Takagi-Sugeno-Kang Fuzzy System Research Articles

A fully interpretable stacking fuzzy classifier with stochastic configuration-based learning for high-dimensional data

This study proposes a stacking fuzzy classifier with stochastic configuration-based learning that can achieve higher training and testing performances and sound interpretability of fuzzy rules. By using the understandable first-order Takagi–Sugeno–Kang fuzzy system, we initially stack each successive subclassifier on both the remaining misclassified training data and the corresponding outputs of the previous subclassifier. Subsequently, a Stacking Fuzzy Classifier with Fully Interpretable and Short fuzzy Rules (FISR-SFC) further improves its prediction by linearly aggregating the outputs of all the subclassifiers. FISR-SFC trains each subclassifier using the proposed stochastic configuration-based learning procedure to utilize its training excellence on gradually smaller misclassified training data and simultaneously maintain the full interpretability of each subclassifier. Experimental results on twelve benchmarking datasets reveal that FISR-SFC is at least comparable to and even better than the comparative classifiers in terms of average testing accuracy/G-mean and/or short rules with full interpretability.

TAKAGI–SUGENO–KANG FUZZY SYSTEM MODELING BASED ON LOW-RANK SPARSE SUBSPACE LEARNING FOR MOTOR IMAGERY ELECTROENCEPHALOGRAM SIGNAL CLASSIFICATION

The classification of electroencephalogram (EEG) signals derived from motor imagery (MI) has always been a hot topic in the field of brain–computer interfaces. Due to its ability to handle the nonstationary and uncertain information contained in EEG signals, the Takagi–Sugeno–Kang fuzzy system (TSK-FS) has become an advantageous classification algorithm. To train a fuzzy system with strong discrimination capabilities from EEG data interspersed with redundant information, this paper proposes a TSK-FS modeling method based on low-rank sparse subspace learning (TSK-LSSL). This method focuses on consequent parameter learning, which transforms the traditional consequent parameter learning strategy into low-rank subspace and sparse subspace learning processes. Low-rank subspace learning is used to mine the global structural information of data and effectively reduce the number of fuzzy rules. During sparse subspace learning, [Formula: see text]-norm regularization is used to constrain the consequent parameters and causes the number of redundant consequent parameters to be zero, thereby simplifying the fuzzy rules. In addition, a local boundary term based on graph matrices is embedded into the objective function to mine the local structural information of the given data. TSK-LSSL simplifies the number of rules and the consequent part of the fuzzy rules. It exhibits good classification performance on two BCI Competition databases.

Takagi–Sugeno–Kang Fuzzy Systems for High-Dimensional Multilabel Classification

Takagi–Sugeno–Kang Fuzzy Systems for High-Dimensional Multilabel Classification

A Multi-view Semi-supervised Takagi–Sugeno–Kang Fuzzy System for EEG Emotion Classification

A Multi-view Semi-supervised Takagi–Sugeno–Kang Fuzzy System for EEG Emotion Classification

A novel multi-task TSK fuzzy system modeling method based on multi-task fuzzy clustering

The traditional multi-task Takagi-Sugeno-Kang (TSK) fuzzy system modeling methods pay more attention to utilizing the inter-task correlation to learn the consequent parameters but ignore the importance of the antecedent parameters of the model. To this end, we propose a novel multi-task TSK fuzzy system modeling method based on multi-task fuzzy clustering. This method first proposes a novel multi-task fuzzy c-means clustering method that learns multiple specific clustering centers for each task and some common clustering centers for all tasks. Secondly, for the consequent parameters of the fuzzy system, the novel low-rank and row-sparse constraints are proposed to better implement multi-task learning. The experimental results demonstrate that the proposed model shows better performance compared with other existing methods.

Multiview Transfer Representation Learning With TSK Fuzzy System for EEG Epilepsy Detection

Automatic analysis of epileptic encephalography (EEG) signals with intelligent models can greatly reduce the workload of doctors. However, the lack of data, insufficient labels, and inconsistent data distribution in real-world scenarios significantly affect the performance of intelligent models. Transfer learning plays an important role in solving the above problems but some challenges remain. First, while various feature extraction methods are available to extract features from the original epilepsy signal, it is difficult to determine which features are effective. Second, transfer learning may lead to domain information loss since the original feature representation from different domains is changed. Third, most of the existing models lack transparency to provide medical practitioners confidence of use. To this end, this paper proposes the novel method Multi-view Information Preservation Transfer Representation Learning based on Fuzzy Systems (MIP-TRL-FS) to address the issues. First, MIP-TRL-FS utilizes multiple views to get rid of the feature selection process. Second, information preservation techniques are utilized to maintain the data information from the aspects of sample level and feature level, thus minimizing information loss during the transfer learning process. Third, by using Takagi-Sugeno-Kang Fuzzy Systems (TSK-FS) as the base model, the output of the proposed method can be interpreted linguistically with IF-THEN rules to makes the model transparent. Extensive experiments were conducted on the CHB-MIT dataset and the results demonstrate the effectiveness of the proposed method.

