Takagi-Sugeno-Kang Fuzzy System Research Articles

Novel multi-view Takagi–Sugeno–Kang fuzzy system for epilepsy EEG detection

Most intelligent algorithms used for recognizing epilepsy electroencephalogram (EEG) have two major deficiencies. The one is the lack of interpretability and the other is unsatisfactory recognition results. In response to these challenges, we propose a dedicated model called multi-view Takagi–Sugeno–Kang (TSK) fuzzy system (MV-TSK-FS) for the epilepsy EEG detection. Our contributions lie in three aspects. First, TSK-FS is selected as the basic model. As one of the most famous fuzzy systems, TSK-FS has the advantage of nice interpretability and thus meets the requirement of clinic trials and applications. Second, MV-TSK-FS uses a multi-view framework to collaboratively handle the collective feature data extracted from diverse extraction perspectives, which strives to avoid the potential performance degradation commonly incurred with single feature extraction. Third, we propose a view-weighted mechanism based on the quadratic regularization to distinguish the importance of each view. The more important the view, the larger the corresponding weight is. The final decision is consequently figured out with the weighted outputs of all views. Experimental results demonstrate that, compared with other epilepsy EEG detection ones, our proposed method has better classification performance as well as more satisfied interpretability on results.

Manifold-Regularized Multitask Fuzzy System Modeling With Low-Rank and Sparse Structures in Consequent Parameters

Multitask modeling methods for Takagi–Sugeno–Kang (TSK) fuzzy systems exhibit better generalization ability attributed to the utilization of the knowledge of intertask correlation. However, existing methods usually ignore the balance between the sharing of the common knowledge across multiple tasks and the preservation of the task-specific characteristics of each rule. To this end, we propose a novel manifold-regularized multitask modeling method for TSK fuzzy system by introducing low-rank and sparse structures into consequent parameters across multiple tasks. Specifically, we decompose the consequent parameters into two components—a task–shared component that represents similar structure across multiple tasks, and a task-specific component that encodes the sparse characteristics of the individual tasks. This can be implemented by imposing low-rank constraints on the task-shared component and applying the sparse constraints on the task-specific component. A new manifold regularization is further devised to reflect the feature-feature relation, which provides prior knowledge in multitask learning. An efficient augmented Lagrange multiplier is developed to solve the optimization problem. The experimental results demonstrate that the proposed model significantly outperforms the existing methods.

An Intelligence EEG Signal Recognition Method via Noise Insensitive TSK Fuzzy System Based on Interclass Competitive Learning.

Epilepsy is an abnormal function disease of movement, consciousness, and nerve caused by abnormal discharge of brain neurons in the brain. EEG is currently a very important tool in the process of epilepsy research. In this paper, a novel noise-insensitive Takagi–Sugeno–Kang (TSK) fuzzy system based on interclass competitive learning is proposed for EEG signal recognition. First, a possibilistic clustering in Bayesian framework with interclass competitive learning called PCB-ICL is presented to determine antecedent parameters of fuzzy rules. Inherited by the possibilistic c-means clustering, PCB-ICL is noise insensitive. PCB-ICL learns cluster centers of different classes in a competitive relationship. The obtained clustering centers are attracted by the samples of the same class and also excluded by the samples of other classes and pushed away from the heterogeneous data. PCB-ICL uses the Metropolis–Hastings method to obtain the optimal clustering results in an alternating iterative strategy. Thus, the learned antecedent parameters have high interpretability. To further promote the noise insensitivity of rules, the asymmetric expectile term and Ho–Kashyap procedure are adopted to learn the consequent parameters of rules. Based on the above ideas, a TSK fuzzy system is proposed and is called PCB-ICL-TSK. Comprehensive experiments on real-world EEG data reveal that the proposed fuzzy system achieves the robust and effective performance for EEG signal recognition.

