Simplified interval type-2 fuzzy neural networks

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.

Data-Knowledge-Driven Self-Organizing Fuzzy Neural Network

Fuzzy neural networks (FNNs) hold the advantages of knowledge leveraging and adaptive learning, which have been widely used in nonlinear system modeling. However, it is difficult for FNNs to obtain the appropriate structure in the situation of insufficient data, which limits its generalization performance. To solve this problem, a data-knowledge-driven self-organizing FNN (DK-SOFNN) with a structure compensation strategy and a parameter reinforcement mechanism is proposed in this article. First, a structure compensation strategy is proposed to mine structural information from empirical knowledge to learn the structure of DK-SOFNN. Then, a complete model structure can be acquired by sufficient structural information. Second, a parameter reinforcement mechanism is developed to determine the parameter evolution direction of DK-SOFNN that is most suitable for the current model structure. Then, a robust model can be obtained by the interaction between parameters and dynamic structure. Finally, the proposed DK-SOFNN is theoretically analyzed on the fixed structure case and dynamic structure case. Then, the convergence conditions can be obtained to guide practical applications. The merits of DK-SOFNN are demonstrated by some benchmark problems and industrial applications.

Recurrent general type-2 fuzzy neural networks for nonlinear dynamic systems identification

This paper introduces a recurrent general type-2 Takagi-Sugeno-Kang fuzzy neural network (RGT2-TSKFNN) for the identification of nonlinear systems. In the proposed structure, the general type-2 fuzzy set (GT2FS) and a recurrent fuzzy neural network (RFNN) are combined to obviate the data uncertainties. The fuzzy firing strengths in the developed structure are returned to the network input as internal variables. In the proposed structure, GT2FS is utilized to characterize the antecedent parts while the consequent parts are performed using TSK type. The issues of constructing a RGT2-TSKFNN involve type reduction, structure learning as well as parameter learning. An efficient strategy is developed by utilizing alpha-cuts to decompose a GT2FS into several interval type-2 fuzzy sets (IT2FSs). In order to solve the computation time of the type-reduction issue, a direct defuzzification method is used instead of iterative nature of Karnik-Mendel​ (KM) algorithm. Type-2 fuzzy clustering and Lyapunov criteria are utilized for online structure learning as well as the antecedent and consequent parameters, respectively for reducing the number of rules and guaranteeing the stability of the proposed RGT2-TSKFNN. The reported comparative analysis of the simulation results is utilized to estimate the performance of the proposed RGT2-TSKFNN with respect to other popular type-2 FNNs (T2FNNs) methodologies.

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.

Design of an interval type-2 fuzzy neural network sliding mode robust controller for higher stability of magnetic spacecraft attitude control

This paper designs an interval type-2 fuzzy neural network sliding mode robust controller (IT2FNNSMRC) to improve the stability of the vibrational angle of the orbital plane in magnetic rigid spacecraft attitude control. The control system consists of an interval type-2 fuzzy neural network (IT2FNN) controller, a PD controller, and a robust controller in parallel connection. The IT2FNN controller, as a nonlinear regulator, compensates the nonlinearity of the controlled object; the PD controller, as a feedback controller, ensures the global asymptotic stability of the control system; the robust controller inhibits input load disturbance. The IT2FNN controller hereof has a self-organizing function which enables it to automatically determine the network structure and parameters online. At the stage of IT2FNN structure learning, the standard on rule growth is set according to the incentive intensities of IT2FNN rule premises. A new rule is generated when the incentive intensities of rules are all smaller than a certain threshold; next, a significance index is set for each rule. When the significance index of some rule decays to a certain threshold, the corresponding rule shall be deleted to achieve the goals of optimizing IT2FNN structure and reducing system complexity. At the stage of parameter learning, adaptive adjustment of IT2FNN parameters is made via the sliding mode control theory learning algorithm, and the stabilities of the algorithm and control system are proven using Lyapunov function. Finally, the proposed control scheme is used in the control of a magnetic rigid spacecraft, as compared to three other designed control methods. Simulation results show that IT2FNNSMRC has superior control precision and stability. And the IT2FNN which adopts the proposed learning algorithm can address uncertainty satisfactorily, with higher computational implementability.

A Novel Evolving Type-2 Fuzzy System for Controlling a Mobile Robot under Large Uncertainties

This paper presents the development of a type-2 evolving fuzzy control system (T2-EFCS) to facilitate self-learning (either from scratch or from a certain predefined rule). Our system has two major learning stages, namely, structure learning and parameters learning. The structure phase does not require previous information about the fuzzy structure, and it can start the construction of its rules from scratch with only one initial fuzzy rule. The rules are then continuously updated and pruned in an online fashion to achieve the desired set point. For the phase of learning parameters, all adjustable parameters of the fuzzy system are tuned by using a sliding surface method, which is based on the gradient descent algorithm. This method is used to minimize the difference between the expected and actual signals. Our proposed control method is model-free and does not require prior knowledge of the plant’s dynamics or constraints. Instead, data-driven control utilizes artificial intelligence-based techniques, such as fuzzy logic systems, to learn the dynamics of the system and adapt to changes in the system, and account for complex interactions between different components. A robustness term is incorporated into the control effort to deal with external disturbances in the system. The proposed technique is applied to regulate the dynamics of a mobile robot in the presence of multiple external disturbances, demonstrating the robustness of the proposed control systems. A rigorous comparative study with respect to three different controllers is performed, where the outcomes illustrate the superiority of the proposed learning method as evidenced by lower RMSE values and fewer fuzzy parameters. Lastly, stability analysis of the proposed control method is conducted using the Lyapunov stability theory.

