Browsing by Author "Lin, Yang-Yin"
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Item type:Item, A Functional-Link based Interval Type-2 Compensatory Fuzzy Neural Network for Nonlinear System modeling(2011) ;Chang, Jyh-Yeong ;Lin, Yang-Yin ;Han, Ming-Feng ;Lin, Chin-Teng電控工程研究所In this paper, the Functional-Link based Interval Type-2 Compensatory Fuzzy Neural Network (FLIT2CFNN) is a six-layer structure, which combines compensatory fuzzy reasoning method, and the consequent part is combined the proposed functional-link neural network with interval weights. The compensatory fuzzy reasoning method uses adaptive fuzzy operations of neuro-fuzzy systems that can make the fuzzy logic system more adaptive and effective. Initially, there is no rule in the FLIT2CFNN. A FLIT2CFNN is constructed using concurrent structure and parameter learning. The advantages of this learning algorithm are that it converges quickly and the obtained fuzzy rules are more precise. All of the antecedent part parameters and compensatory degree values are learned by gradient descent algorithm. Several simulation results show that the FLIT2CFNN achieves better performance than other feedforword type-1 and type-2 FNNs.Item type:Item, A global optimized neuro-fuzzy system using artificial bee colony evolutionary algorithm(2015-01-01) ;Liu, Yu-Ting ;Lin, Yang-Yin ;Hsieh, Tsung-Yu ;Wu, Shang-LinLin, Chin-TengThis paper proposes a novel Takagi-Sugeno-Kang-type (TSK-type) neuro-fuzzy system (NFS), which utilizes the artificial bee colony (ABC) evolutionary algorithm for parameter optimization. The ABC evolutionary algorithm was developed based on imitating foraging behavior of natural bees for numerical optimization problems, and it has been proved to outperform other metaheuristic approaches on different constrain optimization problems in previous studies. The proposed NFS in this paper adopts an adaptive clustering method to generate fuzzy rules for determining the system architecture, and the TSK-type reasoning is employed for the consequent part of each rule. Subsequently, all free parameters in the NFS designed, including the premise and the consequent parameters, will be optimized by ABC algorithm. This study compares the performance of ABC algorithm with that of Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE). The simulation results show that the performance of ABC algorithm is superior to that of the mentioned algorithms for solving dynamic system problems.Item type:Item, A Learning Scheme to Fuzzy C-Means based on a Compromise in Updating Membership Degrees(2014-01-01) ;Wu, Shang-Lin ;Lin, Yang-Yin ;Liu, Yu-Ting ;Chen, Chih-YuLin, Chin-TengFuzzy C-Means (FCM) clustering is the most well-known clustering method according to fuzzy partition for pattern classification. However, there are some disadvantages of using that clustering method, such as computational complexity and execution time. Therefore, to solve these drawbacks of FCM, the two-phase FCM procedure has been proposed in this study. Compared with the conventional FCM, the usage of a compromised learning scheme makes more adaptive and effective. By performing the proposed approach, the unknown data could be rapidly clustered according to the previous information. A synthetic data set with two dimensional variables is generated to estimate the performance of the proposed method, and to further demonstrate that our method not only reduces computational complexity but economizes execution time compared with the conventional FCM in each example.Item type:Item, A Motor Imagery Based Brain-Computer Interface System via Swarm-Optimized Fuzzy Integral and Its Application(2016) ;Wu, Shang-Lin ;Liu, Yu-Ting ;Chou, Kuang-Pen ;Lin, Yang-YinLu, JieA brain-computer interface (BCI) system provides a convenient means of communication between the human brain and a computer, which is applied not only to healthy people but also for people that suffer from motor neuron diseases (MNDs). Motor imagery (MI) is one well-known basis for designing Electroencephalography (EEG)-based real-life BCI systems. However, EEG signals are often contaminated with severe noise and various uncertainties, imprecise and incomplete information streams. Therefore, this study proposes spectrum ensemble based on swam-optimized fuzzy integral for integrating decisions from sub-band classifiers that are established by a sub-band common spatial pattern (SBCSP) method. Firstly, the SBCSP effectively extracts features from EEG signals, and thereby the multiple linear discriminant analysis (MLDA) is employed during a MI classification task. Subsequently, particle swarm