorithm can address the challenge of numerous parameters in the Jacobian matrix and complex calculations and improve the calculation speed and adaptive ability of SLIT2FNN parameter learning. Finally, SLIT2FNN is applied to the prediction of air quality PM2.5 concentration, and the performance is compared with other models. The experiment proves that SLIT2FNN has a high prediction accuracy and fast convergence.

Evaluation of Interval Type-2 Fuzzy Neural Super-Twisting Control Applied to Single-Phase Active Power Filters

This research introduces an improved control strategy for an active power filter (APF) system. It utilizes an adaptive super-twisting sliding mode control (STSMC) scheme. The proposed approach integrates an interval type-2 fuzzy neural network with a self-feedback recursive structure (IT2FNN-SFR) to enhance the overall performance of the APF system. The IT2FNN with STSMC proposed here consists of two components, with one being IT2FNN-SFR, which demonstrates robustness for uncertain systems and the ability to utilize historical information. The IT2FNN-SFR estimator is used to approximate the unknown nonlinear function within the APF. Simultaneously, the STSMC component is integrated to reduce system chattering, improving control precision and overall system performance. STSMC combines the robustness and simplicity of traditional sliding mode control, effectively addressing the chattering problem. To mitigate inaccuracies and complexities associated with manual parameter setting, an adaptive law of sliding mode gain is formulated to achieve optimal gain solutions. This adaptive law is designed within the STSMC framework, facilitating parameter optimization. Experimental validation is conducted to verify the harmonic suppression capability of the control strategy. The THD corresponding to the designed control algorithm is 4.16%, which is improved by 1.24% and 0.55% compared to ASMC and STSMC, respectively, which is below the international standard requirement of 5%. Similarly, the designed controller also demonstrates advantages in dynamic performance: when the load decreases, it is 4.72%, outperforming ASMC and STSMC by 1.15% and 0.38%, respectively; when the load increases, it is 3.87%, surpassing ASMC and STSMC by 1.07% and 0.36%, respectively.

Interval Type-2 Fuzzy Neural Network Based on Active Semi-Supervised Learning for Non-Stationary Industrial Processes

Accurate models ensure the efficient and safe operations of industrial processes. However, modeling of industrial processes with non-stationary characteristic is challenging. In this study, an interval type-2 fuzzy neural network (IT2FNN) based on active semi-supervised learning (ASSL-IT2FNN) is proposed for such industrial processes. First, an IT2FNN with adaptive fuzzy membership function (FMF) and hierarchical learning method is utilized to achieve considerable modeling accuracy and efficiency. Second, to better tackle with the non-stationary characteristic, an unsupervised distribution detection method is proposed to identify the occurrence moments of concept drift actively from the perspective of probability and spatial projection. Then, by an active semi-supervised learning method, the concept drift samples with partial labels are used to build a subnetwork, guaranteeing the performance of the constructed IT2FNN models with incomplete data in non-stationary environments. Finally, the proposed ASSL-IT2FNN is verified by benchmark simulations and real industrial data, and the experimental results demonstrate its outperformance. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Concept drift is an important indicator of a non-stationary environment. It manifests as changes in the distribution of samples over time, which may reduce the accuracy of models constructed based on historical samples. This study aims to alleviate the impact of concept drift on model performance in non-stationary industrial processes while reduce the cost of sample labeling. By using the adaptive FMF and hierarchical learning method, the designed IT2FNN can effectively deal with the inherent nonlinearity of complicated industrial processes. The samples representing concept drift are actively identified by the Kullback-Leibler (KL) divergence and maximum mean difference (MMD), enabling timely detections of concept drift moments in unsupervised situations. The active semi-supervised learning is used to adapt the constructed model to handle the concept drift, wherein a subnetwork is designed based on concept drift samples and similar historical samples.