On the Accuracy–Complexity Tradeoff of Fuzzy Broad Learning System

The fuzzy broad learning system (FBLS) is a recently proposed neuro-fuzzy model that shares the similar structure of a broad learning system (BLS). It shows high accuracy in both classification and regression tasks and inherits the fast computational nature of a BLS. However, the ensemble of several fuzzy subsystems in an FBLS decreases the possibility of understanding the fuzzy model since the fuzzy rules from different fuzzy systems are difficult to combine together while keeping the consistence. To balance the model accuracy and complexity, a synthetically simplified FBLS with better interpretability, named compact FBLS (CFBLS), is developed in this article, which can generate much fewer and more explainable fuzzy rules for understanding. In such a way, only one traditional Takagi–Sugeno–Kang fuzzy system is employed in the feature layer of a CFBLS, and the input universe of discourse is equally partitioned to obtain the fuzzy sets with proper linguistic labels accordingly. The random feature selection matrix and rule combination matrix are employed to reduce the total number of fuzzy rules and to avoid the “curse of dimensionality.” The enhancement layer is kept in the CFBLS that helps to add a nonlinear transformation of input features to the traditional first-order polynomial used in the consequent part of a fuzzy rule. The pseudoinverse is also used to determine the parameters of CFBLS guaranteeing its fast computational nature. The experiments on the popular UCI and KEEL datasets indicate that the CFBLS can generate a smaller set of comprehensible fuzzy rules and achieve much higher accuracy than some state-of-the-art neuro-fuzzy models. Moreover, the advantage of CFBLS is also verified in a real-world application.

Trajectory Tracking of a Flexible Robot Manipulator by a New Optimized Fuzzy Adaptive Sliding Mode-Based Feedback Linearization Controller

This work presents a novel fuzzy adaptive sliding mode-based feedback linearization controller for trajectory tracking of a flexible robot manipulator. To reach this goal, after deriving the dynamical equations of the robot, the feedback linearization approach is utilized to change the nonlinear dynamics to a linear one and find the control law. Then, the sliding mode control strategy is implemented to design a stabilizer for trajectory tracking of the flexible robot. In order to adaptively tune the parameters of the designed controller, the gradient descent approach and the chain derivative rule are employed. Moreover, the Takagi–Sugeno–Kang fuzzy system is applied to regulate the controller gains. Finally, a multiobjective particle swarm optimization algorithm is used to find the optimum fuzzy rules. The conflicting objective functions considered as the integrals of the absolute values of the state error and the control effort should be minimized, simultaneously. The simulation results illustrate the effectiveness and capability of the introduced scenario in comparison with other methods.

TSK Fuzzy System for Multi-View Data Discovery Underlying Label Relaxation and Cross-Rule & Cross-View Sparsity Regularizations

Industry 4.0 places special emphasis on the use of intelligent models to discover patterns in data. In this article, we propose a novel Takagi-Sugeno-Kang (TSK) fuzzy system with low model complexity for multiview data pattern discovery. Compared with the classic TSK fuzzy systems, the proposed one has three merits: First, we introduce a transformation matrix to relax the strict binary label matrix of the training set so that the margins between classes become more discriminative. Second, we introduce two kinds of sparsity regularizations, i.e., cross-rule and cross-view, to reduce indiscriminative fuzzy rules and consequent parameters so that the model complexity is significantly reduced. Third, we introduce the alternating direction method of multipliers to optimize the objective function so that we have compact closed-form solutions in each iteration. Extensive experiments on different kinds of multiview image datasets indicate the promising performance for data pattern discovery with low model complexity.

Optimize TSK Fuzzy Systems for Classification Problems: Minibatch Gradient Descent With Uniform Regularization and Batch Normalization

Takagi-Sugeno-Kang (TSK) fuzzy systems are flexible and interpretable machine learning models; however, they may not be easily optimized when the data size is large, and/or the data dimensionality is high. This paper proposes a mini-batch gradient descent (MBGD) based algorithm to efficiently and effectively train TSK fuzzy classifiers. It integrates two novel techniques: 1) uniform regularization (UR), which forces the rules to have similar average contributions to the output, and hence to increase the generalization performance of the TSK classifier; and, 2) batch normalization (BN), which extends BN from deep neural networks to TSK fuzzy classifiers to expedite the convergence and improve the generalization performance. Experiments on 12 UCI datasets from various application domains, with varying size and dimensionality, demonstrated that UR and BN are effective individually, and integrating them can further improve the classification performance.

Fuzzy Clustering with Self-growing Net

A novel deep feature mapping method self-growing net (SG-Net) is proposed, and its combination with classical fuzzy c-means (FCM) called SG-Net-FCM is further developed. SG-Net is a feedforward learning structure for nonlinear explicit feature mapping and includes four types of layers, i.e., input, fuzzy mapping, hybrid, and output layers. The fuzzy mapping layer maps the data from input layer to a high-dimensional feature space using TSK fuzzy mapping, i.e. the fuzzy mapping of Takagi–Sugeno–Kang fuzzy system (TSK-FS). Afterward, each layer in SG-Net accepts additional inputs from all preceding layers and provides its own distinguished features by using principal component analysis to all subsequent layers. The final output of SG-Net is fed to FCM. Since SG-Net-FCM is developed based on the TSK fuzzy mapping, it is more interpretable than classical kernelized fuzzy clustering methods. The effectiveness of the proposed clustering algorithm is experimentally verified on UCI datasets.