optimization (PSO) is used to regulate the subject-specific parameters for assigning optimal confidence levels for classifiers used in the fuzzy integral during the fuzzy fusion stage of the proposed system. Moreover, BCI systems usually tend to have complex architectures, be bulky in size, and require time-consuming processing. To overcome this drawback, a wireless and wearable EEG measurement system is investigated in this study. Finally, in our experimental result, the proposed system is found to produce significant improvement in terms of the receiver operating characteristic (ROC) curve. Furthermore, we demonstrate that a robotic arm can be reliably controlled using the proposed BCI system. This paper presents novel insights regarding the possibility of using the proposed MI-based BCI system in real-life applications.Item type:Item, A Mutually Recurrent Interval Type-2 Neural Fuzzy System (MRIT2NFS) With Self-Evolving Structure and Parameters(2013-06-01) ;Lin, Yang-Yin ;Chang, Jyh-Yeong ;Pal, Nikhil R. ;Lin, Chin-Teng電控工程研究所In this paper, a mutually recurrent interval type-2 neural fuzzy system (MRIT2NFS) is proposed for the identification of nonlinear and time-varying systems. The MRIT2NFS uses type-2 fuzzy sets in order to enhance noise tolerance of the system. In the MRIT2NFS, the antecedent part of each recurrent fuzzy rule is defined using interval type-2 fuzzy sets, and the consequent part is of the Takagi-Sugeno-Kang type with interval weights. The antecedent part of MRIT2NFS forms a local internal feedback and interaction loop by feeding the rule firing strength of each rule to others including itself. The consequent is a linear combination of exogenous input variables. The learning of MRIT2NFS starts with an empty rule base and all rules are learned online via structure and parameter learning. The structure learning of MRIT2NFS uses online type-2 fuzzy clustering. For parameter learning, the consequent part parameters are tuned by rule-ordered Kalman filter algorithm to reinforce parameter learning ability. The type-2 fuzzy sets in the antecedent and weights representing the mutual feedback are learned by the gradient descent algorithm. After the training, a weight-elimination scheme eliminates feedback connections that do not have much effect on the network behavior. This method can efficiently remove redundant recurrence and interaction weights. Finally, the MRIT2NFS is used for system identification under both noise-free and noisy environments. For this, we consider both time series prediction and nonlinear plant modeling. Compared with type-1 recurrent fuzzy neural networks, simulation results show that our approach produces smaller root-mean-squared errors using the same number of iterations.Item type:Item, A Novel Mechanism to Fuse Various Sub-aspect Brain-computer Interface (BCI) Systems with PSO for Motor Imagery Task(2015-01-01) ;Lin, Chin-Teng ;Hsieh, Tsung-Yu ;Liu, Yu-Ting ;Wu, Shang-LinLin, Yang-YinIn this study, we develop a novel multi-fusion brain-computer interface (BCI) system based on a fuzzy neural network (FNN) and information fusion approaches to cope with a classification task for identifying right/left hand motor imagery. In the proposed system, we utilize a filter bank and sub-band common spatial pattern (SBCSP) to extract features from raw EEG data. A self-organizing neural fuzzy inference network (SONFIN) is then applied for a recognition task. In order to improve the classification performance, we form a committee of networks and employ fuzzy integral (FI) to attain a joint decision. To further optimize the fusion approaches, a particle swarm optimization (PSO) algorithm is exploited to globally update parameters used in the fusion stage. In consequence, our experimental result shows that the proposed fuzzy fusion system possesses superior performance compared to other comparative models.Item type:Item, A Recurrent Self-Evolving Interval Type-2 Fuzzy Neural Network for Dynamic System Processing(2009-10-01) ;Juang, Chia-Feng ;Huang, Ren-Bo ;Lin, Yang-Yin ;電子工程學系及電子研究所Department of Electronics Engineering and Institute of ElectronicsThis paper proposes a recurrent self-evolving interval type-2 fuzzy neural network (RSEIT2FNN) for dynamic system processing. An RSEIT2FNN incorporates type-2 fuzzy sets in a recurrent neural fuzzy system in order to increase the noise resistance of a system. The antecedent parts in each recurrent fuzzy rule in the RSEIT2FNN are interval type-2 fuzzy sets, and the consequent part is of the Takagi-Sugeno-Kang (TSK) type with interval weights. The antecedent part of RSEIT2FNN forms a local internal