Takagi-Sugeno-Kang fuzzy system fusion: A survey at hierarchical, wide and stacked levels

With excellent global approximation performance and interpretability, Takagi-Sugeno-Kang (TSK) fuzzy systems have enjoyed a wide range of applications in various fields, such as smart control, medical, and finance. However, in handling high-dimensional complex data, the performance and interpretability of a single TSK fuzzy system are easily degraded by rule explosion due to the curse of dimensionality. Ensemble learning comes into play to deal with the problem by the fusion of multiple TSK fuzzy systems using appropriate ensemble learning strategies, which has shown to be effective in eliminating the issue of the curse of dimensionality curse problem and reducing the number of fuzzy rules, thereby maintaining the interpretability of fuzzy systems. To this end, this paper gives a comprehensive survey of TSK fuzzy system fusion to provide insights into further research development. First, we briefly review the fundamental concepts related to TSK fuzzy systems, including fuzzy rule structures, training methods, and interpretability, and discuss the three different development directions of TSK fuzzy systems. Next, along the direction of TSK fuzzy system fusion, we investigate in detail the current ensemble strategies for fusion at hierarchical, wide and stacked levels, and discuss their differences, merits and weaknesses from the aspects of time complexity, interpretability (model complexity) and classification performance. We then present some applications of TSK fuzzy systems in real-world scenarios. Finally, the challenges and future directions of TSK fuzzy system fusion are discussed to foster prospective research.

A Fully Interpretable First-Order TSK Fuzzy System and Its Training With Negative Entropic and Rule-Stability-Based Regularization

While interpretable antecedent parts of first-order Takagi-Sugeno-Kang (TSK) fuzzy rules can be properly acquired by adopting some clustering methods, this study aims at avoiding the commonly-used yet fully incomprehensive consequent parts and their intractable training, and simultaneously seeking for enhanced generalization performance by determining the weight of each rule. The central idea is to build a mathematically equivalent bridge between a Gaussian mixture model (GMM) and a fully interpretable first-order TSK fuzzy system called FIMG-TSK, with the help of Gaussian-mixture's mean. The resultant FIMG-TSK has a simple expected output expression without summation-to-one defuzzification, which will be helpful in inducing both smaller output variance and a negative entropic and rule-stability-based regularizer for enhancing the generalization performance. After revealing three factors affecting the output stability of FIMG-TSK, the negative entropic and rule-stability-based regularizer is designed through both these factors and the squared entropy to make the output variance of FIMG-TSK as small as possible. Accordingly, a novel training method, whose objective function takes the proposed regularizer as an additional term and hence compromises both accuracy and output stability of FIMG-TSK, is developed to quickly provide an analytical solution to the weight of each rule. The effectiveness of the proposed training method is manifested by the experimental results on ten regression datasets.

Implementation of Takagi Sugeno Kang Fuzzy with Rough Set Theory and Mini-Batch Gradient Descent Uniform Regularization

The Takagi Sugeno Kang (TSK) fuzzy approach is popular since its output is either a constant or a function. Parameter identification and structure identification are the two key requirements for building the TSK fuzzy system. The input utilized in fuzzy TSK can have an impact on the number of rules produced in such a way that employing more data dimensions typically results in more rules, which causes rule complexity. This issue can be solved by employing a dimension reduction technique that reduces the number of dimensions in the data. After that, the resulting rules are improved with MBGD (Mini-Batch Gradient Descent), which is then altered with uniform regularization (UR). UR can enhance the classifier's fuzzy TSK generalization performance. This study looks at how the rough sets method can be used to reduce data dimensions and use Mini Batch Gradient Descent Uniform Regularization (MBGD-UR) to optimize the rules that come from TSK. 252 respondents' body fat data were utilized as the input, and the mean absolute percentage error (MAPE) was used to analyze the results. Jupyter Notebook software and the Python programming language are used for data processing. The analysis revealed that the MAPE value was 37%, falling into the moderate area. Doi: 10.28991/ESJ-2023-07-03-09 Full Text: PDF