Soft Sensor Modeling of Self-Organizing Interval Type-2 Fuzzy Neural Network Based on Adaptive Quantum-Behaved Particle Swarm Optimization Algorithm

Soft Sensor Modeling of Self-Organizing Interval Type-2 Fuzzy Neural Network Based on Adaptive Quantum-Behaved Particle Swarm Optimization Algorithm

Design and prediction of self-organizing interval type-2 fuzzy wavelet neural network

This paper presents a self-organizing interval type-2 fuzzy wavelet neural network (SIT2FWNN) model for predicting and identifying nonlinear systems. Based on traditional TSK interval type-2 fuzzy neural network (IT2FNN), the proposed SIT2FWNN utilizes the wavelet basis function with the locating abilities of time-domain and frequency-domain as the consequent of fuzzy rules, combining the capacity of IT2FNN to handle the uncertainty and the great learning potentiality of wavelet neural network (WNN). For the structural adjustment of SIT2FWNN, fuzzy rules are added and deleted according to the Euclidean distance between the input layer and the fuzzification layer. The self-organizing algorithm can delete redundant and unimportant fuzzy rules, thus optimizing the structure of SIT2FWNN and simplifying the calculation. In parameter learning, the AdaBound algorithm and self-adaptive gradient learning algorithm are used to find optimal values of unknown parameters of the SIT2FWNN model. Finally, the designed SIT2FWNN model is applied in the predictions of short-term traffic flow, Mackey-Glass time series, and the opening index of the Shanghai stock index. The evaluation comparison between the proposed model and similar studies proves that SIT2FWNN has higher prediction accuracy and speed.

A data-knowledge-driven interval type-2 fuzzy neural network with interpretability and self-adaptive structure

Interval type-2 fuzzy neural networks (IT2FNNs) have gained sustainable attention and wide applications because of their power of adaptive fuzzy modeling. Although the existing models accurately simulate the relationships between inputs and outputs by various adaptive learning algorithms, the parameters and fuzzy rules characterizing the model behaviors no longer have explicit interpretations. To achieve good interpretability and generalization performance, this paper proposes a novel data-knowledge-driven IT2FNN (DKIT2FNN). Unlike accuracy-oriented model fitting, DKIT2FNN pioneers the use of famous association rule mining techniques to automatically explore the interpretable rule knowledge, which intuitively presents conditional relation patterns among features. Using the obtained knowledge, the DKIT2FNN model is accomplished in a single-hidden layer network framework, in which the antecedent structure of each fuzzy rule is determined by the relation patterns provided by rule knowledge. In addition, an adversarial incremental learning algorithm is proposed for the self-organizing modeling of DKIT2FNN. Besides automatically assembling a compact rule base, it integrates the label adversarial training to reinforce the model's capability against label noise. We validate the DKIT2FNN on classification benchmark datasets with label noise and compare it with state-of-the-art non-fuzzy and neuro-fuzzy methods. The results demonstrate that the proposed DKIT2FNN achieves robust classification performance and good interpretability.

Nonsingular Gradient Descent Algorithm for Interval Type-2 Fuzzy Neural Network.

Interval type-2 fuzzy neural network (IT2FNN) is widely used to model nonlinear systems. Unfortunately, the gradient descent-based IT2FNN with uncertain variances always suffers from low convergence speed due to its inherent singularity. To cope with this problem, a nonsingular gradient descent algorithm (NSGDA) is developed to update IT2FNN in this article. First, the widths of type-2 fuzzy rules are transformed into root inverse variances (RIVs) that always satisfy the sufficient condition of differentiability. Second, the singular RIVs are reformulated by the nonsingular Shapley-based matrices associated with type-2 fuzzy rules. It averts the convergence stagnation caused by zero derivatives of singular RIVs, thereby sustaining the gradient convergence. Third, an integrated-form update strategy (IUS) is designed to obtain the derivatives of parameters, including RIVs, centers, weight coefficients, deviations, and proportionality coefficient of IT2FNN. These parameters are packed into multiple subvariable matrices, which are capable to accelerate gradient convergence using parallel calculation instead of sequence iteration. Finally, the experiments showcase that the proposed NSGDA-based IT2FNN can improve the convergence speed through the improved learning algorithm.