feedback loop by feeding the rule firing strength of each rule back to itself. The TSK-type consequent part is a linear model of exogenous inputs. The RSEIT2FNN initially contains no rules; all rules are learned online via structure and parameter learning. The structure learning uses online type-2 fuzzy clustering. For the parameter learning, the consequent part parameters are tuned by a rule-ordered Kalman filter algorithm to improve learning performance. The antecedent type-2 fuzzy sets and internal feedback loop weights are learned by a gradient descent algorithm. The RSEIT2FNN is applied to simulations of dynamic system identifications and chaotic signal prediction under both noise-free and noisy conditions. Comparisons with type-1 recurrent fuzzy neural networks validate the performance of the RSEIT2FNN.Item type:Item, A TSK-Type-Based Self-Evolving Compensatory Interval Type-2 Fuzzy Neural Network (TSCIT2FNN) and Its Applications(2014-01-01) ;Lin, Yang-Yin ;Chang, Jyh-Yeong ;Lin, Chin-Teng ;電控工程研究所腦科學研究中心In this paper, a Takagi-Sugeno-Kang (TSK)-type-based self-evolving compensatory interval type-2 fuzzy neural network (FNN) (TSCIT2FNN) is proposed for system modeling and noise cancellation problems. A TSCIT2FNN uses type-2 fuzzy sets in an FNN in order to handle the uncertainties associated with information or data in the knowledge base. The antecedent part of each compensatory fuzzy rule is an interval type-2 fuzzy set in the TSCIT2FNN, where compensatory-based fuzzy reasoning uses adaptive fuzzy operation of a neural fuzzy system to make the fuzzy logic system effective and adaptive, and the consequent part is of the TSK type. The TSK-type consequent part is a linear combination of exogenous input variables. Initially, the rule base in the TSCIT2FNN is empty. All rules are derived according to online type-2 fuzzy clustering. For parameter learning, the consequent part parameters are tuned by a variable-expansive Kalman filter algorithm to the reinforce parameter learning ability. The antecedent type-2 fuzzy sets and compensatory weights are learned by a gradient descent algorithm to improve the learning performance. The performance of TSCIT2FNN for the identification is validated and compared with several type-1 and type-2 FNNs. Simulation results show that our approach produces smaller root-mean-square errors and converges more quickly.Item type:Item, An Internal/Interconnection Recurrent Type-2 Fuzzy Neural Network (IRT2FNN) for Dynamic System Identification(2010) ;Lin, Yang-Yin ;Chang, Jyh-Yeong ;Lin, Chin-Teng ;電控工程研究所Institute of Electrical and Control EngineeringThis paper proposes an Internal/Interconnection Recurrent Type-2 Fuzzy Neural Network (IRT2FNN) for dynamic system identification. The antecedent part of IRT2FNN forms a self and interconnection feedback loop by feeding the past and current firing strength of each rule. The TSK-type consequent part is a linear model of exogenous inputs with interval weights. The initial rule base in the IRT2FNN is empty, and an on-line constructing method is proposed to generate fuzzy rules which flexibly partition the input space. The recurrent structure in the IRT2FNN enable to handle dynamic system identification problems with a priori knowledge of system input and output delay numbers. Simulations on dynamic system identification verify the performance of IRT2FNN with clean and noisy outputs as well.Item type:Item, An Interval Type-2 Neural Fuzzy Inference System (IT2NFIS) with compensatory operator(2013) ;Lin, Yang-Yin ;Chang, Jyh-Yeong ;Lin, Chin-Teng ;電控工程研究所Institute of Electrical and Control EngineeringIn this paper, an interval type-2 neural fuzzy system (IT2NFIS) with compensatory operator is proposed for system modeling. The IT2NFIS uses type-2 fuzzy sets in the premise clause in order to effectively handle the uncertainties in terms of data and information. The premise part of each compensatory fuzzy rule is an interval type-2 fuzzy set in the IT2NFIS, where compensatory operation is able to adaptively adjust fuzzy membership functions and to dynamically optimize fuzzy operations. The consequent part in the IT2NFIS consists of the Takagi-Sugeno-Kang (TSK) type that is a linear combination of exogenous input variables. Initially the rule base in the IT2NFIS is empty. All rules generated are based on on-line type-2 fuzzy clustering. All free weights are learned by a gradient descent algorithm to improve the learning performance. Simulation results show that our approach yields smaller root mean squared errors than its rivals.Item type:Item, An Interval Type-2 Neural Fuzzy System for Online System