Multiple source partial knowledge transfer for manufacturing system modelling

Transfer learning has shown its attractiveness for manufacturing system modelling by leveraging previously acquired knowledge to assist in training the target model, whereas most techniques focus on single-source transfer settings. Since there are usually multiple source domains available in practice, multi-source transfer learning is attracting more attention. Existing researches regard the source instance or the source model as the basic information granularity, which makes it difficult to reduce the global shift and the local discrepancy across domains simultaneously. Therefore, this paper presents a multiple source partial knowledge transfer method (MSPKT) for manufacturing system modelling tasks, in which partial knowledge is defined as a novel information granularity between the instance granularity and model granularity. Firstly, TSK (Takagi-Sugeno-Kang) fuzzy system is introduced as the basic learner to represent partial knowledge effectively. Then, we design a transferability measurement of partial knowledge by considering the similarity and reliability to support transfer learning with multiple source domains. Finally, a synthetic dataset and two manufacturing system datasets are used to verify the effectiveness of the proposed method.

Crude oil production prediction based on an intelligent hybrid modelling structure generated by using the clustering algorithm in big data

Since the behavior of a complex dynamic system for a large oil field in Iraq is significantly influenced by many nonlinearities, its dependent parameters exhibit non-stationary with a very high delay time. Developing white-box modelling approaches for such dynamic oil well production cannot handle these large data sets with all dependent dimensions and their non-linear effects. Therefore, this study adopts the hybrid model that combines white-box and black-box to address such problems because the model outputs require various variable types to achieve optimal fitness to measured values. The hybrid model structure needs to evolve with changes in the physical parameters (white-box part) and Neural Networks' Weights (black-box part). The model structure of the proposed hybrid network relied on converting fuzzy rules in a Takagi–Sugeno–Kang Fuzzy System (TSK-FS) into a multilayer perceptron network (MLP). The hybrid parameters are formulated concerning six-dimensional dependent variables to describe them in matrix form or layer and by which can quantify total model outputs. After mapping categorical variables to tuples of MLP, the Gauss-Newton regression (GNR) provides an optimal update of the hybrid parameters to get the best fitting of the model outputs with the target of the dataset. The clustering technique and GNR promote predictive performance due to reducing uncertainties in the hybrid parameters. Due to time being the most effective of the independent variables for predicting oil production, datasets are classified into different clusters based on time. The actual field dataset for training and validation is collected from Zubair Oil Field (9 oil wells), which is implemented to build the proposed model. The results of the hybrid model indicate that the development of the proposed structure has achieved the high capability to represent such big data which is the most imperative feature of the proposed model. Furthermore, obtained results show its accuracy far outpacing competitors and achieving a significant improvement in predictive performance.

Layer Normalization for TSK Fuzzy System Optimization in Regression Problems

Recently, mini-batch gradient descent (MBGD)-based optimization has become popular in Takagi–Sugeno–Kang (TSK) fuzzy system optimization. However, it suffers from some challenges, including the curse of dimensionality and the sensitivity to the choice of the optimizer. The former has been alleviated by our previously proposed high-dimensional TSK (HTSK) algorithm. In this article, we point out that the latter is caused by the gradient vanishing problem on the rule consequent parameters, which in turn is caused by the small magnitude of the normalized rule firing levels, especially when the number of rules is large. Thus, the rule consequents are easily trapped into a bad local minimum with poor generalization performance. We propose to use first layer normalization (LN) to amplify the small firing levels, and then rectified linear unit (ReLU) to discard rules far away from the current training sample. We evaluated our proposed HTSK-LN and HTSK-LN-ReLU on twelve regression datasets with various sizes and dimensionalities. Experiments demonstrated that they can significantly improve the generalization performance, regardless of the training set size, feature dimensionality, choice of the optimizer, and rulebase size.