Adaptive fuzzy sliding mode control of magnetic levitation system based on Interval Type-2 Fuzzy Neural Network Identification with an Extended Kalman–Bucy filter

The electromagnet levitation control system (EMS) is the core component of the magnetic levitation train. However, its nature is characterized by an inherent instability and strongly nonlinear dynamic. Additionally, modeling uncertainties and numerous exogenous perturbations make the design of the controller even more difficult for this system. To overcome these limitations, a Fuzzy Sliding Mode Control based on Interval Type-2 Fuzzy Neural Network Identification (FSMCF2NN) is designed for the EMS system. The suggested controller has a unique feature that allows the sliding surface and controller effort to be designed by using model-free techniques. As a result, the drawbacks of the conventional SMC schemes, such as the chattering effect, requiring prior knowledge of the system’s uncertainties bounds, and selection of the appropriate control gains, are eliminated. Also, the FSMCF2NN method, since it is designed based on intelligence methods not only minimizes the accumulation of state errors, but also generates the optimum control efforts of the EMS system to ensure stability in different situations. Furthermore, since the measurement of all EMS states is not achievable in reality, a qualified observer is needed to estimate unmeasured states. For this purpose, the Extended Kalman-Bucy filter (EKBF) is selected because of its superiority in managing disturbances for nonlinear systems. Furthermore, to confirm the robustness of the FSMCF2NN scheme in different scenarios, the results of the controller based on Linear Matrix Inequality (LMI), Linear Quadratic Regulation (LQR) controller, and the conventional Sliding Mode Controller (SMC) are compared with the proposed controller. Analyzing the results of simulation demonstrates that maintaining the levitated object is achievable with the proposed control scheme, effectively. At the same time, it attempts to adequately compensate for the uncertainties and disturbances present in the EMS structure.

Anti-lock braking control using an interval type-2 fuzzy neural network scheme for electric vehicles

Control precision and robustness can be regarded as essential challenges of slip ratio control because of the external uncertainties of road conditions and the internal delay response of braking actuators. In addition, it is difficult to obtain a trade-off between braking energy recovery efficiency and braking safety under some extreme braking conditions. To synchronously improve both slip ratio control and braking energy recovery efficiency for different road conditions, an anti-lock braking system (ABS) using a novel interval type-2 fuzzy neural network (IT2FNN) control scheme is proposed for electrohydraulic braking systems. The novel IT2FNN control scheme with five layers is designed to calculate the commanded braking torque. The membership function layer utilizes type-2 fuzzy sets to describe the slip ratio error degree, which enhances the scheme’s anti-interference ability, and the enhanced Karnik-Mendel (EKM) algorithm is used in the type-reduction layer to accelerate computation. Additionally, the network adjusts the parameters of the membership function and rules by decreasing the performance function value corresponding to the braking torque error to improve slip ratio control and enhance the self-adaptation capacity. Simulations showed that IT2FNN control can not only improve slip ratio control performance and decrease the braking torque error but also enhance the energy recovery efficiency of regenerative braking on different road surfaces.

A Comprehensively Improved Interval Type-2 Fuzzy Neural Network for NOx Emissions Prediction in MSWI Process

The accurate and timely prediction of nitrogen oxides (NOx) emissions ensures eco-friendly and efficient operations for municipal solid waste incineration (MSWI) plants. Due to the high nonlinearity and uncertainty in MSWI processes, constructing an efficient prediction model remains challenging. This work proposes a comprehensively improved interval type-2 fuzzy neural network (CI-IT2FNN) for NOx emissions prediction. First, the neighborhood rough set (NRS) is introduced to determine the structure of this fuzzy neural network automatically, including the number of fuzzy rules and their corresponding consequent parameters. Second, an adaptive shape factor is added to the fuzzy membership function to better cope with the uncertainty, which can help to improve the generalization ability of network. Furthermore, to reduce the computational complexity, the Begian-Melek-Mendel (BMM) method is utilized as the defuzzification method in this study. Then, by integrating the linear least square estimation (LSE) and gradient decent (GD), a hierarchical learning algorithm is applied to adjust the network parameters to further enhance the learning efficiency and accuracy. Finally, after being evaluated by a benchmark simulation, the proposed CI-IT2FNN demonstrates its effectiveness and superiority on NOx emissions prediction.

