Traditional Takagi-Sugeno-Kang Research Articles

Wavelet-TSK-Type Fuzzy Cerebellar Model Neural Network for Uncertain Nonlinear Systems

In this paper, a novel fuzzy neural network structure for uncertain nonlinear systems is proposed. This network is called wavelet Takagi–Sugeno–Kang (TSK) fuzzy cerebellar model neural network, which includes the framework of a cerebellar model neural network (CMNN) and the wavelet-function-based TSK fuzzy inference model. In order to effectively solve the uncertainty problem of nonlinear systems, a new structure is proposed where the wavelet function is used in the consequent parts of TSK-type fuzzy CMNN instead of the linear combination of the input variables in the traditional TSK fuzzy systems. This structure combines the advantages of the wavelet function, the CMNN and the TSK fuzzy inference system; thus, it is a more effective model for the uncertain nonlinear systems. In order to provide fast training, parameter update laws of the proposed model are derived based on the gradient descent method in which the learning-rates are online adapted. Furthermore the Lyapunov function is used to analyze the convergence of the considered systems. Finally, four different types of applications are applied to demonstrate the effectiveness of the proposed model. The simulation comparisons with other neural network models have verified the effectiveness of the new model.

Application of hydrologic forecast model

In order to overcome the shortcoming of the solution may be trapped into the local minimization in the traditional TSK (Takagi-Sugeno-Kang) fuzzy inference training, this paper attempts to consider the TSK fuzzy system modeling approach based on the visual system principle and the Weber law. This approach not only utilizes the strong capability of identifying objects of human eyes, but also considers the distribution structure of the training data set in parameter regulation. In order to overcome the shortcoming of it adopting the gradient learning algorithm with slow convergence rate, a novel visual TSK fuzzy system model based on evolutional learning is proposed by introducing the particle swarm optimization algorithm. The main advantage of this method lies in its very good optimization, very strong noise immunity and very good interpretability. The new method is applied to long-term hydrological forecasting examples. The simulation results show that the method is feasible and effective, the new method not only inherits the advantages of traditional visual TSK fuzzy models but also has the better global convergence and accuracy than the traditional model.

Supervised and Reinforcement Evolutionary Learning for Wavelet-based Neuro-fuzzy Networks

This study presents a wavelet-based neuro-fuzzy network (WNFN). The proposed WNFN model combines the traditional Takagi---Sugeno---Kang (TSK) fuzzy model and the wavelet neural networks (WNN). This study adopts the non-orthogonal and compactly supported functions as wavelet neural network bases. A novel supervised evolutionary learning, called WNFN-S, is proposed to tune the adjustable parameters of the WNFN model. The proposed WNFN-S learning scheme is based on dynamic symbiotic evolution (DSE). The proposed DSE uses the sequential-search-based dynamic evolutionary (SSDE) method. In some real-world applications, exact training data may be expensive or even impossible to obtain. To solve this problem, the reinforcement evolutionary learning, called WNFN-R, is proposed. Computer simulations have been conducted to illustrate the performance and applicability of the proposed WNFN-S and WNFN-R learning algorithms.

An efficient quantum neuro-fuzzy classifier based on fuzzy entropy and compensatory operation

In this paper, a quantum neuro-fuzzy classifier (QNFC) for classification applications is proposed. The proposed QNFC model is a five-layer structure, which combines the compensatory-based fuzzy reasoning method with the traditional Takagi---Sugeno---Kang (TSK) fuzzy model. The compensatory-based fuzzy reasoning method uses adaptive fuzzy operations of neuro-fuzzy systems that can make the fuzzy logic system more adaptive and effective. Layer 2 of the QNFC model contains quantum membership functions, which are multilevel activation functions. Each quantum membership function is composed of the sum of sigmoid functions shifted by quantum intervals. A self-constructing learning algorithm, which consists of the self-clustering algorithm (SCA), quantum fuzzy entropy and the backpropagation algorithm, is also proposed. The proposed SCA method is a fast, one-pass algorithm that dynamically estimates the number of clusters in an input data space. Quantum fuzzy entropy is employed to evaluate the information on pattern distribution in the pattern space. With this information, we can determine the number of quantum levels. The backpropagation algorithm is used to tune the adjustable parameters. The simulation results have shown that (1) the QNFC model converges quickly; (2) the QNFC model has a higher correct classification rate than other models.

A Novel Neuro-Fuzzy Inference System with Multi-Level Membership Function for Classification Applications

In this paper, a novel neuro-fuzzy inference system with multi-level membership function (NFIS_MMF) for classification applications is proposed. The NFIS_MMF model is a five-layer structure, which combines the traditional Takagi-Sugeno-Kang (TSK). Layer 2 of the NFIS_MMF model contains multi-level membership functions, which are multilevel activation functions. A self-constructing learning algorithm, which consists of the self-clustering algorithm (SCA), fuzzy entropy, and the backpropagation algorithm, is also proposed to construct the NFIS_MMF model and perform parameter learning. Simulations were conducted to show the performance and applicability of the proposed model.