Identification and Feature Elimination(2015-07-01) ;Lin, Chin-Teng ;Pal, Nikhil R. ;Wu, Shang-Lin ;Liu, Yu-TingLin, Yang-YinWe propose an integrated mechanism for discarding derogatory features and extraction of fuzzy rules based on an interval type-2 neural fuzzy system (NFS)-in fact, it is a more general scheme that can discard bad features, irrelevant antecedent clauses, and even irrelevant rules. High-dimensional input variable and a large number of rules not only enhance the computational complexity of NFSs but also reduce their interpretability. Therefore, a mechanism for simultaneous extraction of fuzzy rules and reducing the impact of (or eliminating) the inferior features is necessary. The proposed approach, namely an interval type-2 Neural Fuzzy System for online System Identification and Feature Elimination (IT2NFS-SIFE), uses type-2 fuzzy sets to model uncertainties associated with information and data in designing the knowledge base. The consequent part of the IT2NFS-SIFE is of Takagi-Sugeno-Kang type with interval weights. The IT2NFS-SIFE possesses a self-evolving property that can automatically generate fuzzy rules. The poor features can be discarded through the concept of a membership modulator. The antecedent and modulator weights are learned using a gradient descent algorithm. The consequent part weights are tuned via the rule-ordered Kalman filter algorithm to enhance learning effectiveness. Simulation results show that IT2NFS-SIFE not only simplifies the system architecture by eliminating derogatory/ irrelevant antecedent clauses, rules, and features but also maintains excellent performance.Item type:Item, Assessment of Mental Fatigue: An EEG-based Forecasting System for Driving Safety(2015-01-01) ;Liu, Yu-Ting ;Lin, Yang-Yin ;Wu, Shang-Lin ;Hsieh, Tsung-YuLin, Chin-TengThis study proposes an EEG-based forecasting system based on a functional-link recurrent self-evolving fuzzy neural network (FL-RSEFNN) for assessing mental fatigue during a highway driving task. Drivers\' cognitive states significantly affect driving safety, especially for fatigue or drowsy driving which is one of common factors to endanger individuals and the public safety. In this study, a FL-RSEFNN employs an on-line gradient descent (GD) learning rule to address the EEG regression problem in brain dynamics for estimation of driving fatigue. We analyze brain dynamics in a car driving task, which is constructed in a simulated virtual reality (VR) environment. The EEG-based forecasting system is evaluated using the generalized cross-subject approach, and the results indicate that the FL-RSEFNN is superior to state-of-the-art models regardless of the use of recurrent or non-recurrent structures.Item type:Item, Brain Dynamics in Predicting Driving Fatigue Using a Recurrent Self-Evolving Fuzzy Neural Network(2016-02) ;Liu, Yu-Ting ;Lin, Yang-Yin ;Wu, Shang-Lin ;Chuang, Chun-HsiangLin, Chin-TengThis paper proposes a generalized prediction system called a recurrent self-evolving fuzzy neural network (RSEFNN) that employs an on-line gradient descent learning rule to address the electroencephalography (EEG) regression problem in brain dynamics for driving fatigue. The cognitive states of drivers significantly affect driving safety; in particular, fatigue driving, or drowsy driving, endangers both the individual and the public. For this reason, the development of brain-computer interfaces (BCIs) that can identify drowsy driving states is a crucial and urgent topic of study. Many EEG-based BCIs have been developed as artificial auxiliary systems for use in various practical applications because of the benefits of measuring EEG signals. In the literature, the efficacy of EEG-based BCIs in recognition tasks has been limited by low resolutions. The system proposed in this paper represents the first attempt to use the recurrent fuzzy neural network (RFNN) architecture to increase adaptability in realistic EEG applications to overcome this bottleneck. This paper further analyzes brain dynamics in a simulated car driving task in a virtual-reality environment. The proposed RSEFNN model is evaluated using the generalized cross-subject approach, and the results indicate that the RSEFNN is superior to competing models regardless of the use of recurrent or nonrecurrent structures.Item type:Item, Developing a Novel Multi-fusion Brain-Computer Interface (BCI) System with Particle Swarm Optimization for Motor Imagery Task(2015) ;Hsieh, Tsung-Yu ;Lin, Yang-Yin ;Liu, Yu-Ting ;Fang, Chieh-NingLin, Chin-TengIn this paper, we develop a novel multi-fusion brain-computer interface (BCI) based on linear