Anxiety Recognition of College Students Using a Takagi-Sugeno-Kang Fuzzy System Modeling Method and Deep Features

College students are the most active, most sensitive, and most prone group with respect to various psychological problems in contemporary society. In recent years, with the intensification of social competition, including various pressures such as studies, examinations, economic loss, emotional loss, and employment, the incidence of anxiety, depression and suicide rates has increased. To effectively pay attention to the psychological development of college students and to strengthen mental health education, this research proposes a method to automatically identify the anxiety of college students using a Takagi-Sugeno-Kang (TSK) fuzzy system and deep features. First, preprocess the collected EEG of college students. Secondly, use convolutional neural network (CNN) to extract deep features from the input data. Finally, TSK fuzzy system is used to classify features to obtain the final recognition result. Through experiments on standard data sets and self-made data sets, the experimental results verify the superiority of the anxiety identification method used in this study. The experimental results further demonstrate that the depth features have richer information than traditional features. The noise immunity of TSK fuzzy system makes it show good classification performance and generalization. The recognition results can quickly locate students with anxiety disorders and narrow the scope of investigation for students with psychological problems. The automatic recognition of college students' anxiety can improve the efficiency of schools and teachers in investigating students' psychological problems. This research has very good practical application value.

Optimize TSK Fuzzy Systems for Regression Problems: Minibatch Gradient Descent With Regularization, DropRule, and AdaBound (MBGD-RDA)

Takagi–Sugeno–Kang (TSK) fuzzy systems are very useful machine learning models for regression problems. However, to our knowledge, there has not existed an efficient and effective training algorithm that ensures their generalization performance and also enables them to deal with big data. Inspired by the connections between TSK fuzzy systems and neural networks, we extend three powerful neural network optimization techniques, i.e., minibatch gradient descent (MBGD), regularization, and AdaBound, to TSK fuzzy systems, and also propose three novel techniques (DropRule, DropMF, and DropMembership) specifically for training TSK fuzzy systems. Our final algorithm, MBGD with regularization, DropRule, and AdaBound, can achieve fast convergence in training TSK fuzzy systems, and also superior generalization performance in testing. It can be used for training TSK fuzzy systems on datasets of any size; however, it is particularly useful for big datasets, on which currently no other efficient training algorithms exist.

A view-reduction based multi-view TSK fuzzy system and its application for textile color classification

Takagi–Sugeno–Kang (TSK) fuzzy systems are well known for their good balance between approximation accuracy and interpretability. Nowadays, multi-view TSK fuzzy systems have drawn world-wide attention since the multi-view data has emerged in many application scenarios. However, many multi-view data contains weak views which may bring negative influences on the task of pattern recognition. How to reduce the weak views and hence improve the performance of multi-view TSK fuzzy systems have become a hot topic. In this paper, we propose a view-reduction based multi-view TSK fuzzy system termed as VR-MV-TSK-FS in which two powerful mechanisms are developed: (1) during the collaborative learning of data in each view, an object-distribution-dependent parameter is defined to control the learning of the weight of each view. The parameter is not fixed by users, it is set according to the feature space in advance such that the learnt weight of each view indeed reflects the amount of pattern information involved in each view; (2) during the iteration of VR-MV-TSK-FS, weak views are automatically reduced by comparing the learnt weight with a fixed threshold which is also automatically set according to the number of objects and the dimension of the feature space. With the two mechanisms, a training algorithm is developed. Extensive experiments on synthetic datasets, UCI datasets and a case study of textile color classification indicate that the proposed algorithm can effectively reduce weak views and achieves better performance than other benchmarking algorithms.