A Wavelet-Based Neuro-Fuzzy System and its Applications

Abstract This paper addresses a Wavelet-Based Neuro-Fuzzy System (WNF’S) for non-linear system identification and control. The proposed WNFS model combines the traditional TakagiSugeno-Kang (TSK) fuzzy model and the wavelet neural networks (WNN). This study adopts the non-orthogonal and compactly supported functions as wavelet neural network bases. An online learning algorithm, which consists of structure learning and parameter learning, is also presented. The structure learning depends on the degree measure to obtain the number of fuzzy rules and wavelet functions. Meanwhile, the parameter learning is based on the gradient descent method for adjusting the shape of the membership function and the connection weights of WNN. Several simulation examples have been given to illustrate the performance and effectiveness of the proposed model.

An entropy-based quantum neuro-fuzzy inference system for classification applications

In this paper, an entropy-based quantum neuro-fuzzy inference system (EQNFIS) for classification applications is proposed. The EQNFIS model is a five-layer structure, which combines the traditional Takagi-Sugeno-Kang (TSK). Layer 2 of the EQNFIS model contains quantum membership functions, which are multilevel activation functions. Each quantum membership function is composed of the sum of sigmoid functions shifted by quantum intervals. A self-constructing learning algorithm, which consists of the self-clustering algorithm (SCA), quantum fuzzy entropy, and the backpropagation algorithm, is also proposed. The proposed SCA method is a fast, one-pass algorithm that dynamically estimates the number of clusters in an input data space. Quantum fuzzy entropy is employed to evaluate the information on pattern distribution in the pattern space. With this information, we can determine the number of quantum levels. The backpropagation algorithm is used to tune the adjustable parameters. Simulations were conducted to show the performance and applicability of the proposed model.

A TSK-type quantum neural fuzzy network for temperature control

In this paper, a TSK-type quantum neural fuzzy network (TQNFN) for temperature control is proposed. The TQNFN model is a five-layer structure, which combines the traditional Takagi-Sugeno-Kang (TSK). Layer 2 of the TQNFN model contains quantum membership functions, which are multilevel activation functions. Each quantum membership function is composed of the sum of sigmoid functions shifted by quantum intervals. A self-constructing learning algorithm, which consists of the self-clustering algorithm (SCA) and the backpropagation algorithm, is also proposed. The proposed the SCA method is a fast, one-pass algorithm for a dynamic estimation of the number of clusters in an input data space. The backpropagation algorithm is used to tune the adjustable parameters. Simulation results have been given to illustrate the performance and effectiveness of the proposed model.

A new approach to fuzzy wavelet system modeling

In this paper, we propose simple but effective two different fuzzy wavelet networks (FWNs) for system identification. The FWNs combine the traditional Takagi–Sugeno–Kang (TSK) fuzzy model and discrete wavelet transforms (DWT). The proposed FWNs consist of a set of if–then rules and, then parts are series expansion in terms of wavelets functions. In the first system, while the only one scale parameter is changing with it corresponding rule number, translation parameter sets are fixed in each rule. As for the second system, DWT is used completely by using wavelet frames. The performance of proposed fuzzy models is illustrated by examples and compared with previously published examples. Simulation results indicate the remarkable capabilities of the proposed methods. It is worth noting that the second FWN achieves high function approximation accuracy and fast convergence.

A novel evolution learning for recurrent wavelet-based neuro-fuzzy networks

This study presents a recurrent wavelet-based neuro-fuzzy network with dynamic symbiotic evolution (RWNFN-DSE) for dynamic system processing. The proposed RWNFN-DSE model combines the traditional Takagi-Sugeno-Kang (TSK) fuzzy model and the wavelet neural networks (WNN). This study adopts the non-orthogonal and compactly supported functions as wavelet neural network bases. Temporal relations embedded in the network are caused by adding some feedback connections representing the memory units into the second layer. A novel evolution learning called dynamic symbiotic evolution (DSE) is used to tune the parameter of the RWNFN-DSE model. The better chromosomes will be initially generated while the better mutation points will be determined for performing dynamic-mutation. Simulation results have shown that the proposed RWNFN-DSE model obtain better performance than other existing models.

Prediction and Identification Using Wavelet-Based Recurrent Fuzzy Neural Networks

This paper presents a wavelet-based recurrent fuzzy neural network (WRFNN) for prediction and identification of nonlinear dynamic systems. The proposed WRFNN model combines the traditional Takagi-Sugeno-Kang (TSK) fuzzy model and the wavelet neural networks (WNN). This paper adopts the nonorthogonal and compactly supported functions as wavelet neural network bases. Temporal relations embedded in the network are caused by adding some feedback connections representing the memory units into the second layer of the feedforward wavelet-based fuzzy neural networks (WFNN). An online learning algorithm, which consists of structure learning and parameter learning, is also presented. The structure learning depends on the degree measure to obtain the number of fuzzy rules and wavelet functions. Meanwhile, the parameter learning is based on the gradient descent method for adjusting the shape of the membership function and the connection weights of WNN. Finally, computer simulations have demonstrated that the proposed WRFNN model requires fewer adjustable parameters and obtains a smaller rms error than other methods.