discriminant analysis (LDA) to deal with motor imagery (MI) classification problem. We combine filter bank and sub-band common spatial pattern (SBCSP) to extract features from EEG data in the preprocessing phase, and then LDA classifiers are applied to classify brain activities to identify either left or right hand imagery. To further foster the performance of the proposed system, a fuzzy integral (FI) approach is employed to fuse information sources, and particle swarm optimization (PSO) algorithm is exploited to globally update parameters in the fusion structure. Consequently, our experimental results indicate that the proposed system provides superior performance compared to other approaches.Item type:Item, Driving Fatigue Prediction with Pre-Event Electroencephalography (EEG) via a Recurrent Fuzzy Neural Network(2016) ;Liu, Yu-Ting ;Wu, Shang-Lin ;Chou, Kuang-Pen ;Lin, Yang-YinLu, JieWe propose an electroencephalography (EEG) prediction system based on a recurrent fuzzy neural network (RFNN) architecture to assess drivers\' fatigue degrees during a virtual-reality (VR) dynamic driving environment. Prediction of fatigue degrees is a crucial and arduous biomedical issue for driving safety, which has attracted growing attention of the research community in the recent past. Meanwhile, combined with the benefits of measuring EEG signals facilitates, many EEG-based brain-computer interfaces (BCIs) have been developed for use in real-time mental assessment. In the literature, EEG signals are severely blended with stochastic noise; therefore, the performance of BCIs is constrained by low resolution in recognition tasks. For this rationale, independent component analysis (ICA) is usually used to find a source mapping from original data that has been blended with unrelated artificial noise. However, the mechanism of ICA cannot be used in real-time BCI design. To overcome this bottleneck, the proposed system in this paper utilizes a recurrent self-evolving fuzzy neural work (RSEFNN) to increase memory capability for adaptive noise cancellation when assessing drivers\' mental states during a car driving task. The experimental results without the use of ICA procedure indicate that the proposed RSEFNN model remains superior performance compared with the state-of-thearts models.Item type:Item, EEG-based Driving Fatigue Prediction System Using Functional-link-based Fuzzy Neural Network(2014) ;Liu, Yu-Ting ;Lin, Yang-Yin ;Wu, Shang-Lin ;Chuang, Chun-HsiangPrasad, MukeshThis study presents a fuzzy prediction system for the forecasting and estimation of driving fatigue, which utilizes a functional-link-based fuzzy neural network (FLFNN) to predict the drowsiness (DS) level in car driving task. The cognitive state in car driving task is one of key issue in cognitive neuroscience because fatigue driving usually causes enormous losses nowadays. The damage can be extremely decreased by the assistant of various artificial systems. Many Electroencephalography (EEG)based interfaces have been widely developed recently due to its convenient measurement and real-time response. However, the improvement of recognition accuracy is still confined to some specific problems (e.g., individual difference). In order to solve this issue, the proposed methodology in this paper utilizes a non-linear fuzzy neural network structure to increase the adaptability in the real-world environment. Therefore, this study is further to analysis the brain activities in car driving, which is constructed in a simulated three-dimensional virtual-reality (VR) environment. Finally, through the development of brain cognitive model in car driving task, this system can predict the cognitive state effectively before drivers\' action and then provide correct feedback to users. This study also compared the result with the-state-of-art systems, including Linear Regression (LR), Multi-Layer Perceptron Neural Network (MLPNN) and Support Vector Regression (SVR). Results of this study demonstrate the effectiveness of the proposed FLFNN model.Item type:Item, Fuzzy Integral With Particle Swarm Optimization for a Motor-Imagery-Based Brain-Computer Interface(2017-02) ;Wu, Shang-Lin ;Liu, Yu-Ting ;Hsieh, Tsung-Yu ;Lin, Yang-YinChen, Chih-YuA brain-computer interface (BCI) system using electroencephalography signals provides a convenient means of communication between the human brain and a computer. Motor imagery (MI), in which motor actions are mentally rehearsed without engaging in actual physical execution, has been widely used as a major BCI approach. One robust algorithm that can successfully cope with the individual differences in