Pitch Control of Wind Turbine Blades Using Fractional Particle Swarm Optimization

To achieve the maximum power from wind in variable-speed regions of wind turbines (WTs), a suitable control signal should be applied to the pitch angle of the blades. However, the available uncertainty in the modeling of WTs complicates calculations of these signals. To cope with this problem, an optimal controller is suitable, such as particle swarm optimization (PSO). To improve the performance of the controller, fractional order PSO (FPSO) is proposed and implemented. In order to construct this approach for a two-mass WT, we propose a new state feedback, which was first applied to the turbine. The idea behind this state feedback was based on the Taylor series. Then, a linear model with uncertainty was obtained with a new input control signal. Thereafter, the conventional PSO (CPSO) and FPSO were used as optimal controllers for the resulting linear model. Finally, a comparison was performed between CPSO and FPSO and the fuzzy Takagi–Sugeno–Kang (TSK) inference system. The provided comparison demonstrates the advantages of the Taylor series with combination to these controllers. Notably, without the state feedback, CPSO, FPSO, and TSK fuzzy systems cannot stabilize WTs in tracking the desired trajectory.

A reinforcement learning fuzzy system for continuous control in robotic odor plume tracking

AbstractIn dynamic outdoor environments characterized by turbulent airflow and intermittent odor plumes, robotic odor plume tracking remains challenging, because existing algorithms heavily rely on manually tuning or learning from expert experience, which are hard to implement in an unknown environment. In this paper, a multi-continuous-output Takagi–Sugeno–Kang fuzzy system was designed and tuned with reinforcement learning to solve the robotic odor source localization problem in dynamic odor plumes. Based on the Lévy Taxis plume tracking controller, the proposed fuzzy system determined the parameters of the controller based on the robot’s observation and guided the robot to turn and move towards the odor source at each searching step. The trained fuzzy system was tested in simulated filament-based odor plumes dispersed by a changing wind field. The results showed that the performance of the proposed fuzzy system-based controller trained with reinforcement learning can achieve a similar success rate and higher efficiency compared with a manually tuned and well-designed fuzzy system-based controller. The fuzzy system-based plume tracking controller was also validated through real robotic experiments.

A Concise TSK Fuzzy Ensemble Classifier Integrating Dropout and Bagging for High-Dimensional Problems

Improving the tradeoff between accuracy and interpretability is essential for the problem of handling high-dimensional data in Takagi–Sugeno–Kang (TSK) fuzzy systems and providing insights into real-world tasks. However, the TSK fuzzy system becomes complex and challenging to interpret as the data dimension increases. Here, we report an ensemble classifier, which is an enhanced adaptive network-based fuzzy inference system (ANFIS) integrating improved bagging and dropout to build concise fuzzy rule sets. First, the high-dimensional feature space is decomposed into a series of low-dimensional feature subsets using the bagging and random subspace method to train multiple ANFISs. An improved dropout strategy is then applied in training ANFISs by temporarily disabling rules in each training epoch and deleting rules after training to obtain sparse rulesets with high-quality rules. These sub-models are subsequently aggregated to perform the fuzzy inference. Results on high-dimensional benchmark datasets confirm that both the bagging and dropout strategies are effective, providing high interpretability by reducing the co-firing degrees and rules of sub-models while guaranteeing accuracy at the same time.

Broad Learning Based Dynamic Fuzzy Inference System With Adaptive Structure and Interpretable Fuzzy Rules

This article investigates the feasibility of applying the broad learning system (BLS) to realize a novel Takagi–Sugeno–Kang (TSK) neuro-fuzzy model, namely a broad learning based dynamic fuzzy inference system (BL-DFIS). It not only improves the accuracy and interpretability of neuro-fuzzy models but also solves the challenging problem that models are incapable of determining the optimal architecture autonomously. BL-DFIS first accomplishes a TSK fuzzy system under the framework of BLS, in which an extreme learning machine auto-encoder is employed to obtain feature representation in a fast and analytical way, and an interpretable linguistic fuzzy rule is integrated into the enhancement node to ensure the high interpretability of the system. Meanwhile, the extended-enhancement unit is designed to achieve the first-order TSK fuzzy system. In addition, a dynamic incremental learning algorithm with internal pruning and updating mechanism is developed for the learning of BL-DFIS, which enables the system to automatically assemble the optimal structure to obtain a compact rule base and an excellent classification performance. Experiments on benchmark datasets demonstrate that the proposed BL-DFIS can achieve a better classification performance than some state-of-the-art nonfuzzy and neuro-fuzzy methods, simultaneously using the most parsimonious model structure.