Multitask TSK Fuzzy System Modeling by Jointly Reducing Rules and Consequent Parameters

Existing multitask Takagi-Sugeno-Kang (TSK) fuzzy modeling methods always produce high complex fuzzy models with numerous redundant rules and consequent parameters. To this end, we propose a novel multitask TSK fuzzy modeling method called mtSparseTSK, which learns a compact set of fuzzy rules and shared consequent parameters across tasks in a unified procedure. Specifically, we consider the fuzzy rule reduction and consequent parameter selection across tasks by devising novel group sparsity regularizations in the learning criterion of the model. We also integrate the intertask relations in the proposed TSK model for multitask learning. We fully utilize the block structure in the TSK fuzzy models in formulating a joint block sparse optimization problem and develop a procedure for alternating direction method of multipliers (ADMMs) to find the optimal solution of the problem. Experiments on the synthetic and real-world datasets demonstrate the distinctive performance of the proposed methods over the existing ones on multitask fuzzy system modeling.

Comparing Performance Potentials of Classical and Intuitionistic Fuzzy Systems in Terms of Sculpting the State Space

This article provides new application-independent perspectives about the performance potential of an intuitionistic (I-) fuzzy system over a (classical) Takagi-Sugeno-Kang (TSK) fuzzy system. It does this by extending sculpting the state-space works from a TSK fuzzy system to an I-fuzzy system. It demonstrates that, for piecewise-linear membership functions (trapezoids and triangles), an I-fuzzy system always has significantly more first-order rule partitions of the state space-the coarse sculpting of the state space-than does a TSK fuzzy system, and that some I-fuzzy systems also have more second-order rule partitions of the state space-the fine sculpting of the state space-than does a TSK fuzzy system. It is the author's conjecture that for piecewise-linear membership functions (trapezoids and triangles): it is the always significantly greater coarse (and possibly fine) sculpting of the state space that provides an I-fuzzy system with the potential to outperform a TSK fuzzy system, and that a type-1 I-fuzzy system has the potential to outperform an interval type-2 fuzzy system.

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.

Common and Special Knowledge-Driven TSK Fuzzy System and Its Modeling and Application for Epileptic EEG Signals Recognition

Takagi-Sugeno-Kang (TSK) fuzzy systems are well known for their good balances between approximation accuracy and interpretability. Among a wide variety of existing TSK fuzzy systems, most of them are driven by special knowledge since the learned parameters of each fuzzy rule are totally different. However, common knowledge is equally important and useful in practice and hence a TSK fuzzy system embedded with common knowledge should be more intuitive and interpretable when tackling with real-world problems. In this paper, we propose a common and special knowledge-driven TSK fuzzy system (CSK-TSK-FS), in which the parameters corresponding to each feature in then-parts of fuzzy rules always keep invariant and these parameters are viewed as common knowledge. As for its modeling, except the gradient descent techniques and other existing training algorithms, we can obtain a trained CSK-TSK-FS from a trained GMM or a trained FLNN because the proposed fuzzy system CSK-TSK-FS is mathematically equivalent to a special GMM and a FLNN. CSK-TSK-FS has three characteristics: (1) with the classical centroid defuzzification strategy, the involved common knowledge can be separated from fuzzy rules such that the interpretability of CSK-TSK-FS can be enhanced; (2) it can be trained quickly by the proposed LLM-based training algorithm; (3) the equivalence relationships among CSK-TSK-FS, GMM and FLNN allow them to share some commonality in training such that the proposed LLM-based training algorithm provides a novel fast training tool for training GMM and FLNN. Experimental results on UCI, KEEL and epileptic EEG datasets demonstrate the promising classification of CSK-TSK-FS.

Intelligent diagnosis of cardiac valve calcification in ESRD patients with peritoneal dialysis based on improved Takagi-Sugeno-Kang fuzzy system

Without a B-ultrasound result, if a doctor diagnoses a suspected patient using only the basic clinical features, such as age, gender, serum calcium, and urea clearance index (KT/V), the diagnostic accuracy will be very low (even less than 50%). To solve this problem, a machine learning technology is proposed to intelligently diagnose cardiac valve calcification in end-stage renal disease (ESRD) patients with peritoneal dialysis. Compared with classical classification technologies, the proposed method aims to develop a model that has both medical interpretability and high recognition performance. In terms of interpretability, the Takagi-Sugeno-Kang fuzzy system is considered a basic model due to its built-in interpretable ability. In addition, because the distribution of the positive class (cardiac valve calcification is positive) and negative class (cardiac valve calcification is negative) in the peritoneal dialysis patient dataset is unbalanced, a novel unbalanced TSK (Takagi-Sugeno-Kang) fuzzy system (B-TSK-FS) is developed using a novel unbalanced fuzzy learning mechanism. The corresponding results reveal that the B-TSK-FS method obtains promising results (the max testing accuracy is over 98%) compared with classical machine learning methods for intelligently diagnosing cardiac valve calcification in ESRD patients with peritoneal dialysis.