MI-related rhythmic patterns is to create diverse ensemble classifiers using the subband common spatial pattern (SBCSP) method. To aggregate outputs of ensemble members, this study uses fuzzy integral with particle swarm optimization (PSO), which can regulate subject-specific parameters for the assignment of optimal confidence levels for classifiers. The proposed system combining SBCSP, fuzzy integral, and PSO exhibits robust performance for offline single-trial classification of MI and real-time control of a robotic arm using MI. This paper represents the first attempt to utilize fuzzy fusion technique to attack the individual differences problem of MI applications in real-world noisy environments. The results of this study demonstrate the practical feasibility of implementing the proposed method for real-world applications.Item type:Item, Identification and Prediction of Dynamic Systems Using an Interactively Recurrent Self-Evolving Fuzzy Neural Network(2013-02-01) ;Lin, Yang-Yin ;Chang, Jyh-Yeong ;Lin, Chin-Teng ;電控工程研究所Institute of Electrical and Control EngineeringThis paper presents a novel recurrent fuzzy neural network, called an interactively recurrent self-evolving fuzzy neural network (IRSFNN), for prediction and identification of dynamic systems. The recurrent structure in an IRSFNN is formed as an external loops and internal feedback by feeding the rule firing strength of each rule to others rules and itself. The consequent part in the IRSFNN is composed of a Takagi-Sugeno-Kang (TSK) or functional-link-based type. The proposed IRSFNN employs a functional link neural network (FLNN) to the consequent part of fuzzy rules for promoting the mapping ability. Unlike a TSK-type fuzzy neural network, the FLNN in the consequent part is a nonlinear function of input variables. An IRSFNNs learning starts with an empty rule base and all of the rules are generated and learned online through a simultaneous structure and parameter learning. An on-line clustering algorithm is effective in generating fuzzy rules. The consequent update parameters are derived by a variable-dimensional Kalman filter algorithm. The premise and recurrent parameters are learned through a gradient descent algorithm. We test the IRSFNN for the prediction and identification of dynamic plants and compare it to other well-known recurrent FNNs. The proposed model obtains enhanced performance results.Item type:Item, Neuro-Fuzzy System Design Using Differential Evolution with Local Information(2011) ;Lin, Chin-Teng ;Han, Ming-Feng ;Lin, Yang-Yin ;Liao, Shih-HuiChang, Jyh-YeongThis paper proposes a differential evolution with local information for TSK-type neuro-fuzzy system optimization. The differential evolution with local information consider neighborhood between each individual to keep the diversity of population. An adaptive parameter tuning based on 1/5th rule is used to trade off between local search and global search. For structure learning algorithm, the on-line clustering algorithm is used for rule generation. The structure learning algorithm generates a new rule which compares the firing strength. Initially, there is no rule in neuro-fuzzy system model. The rules are automatically generated by fuzzy measure. For parameter learning, the parameters are optimized by differential evolution algorithm. Finally, the proposed neuro-fuzzy system with novel differential evolution model is applied in chaotic sequence prediction problem. Results of this paper demonstrate the effectiveness of the proposed model.Item type:Item, Simplified Interval Type-2 Fuzzy Neural Networks(2014-05-01) ;Lin, Yang-Yin ;Liao, Shih-Hui ;Chang, Jyh-Yeong ;Lin, Chin-Teng電控工程研究所This paper describes a self-evolving interval type-2 fuzzy neural network (FNN) for various applications. As type-1 fuzzy systems cannot effectively handle uncertainties in information within the knowledge base, we propose a simple interval type-2 FNN, which uses interval type-2 fuzzy sets in the premise and the Takagi-Sugeno-Kang (TSK) type in the consequent of the fuzzy rule. The TSK-type consequent of fuzzy rule is a linear combination of exogenous input variables. Given an initially empty the rule-base, all rules are generated with on-line type-2 fuzzy clustering. Instead of the time-consuming K-M iterative procedure, the design factors q(l) and q(r) are learned to adaptively adjust the upper and lower positions on the left and right limit outputs, using the parameter update rule based on a gradient descent algorithm. Simulation results demonstrate that our approach yields fewer test errors and less computational complexity than other type-2 FNNs.