Fractional order sliding mode control for an omni-directional mobile robot based on self-organizing interval type-2 fuzzy neural network

Four-wheeled omnidirectional mobile robots (FM-OMR) are widely used in various fields due to their excellent steering ability and adaptability. As application scenarios expand, higher requirements are placed on their trajectory tracking capabilities. FM-OMR is highly complex and difficult to model accurately, and the system contains uncertainties. Therefore, achieving accurate trajectory tracking in the presence of system uncertainty is a pressing problem. Traditional control methods struggle to accurately estimate uncertainty, and existing controllers often rely on model parameters, resulting in poor transferability. To address this issue, this paper proposes a new control method based on an online self-organizing interval type II fuzzy neural network (SOIT2FNNFSMC). This method employs an online self-organizing algorithm to dynamically compensate for uncertainty, providing greater flexibility and accuracy compared to traditional approximation networks in terms of network construction and approximation performance. A new combined reaching law is proposed based on the characteristics of traditional reaching laws, resulting in improved chattering reduction. Additionally, fractional calculus is introduced to enhance the dynamic characteristics of the controller. Simulation and experimental results demonstrate the effectiveness of this method in achieving precise trajectory tracking while handling uncertainty and not relying on model parameter features. The self-organizing algorithm proposed in this method also provides a reference for the application of SOIT2FNN in FM-OMR.

A smoothing Group Lasso based interval type-2 fuzzy neural network for simultaneous feature selection and system identification

Inspired by the life philosophy, an ingenious gate (membership) function, which can mimic the open and close of the gate in the real world, is proposed to realize feature selection (FS) for interval type-2 fuzzy neural network. Based on the widths of gate functions, a smoothing integrated learning strategy is designed, and in the regularized FS error function the gate widths corresponding to one feature are grouped as one Group Lasso (GL) regularization term. During the training procedure of feature selection, all the group terms with respect to bad features will be punished, but for the good features the corresponding group terms converge to different nonzero values. When feature selection is finished, using the selected features, the interpretable clustering algorithm based initial interval type-2 rule generation method is detailedly introduced firstly, then a simple and efficient memory-based gradient method is presented for the tuning of rule structure parameters. Lastly, employing the simulation results of four regression problems and four classification problems, the effectiveness on simultaneous feature selection and system identification of our proposed model, i.e., the smoothing Group Lasso based interval type-2 fuzzy neural network (SGLIT2FNN), is proved, which illustrates that SGLIT2FNN not only simplifies the model structure by deleting the bad features, but also maintains the performance.

Self-Organizing Interval Type-2 Fuzzy Neural Network Using Information Aggregation Method.

Interval type-2 fuzzy neural networks (IT2FNNs) usually stack adequate fuzzy rules to identify nonlinear systems with high-dimensional inputs, which may result in an explosion of fuzzy rules. To cope with this problem, a self-organizing IT2FNN, based on the information aggregation method (IA-SOIT2FNN), is developed to avoid the explosion of fuzzy rules in this article. First, a relation-aware strategy is proposed to construct rotatable type-2 fuzzy rules (RT2FRs). This strategy uses the individual RT2FR, instead of multiple standard fuzzy rules, to interpret interactive features of high-dimensional inputs. Second, a comprehensive information evaluation mechanism, associated with the interval information and rotation information of RT2FR, is developed to direct the structural adjustment of IA-SOIT2FNN. This mechanism can achieve a compact structure of IA-SOIT2FNN by growing and pruning RT2FRs. Third, a multicriteria-based optimization algorithm is designed to optimize the parameters of IA-SOIT2FNN. The algorithm can simultaneously update the rotatable parameters and the conventional parameters of RT2FR, and further maintain the accuracy of IA-SOIT2FNN. Finally, the experiments showcase that the proposed IA-SOIT2FNN can compete with the state-of-the-art approaches in terms of identification performance.

Adaptive Super-Twisting Sliding Mode Control of Active Power Filter Using Interval Type-2-Fuzzy Neural Networks

Aiming at the unknown uncertainty of an active power filter system in practical operation, combining the advantages of self-feedback structure, interval type-2 fuzzy neural network, and super-twisting sliding mode, an adaptive super-twisting sliding mode control method of interval type-2 fuzzy neural network with self-feedback recursive structure (IT2FNN-SFR STSMC) is proposed in this paper. IT2FNN has an uncertain membership function, which can enhance the nonlinear ability and robustness of the network. The historical information will be stored and utilized by the self-feedback recursive structure (SFR) at runtime. Therefore, the novel IT2FNN-SFR is designed to improve the dynamic approximation effect of the neural network and reduce the dependence of the controller on the actual mathematical model. The adaptive rate of each weight of the neural network is designed by the Lyapunov method and gradient descent (GD) algorithm to ensure the convergence and stability of the system. Super-twisting sliding mode control (STSMC) has strong robustness, which can effectively reduce system chattering, and improve control accuracy and system performance. The gain of the integral term in the STSMC is set as a constant, and the other gain is changed adaptively whose adaptive rate is deduced through the stability proof of the neural network, which greatly reduces the difficulty of parameter adjustment. The harmonic suppression ability of the designed control strategy is verified by simulation experiments.