A Novel Interval Type-2 Fuzzy System Identification Method Based on the Modified Fuzzy C-Regression Model

In this article, a novel interval type-2 Takagi-Sugeno fuzzy c -regression modeling method with a modified distance definition is proposed. The modified distance definition is developed to describe the distance between each data point and the local type-2 fuzzy model. To improve the robustness of the proposed identification method, a modified objective function is presented. In addition, different from most previous studies that require numerous free parameters to be determined, an interval type-2 fuzzy c -regression model is developed to reduce the number of such free parameters. Furthermore, an improved ratio between the upper and lower weights is proposed based on the upper and lower membership function with each input data, and the ordinary least-squares method is adopted to establish the type-2 fuzzy model. The Box-Jenkins model and two numerical models are given to illustrate the effectiveness and robustness of the proposed results.

Optimization of Interval Type-2 Intuitionistic Fuzzy Logic System for Prediction Problems

Derivative-based algorithms have been adopted in the literature for the optimization of membership and non-membership function parameters of interval type-2 (T2) intuitionistic fuzzy logic systems (FLSs). In this study, a non-derivative-based algorithm called sliding mode control learning algorithm is proposed to tune the parameters of interval T2 intuitionistic FLS for the first time. The proposed rule-based learning system employs the Takagi–Sugeno–Kang inference with artificial neural network to pilot the learning process. The new learning system is evaluated using some nonlinear prediction problems. Analyses of results reveal that the proposed learning apparatus outperforms its type-1 version and many existing solutions in the literature and competes favorably with others on the investigated problem instances with low cost in terms of running time.

Electrical Load Prediction Using Interval Type-2 Atanassov Intuitionist Fuzzy System: Gravitational Search Algorithm Tuning Approach

Establishing accurate electrical load prediction is vital for pricing and power system management. However, the unpredictable behavior of private and industrial users results in uncertainty in these power systems. Furthermore, the utilization of renewable energy sources, which are often variable in their production rates, also increases the complexity making predictions even more difficult. In this paper an interval type-2 intuitionist fuzzy logic system whose parameters are trained in a hybrid fashion using gravitational search algorithms with the ridge least square algorithm is presented for short-term prediction of electrical loading. Simulation results are provided to compare the performance of the proposed approach with that of state-of-the-art electrical load prediction algorithms for Poland, and five regions of Australia. The simulation results demonstrate the superior performance of the proposed approach over seven different current state-of-the-art prediction algorithms in the literature, namely: SVR, ANN, ELM, EEMD-ELM-GOA, EEMD-ELM-DA, EEMD-ELM-PSO and EEMD-ELM-GWO.

Interval Type-2 Fuzzy Neural Networks for Chaotic Time Series Prediction: A Concise Overview

Chaotic time series widely exists in nature and society (e.g., meteorology, physics, economics, etc.), which usually exhibits seemingly unpredictable features due to its inherent nonstationary and high complexity. Thankfully, multifarious advanced approaches have been developed to tackle the prediction issues, such as statistical methods, artificial neural networks (ANNs), and support vector machines. Among them, the interval type-2 fuzzy neural network (IT2FNN), which is a synergistic integration of fuzzy logic systems and ANNs, has received wide attention in the field of chaotic time series prediction. This paper begins with the structural features and superiorities of IT2FNN. Moreover, chaotic characters identification and phase-space reconstruction matters for prediction are presented. In addition, we also offer a comprehensive review of state-of-the-art applications of IT2FNN, with an emphasis on chaotic time series prediction and summarize their main contributions as well as some hardware implementations for computation speedup. Finally, this paper trends and extensions of this field, along with an outlook of future challenges are revealed. The primary objective of this paper is to serve as a tutorial or referee for interested researchers to have an overall picture on the current developments and identify their potential research direction to further investigation.

Nonlinear dynamic systems identification using recurrent interval type-2 TSK fuzzy neural network - A novel structure

In this study, a novel structure of a recurrent interval type-2 Takagi-Sugeno-Kang (TSK) fuzzy neural network (FNN) is introduced for nonlinear dynamic and time-varying systems identification. It combines the type-2 fuzzy sets (T2FSs) and a recurrent FNN to avoid the data uncertainties. The fuzzy firing strengths in the proposed structure are returned to the network input as internal variables. The interval type-2 fuzzy sets (IT2FSs) is used to describe the antecedent part for each rule while the consequent part is a TSK-type, which is a linear function of the internal variables and the external inputs with interval weights. All the type-2 fuzzy rules for the proposed RIT2TSKFNN are learned on-line based on structure and parameter learning, which are performed using the type-2 fuzzy clustering. The antecedent and consequent parameters of the proposed RIT2TSKFNN are updated based on the Lyapunov function to achieve network stability. The obtained results indicate that our proposed network has a small root mean square error (RMSE) and a small integral of square error (ISE) with a small number of rules and a small computation time compared with other type-2 FNNs.

Efficient Approach for RLS Type Learning in TSK Neural Fuzzy Systems

This paper presents an efficient approach for the use of recursive least square (RLS) learning algorithm in Takagi-Sugeno-Kang neural fuzzy systems. In the use of RLS, reduced covariance matrix, of which the off-diagonal blocks defining the correlation between rules are set to zeros, may be employed to reduce computational burden. However, as reported in the literature, the performance of such an approach is slightly worse than that of using the full covariance matrix. In this paper, we proposed a so-called enhanced local learning concept in which a threshold is considered to stop learning for those less fired rules. It can be found from our experiments that the proposed approach can have better performances than that of using the full covariance matrix. Enhanced local learning method can be more active on the structure learning phase. Thus, the method not only can stop the update for insufficiently fired rules to reduce disturbances in self-constructing neural fuzzy inference network but also raises the learning speed on structure learning phase by using a large backpropagation learning constant.