Epileptic EEG Signals Recognition Using a Deep View-Reduction TSK Fuzzy System With High Interpretability

Takagi-Sugeno-Kang (TSK) fuzzy systems are well known for their good balance between approximation accuracy and interpretability. In this paper, we propose a deep view-reduction TSK fuzzy system termed as DVR-TSK-FS in which two powerful mechanisms associating with a deep structure are developed: 1) during the multi-view learning in each component, a sample-distribution-dependent parameter is defined to control the learning of the weight of each view. The parameter is not fixed by users, it is set according to the feature space in advance such that the learnt weight of each view indeed reflects the amount of pattern information involved in each view; 2) during the iteration of DRV-TSK-FS in each component, weak views are automatically reduced by comparing the learnt weight with a fixed threshold which is also automatically set according to the number of objects and the dimension of the feature space. 3) All components are linked in a stacked way based on the stacked generalization principle such that the outputs of all previous components are augmented into the current one which can help open the manifold structure of the original feature space. DRV-TSK-FS is testified on a multi-view EEG dataset for epileptic EEG signals recognition.

Evaluation of Takagi-Sugeno-Kang fuzzy method in entropy-based detection of DDoS attacks

The detection of distributed denial of service (DDoS) attacks based on internet traffic anomalies is a method which is general in nature and can detect unknown or zero-day attacks. One of the statistical characteristics used for this purpose is network traffic entropy: a sudden change in entropy may indicate a DDoS attack. However, this approach often gives false positives, and this is the main obstacle to its wider deployment within network security equipment. In this paper, we propose a new, two-step method for detection of DDoS attacks. This method combines the approaches of network traffic entropy and the Takagi-Sugeno-Kang fuzzy system. In the first step, the detection process calculates the entropy distribution of the network packets. In the second step, the Takagi-Sugeno-Kang fuzzy system (TSK-FS) method is applied to these entropy values. The performance of the TSK-FS method is compared with that of the typically used approach, in which cumulative sum (CUSUM) change point detection is applied directly to entropy time series. The results show that the TSK-FS DDoS detector reaches enhanced sensitivity and robustness in the detection process, achieving a high true-positive detection rate and a very low false-positive rate. As it is based on entropy, this combined method retains its generality and is capable of detecting various types of attack.

Intelligent control of nonlinear inverted pendulum system using Mamdani and TSK fuzzy inference systems: a performance analysis without and with disturbance input

Fuzzy control, an intelligent control technique uses the human expert knowledge to make control decisions. The inverted pendulum, a highly nonlinear unstable system is used as a benchmark for implementing the control methods. In this paper the modelling and control design of nonlinear inverted pendulum-cart dynamic system with and without disturbance input have been presented. Here PID control and fuzzy control methods using Mamdani type and Takagi-Sugeno-Kang (TSK) type fuzzy inference systems (FIS) have been implemented to control the cart position and to stabilise the inverted pendulum in vertically upright position. The MATLAB-Simulink models have been developed for simulation of the control schemes. The simulation results and performance analysis justify the comparative advantages of fuzzy control methods.

Learning compact zero-order TSK fuzzy rule-based systems for high-dimensional problems using an Apriori + local search approach

Learning fuzzy rule-based systems entails searching a set of fuzzy rules which fits the training data. Even if using fix fuzzy partitions, the amount of rules that can be formed is exponential in the number of variables. Thus, the search must be carried out by means of metaheuristics such as genetic algorithms, and sometimes restricted to the set of candidate rules which reach a minimum support.In this article, we propose and evaluate two methods to learn zero-order Takagi–Sugeno–Kang fuzzy systems in medium-high dimensional domains. First, we introduce the minimum individual error of a rule in the criterion for candidate selection. Then, due to the intrinsic locality of fuzzy rule-based systems, where each rule mainly interacts with adjacent rules, we study the use of local search algorithms to carry out the search of the final rule base.Results show that the proposed scheme for candidate rule selection leads to an improvement in the results, regardless of the subsequent search algorithm. Moreover, local search-based algorithms achieve competitive results, reducing substantially the number of rules of the learnt systems.