Refined fault tolerant tracking control of fixed-wing UAVs via fractional calculus and interval type-2 fuzzy neural network under event-triggered communication

The refined fault tolerant tracking control (FTTC) scheme is developed for multiple fixed-wing unmanned aerial vehicles (UAVs) against actuator faults and wind effects under event-triggered communication. To decrease the communication overload caused by the continuous information transmissions among neighboring UAVs, an event-triggered communication mechanism is incorporated to dynamically reduce and increase the triggering frequency at the pre-fault and post-fault phases, respectively, thus reducing the communication burden while ensuring the synchronization tracking performance of faulty UAVs. Moreover, refined FTTC performance with event-triggered communications can be achieved by skillfully invoking fractional-order calculus. Furthermore, interval type-2 fuzzy neural networks with fractional-order adaptive modulation factors are constructed to compensate for the unknown nonlinearities. Lyapunov stability analysis has revealed that all attitudes can synchronously track their references. Simulation results are presented to demonstrate that communication resource-saving refined FTTC performance can be guaranteed with different fractional-order operators.

Self-Organizing Interval Type-2 Fuzzy Neural Network With Adaptive Discriminative Strategy

Covariate shift is a critical issue of interval type-2 fuzzy neural networks (IT2FNNs) due to the distribution discrepancy between training and testing samples. In this situation, IT2FNNs usually struggle to identify potential features from samples with explicit inductive biases. To address this problem, a self-organizing IT2FNN with an adaptive discriminative strategy (ADS-SOIT2FNN) is developed to maintain the identification performance in the presence of covariate shift. First, a granularity-based metric (GM), using higher-order statistics of local samples, is designed to distinguish the distribution discrepancy caused by covariate shift. The multiple kernels incorporated into GM are able to cover the sample features of the whole Hilbert space. Second, a self-organizing strategy, associated with GM-based discriminative information, is presented to alleviate the structural bias by growing and pruning fuzzy rules. Then, a compact structure of ADS-SOIT2FNN is achieved to adapt to the covariate shift of samples and further strengthen its inductive ability. Third, an adaptive risk mitigation learning algorithm (RMLA) is introduced to update the parameters of ADS-SOIT2FNN. RMLA can regulate the derivatives of parameters with arbitrary distribution samples, which is beneficial for maintaining the global accuracy by relieving the risk of parameter biases. Finally, the effectiveness of ADS-SOIT2FNN is verified by some experiments for identifying nonlinear systems with covariate shift.

Self-Organizing Interval Type-2 Fuzzy Neural Network Compensation Control Based on Real-Time Data Information Entropy and Its Application in n-DOF Manipulator.

In order to solve the high-precision motion control problem of the n-degree-of-freedom (n-DOF) manipulator driven by large amount of real-time data, a motion control algorithm based on self-organizing interval type-2 fuzzy neural network error compensation (SOT2-FNNEC) is proposed. The proposed control framework can effectively suppress various types of interference such as base jitter, signal interference, time delay, etc., during the movement of the manipulator. The fuzzy neural network structure and self-organization method are used to realize the online self-organization of fuzzy rules based on control data. The stability of the closed-loop control systems are proved by Lyapunov stability theory. Simulations show that the algorithm is superior to a self-organizing fuzzy error compensation network and conventional sliding mode variable structure control methods in control performance.

Neuroadaptive Optimal Fixed-Time Synchronization and its Circuit Realization for Unidirectionally Coupled FO Self-Sustained Electromechanical Seismograph Systems.