A hybrid Genetic–Grey Wolf Optimization algorithm for optimizing Takagi–Sugeno–Kang fuzzy systems

Nature-inspired optimization techniques have been applied in various fields of study to solve optimization problems. Since designing a Fuzzy System (FS) can be considered one of the most complex optimization problems, many meta-heuristic optimizations have been developed to design FS structures. This paper aims to design a Takagi–Sugeno–Kang fuzzy Systems (TSK-FS) structure by generating the required fuzzy rules and selecting the most influential parameters for these rules. In this context, a new hybrid nature-inspired algorithm is proposed, namely Genetic–Grey Wolf Optimization (GGWO) algorithm, to optimize TSK-FSs. In GGWO, a hybridization of the genetic algorithm (GA) and the grey wolf optimizer (GWO) is applied to overcome the premature convergence and poor solution exploitation of the standard GWO. Using genetic crossover and mutation operators accelerates the exploration process and efficiently reaches the best solution (rule generation) within a reasonable time. The proposed GGWO is tested on several benchmark functions compared with other nature-inspired optimization algorithms. The result of simulations applied to the fuzzy control of nonlinear plants shows the superiority of GGWO in designing TSK-FSs with high accuracy compared with different optimization algorithms in terms of Root Mean Squared Error (RMSE) and computational time.

A novel heuristic for handover priority in mobile heterogeneous networks based on a multimodule Takagi–Sugeno–Kang fuzzy system

H2RDC (heuristic handover based on RCC-DTSK-C), a heuristic algorithm based on a highly interpretable deep Takagi–Sugeno–Kang fuzzy classifier, is proposed for suppressing the mobile heterogeneous networks problem of frequent handover and handover ping-pong in the multibase-station scenario. This classifier uses a stack structure between subsystems to form a deep classifier before generating a base station (BS) priority sequence during the handover process, and adaptive handover hysteresis is calculated. Simulation results show that H2RDC allows user equipment to switch to the best antenna at the optimal time. In high-BS density load and mobility scenarios, the proposed algorithm's handover success rate is similar to those of classic algorithms such as best connection (BC), self tuning handover algorithm (STHA), and heuristic for handover based on AHP-TOPSIS-FUZZY (H2ATF). Moreover, the handover rate is 83% lower under H2RDC than under BC, whereas the handover ping-pong rate is 76% lower.

Structured Sparse Regularized TSK Fuzzy System for predicting therapeutic peptides.

Therapeutic peptides act on the skeletal system, digestive system and blood system, have antibacterial properties and help relieve inflammation. In order to reduce the resource consumption of wet experiments for the identification of therapeutic peptides, many computational-based methods have been developed to solve the identification of therapeutic peptides. Due to the insufficiency of traditional machine learning methods in dealing with feature noise. We propose a novel therapeutic peptide identification method called Structured Sparse Regularized Takagi-Sugeno-Kang Fuzzy System on Within-Class Scatter (SSR-TSK-FS-WCS). Our method achieves good performance on multiple therapeutic peptides and UCI datasets.

Forecasting Trend of Coronavirus Disease 2019 using Multi-Task Weighted TSK Fuzzy System

Artificial intelligence– (AI) based fog/edge computing has become a promising paradigm for infectious disease. Various AI algorithms are embedded in cooperative fog/edge devices to construct medical Internet of Things environments, infectious disease forecast systems, smart health, and so on. However, these systems are usually done in isolation, which is called single-task learning. They do not consider the correlation and relationship between multiple/different tasks, so some common information in the model parameters or data characteristics is lost. In this study, each data center in fog/edge computing is considered as a task in the multi-task learning framework. In such a learning framework, a multi-task weighted Takagi-Sugeno-Kang (TSK) fuzzy system, called MW-TSKFS, is developed to forecast the trend of Coronavirus disease 2019 (COVID-19). MW-TSKFS provides a multi-task learning strategy for both antecedent and consequent parameters of fuzzy rules. First, a multi-task weighted fuzzy c-means clustering algorithm is developed for antecedent parameter learning, which extracts the public information among all tasks and the private information of each task. By sharing the public cluster centroid and public membership matrix, the differences of commonality and individuality can be further exploited. For consequent parameter learning of MW-TSKFS, a multi-task collaborative learning mechanism is developed based on ε-insensitive criterion and L2 norm penalty term, which can enhance the generalization and forecasting ability of the proposed fuzzy system. The experimental results on the real COVID-19 time series show that the forecasting tend model based on multi-task the weighted TSK fuzzy system has a high application value.