This article investigates the neuroadaptive optimal fixed-time synchronization and its circuit realization along with dynamical analysis for unidirectionally coupled fractional-order (FO) self-sustained electromechanical seismograph systems under subharmonic and superharmonic oscillations. The synchronization model of the coupled FO seismograph system is established based on drive and response seismic detectors. The dynamical analysis reveals this coupled system generating transient chaos and homoclinic/heteroclinic oscillations. The test results of the constructed equivalent analog circuit further testify its complex nonlinear dynamics. Then, a neuroadaptive optimal fixed-time synchronization controller integrated with the FO hyperbolic tangent tracking differentiator (HTTD), interval type-2 fuzzy neural network (IT2FNN) with transformation, and prescribed performance function (PPF) together with the constraint condition is developed in the backstepping recursive design. Furthermore, it is proved that all signals of this closed-loop system are bounded, and the tracking errors fall into a trap of the prescribed constraint along with the minimized cost function. Extensive studies confirm the effectiveness of the proposed scheme.

Advanced Control of Three-Phase PWM Rectifier Using Interval Type-2 Fuzzy Neural Network Optimized by Modified Golden Sine Algorithm

Three-phase Pulse-Width Modulated (PWM) rectifiers used between the power grid and the load in applications requiring DC voltage have features such as high efficiency, high power factor, and low harmonics. This paper proposes a hybrid control approach to improve the dynamic performance of three-phase PWM rectifiers under different operating conditions. Operating conditions are considered as step response, internal disturbance, and regenerative operation. First, Interval Type-2 Fuzzy Neural Network (IT2FNN) is designed and then antecedent and consequent parameters of IT2FNN are optimized with Modified Golden Sine Algorithm (GoldSA-II). The dynamic performance of the hybrid controller, named GoldSA-II-IT2FNN, is analyzed for all operating conditions in Matlab/Simulink environment. The simulation studies are realized to evaluate the performance of the proposed controller. In the simulations, settling times of proposed controller are observed as 27.2 ms, and 10.8 ms for step response, respectively. Moreover, recovery times are calculated as being 12 ms to 5.5 ms for internal disturbance, and 7.2 ms to 19 ms for regenerative operation, respectively. The obtained results demonstrate that the proposed controller not only provides better dynamic performance but also improves the stability of PWM rectifier.

Interval type-2 fuzzy neural networks with asymmetric MFs based on the twice optimization algorithm for nonlinear system identification

This paper proposes a novel algorithm twice optimization for interval type-2 fuzzy neural networks with asymmetric membership functions (TOIT2FNN-AMF), for nonlinear system identification problems. The proposed TOIT2FNN-AMF uses an asymmetric Gaussian interval type-2 membership function to enhance the network’s ability to describe and solve nonlinear and uncertain problems. The twice optimization algorithm consists of structure learning and parameter learning. Firstly, this paper proposes a multi-strategy adaptive differential evolution (MSADE) algorithm as the first optimization algorithm, which is used to determine the structure and the initial values of the parameters of the TOIT2FNN-AMF. It applies the root mean square error (RMSE) of the TOIT2FNN-AMF as the fitness function to determine the structure (number of rules) and initial parameters of the IT2FNN by searching for the RMSE values under different structures. When the fitness value reaches the minimum, that is, the RMSE value of the TOIT2FNN-AMF, the corresponding number will become the optimal one of fuzzy rules of the TOIT2FNN-AMF. Then, the second optimization algorithm of the TOIT2FNN-AMF turns into a hybrid optimization algorithm composed of an adaptive moment estimation (Adam) algorithm and recursive least squares (RLS) algorithm. Adam is used to optimize the antecedent parameters of TOIT2FNN-AMF rules, so as to maintain rapid convergence without generating oscillation during the training process; RLS is used to optimize the consequent parameters of TOIT2FNN-AMF rules, so that the network parameters can be optimized rapidly. In this way, the problems of excessive parameters to be adjusted and excessive slow convergence of the network can be solved. Finally, this paper evaluates the proposed TOIT2FNN-AMF by testing on problems of nonlinear system identification and chaotic time-series prediction. The simulation results are compared with those of similar methods in the existing literatures, which demonstrates that the proposed TOIT2FNN-AMF model yields a lower RMSE value and a simpler network structure than the other type-2 fuzzy neural networks (T2FNNs).