Parameters Of Fuzzy Rules Research Articles

A Symmetrical Fuzzy Neural Network Regression Method Coordinating Structure and Parameter Identifications for Regression

Fuzzy neural networks have both the interpretability of fuzzy systems and the self-learning ability of neural networks, but they will face the challenge of “rule explosion” when dealing with high-dimensional data. Moreover, the structure and parameter identifications of models are generally performed in two stages, and this always attends to one thing and loses another in terms of interpretability and predictive performance. In this paper, a fuzzy neural network regression method (FNNR) that coordinates structure identification and parameter identification is proposed. To alleviate the problem of rule explosion, the structure identification and parameter identification are coordinated in the training process, and the numbers of fuzzy rules and fuzzy partitions are effectively limited, while the parameters of fuzzy rules are optimized. The symmetrical architecture of the FNNR is designed for automatic structure identification. An alternate training strategy is adopted by treating discrete and continuous parameters differently, and thus the convergence efficiency of the algorithm is improved. To enhance interpretability, regularized terms are designed from fuzzy rule level and fuzzy partition level to guide the model to learn fuzzy rules with simple structures and clear semantics. The experimental results show that the proposed method has both a compact structure and high precision.

A CNN-Based Born-Again TSK Fuzzy Classifier Integrating Soft Label Information and Knowledge Distillation

This paper proposes a CNN-based born-again Takagi-Sugeno-Kang (TSK) fuzzy classifier denoted as CNNBaTSK. CNNBaTSK achieves the following distinctive characteristics: 1) CNNBaTSK provides a new perspective of knowledge distillation with a non-iterative learning method (least learning machine with knowledge distillation, LLM-KD) to solve the consequent parameters of fuzzy rule, where consequent parameters are trained jointly on the ground-truth label loss, knowledge distillation loss, and regularization term; 2) with the inherent advantage of the fuzzy rule, CNNBaTSK has the capability to express the dark knowledge acquired from the CNN in an interpretable manner. Specifically, the dark knowledge (soft label information) is partitioned into five fixed antecedent fuzzy spaces. The centers of each soft label information in different fuzzy rules are {0, 0.25, 0.5, 0.75, 1}, which may have corresponding linguistic explanations: { <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">very low, low, medium, high, very high</i> }. For the consequent part of the fuzzy rule, the original features are employed to train the consequent parameters that ensure the direct interpretability in the original feature space. The experimental results on the benchmark datasets and the CHB-MIT EEG dataset demonstrate that CNNBaTSK can simultaneously improve the classification performance and model interpretability.

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.

A novel learning algorithm based on computing the rules’ desired outputs of a TSK fuzzy neural network with non-separable fuzzy rules

In this paper, a novel learning approach to train fuzzy neural networks’ parameters based on calculating the desired outputs of their rules, is proposed. We describe the desired outputs of fuzzy rules as values that make the output error equal to the minimum. To find these desired outputs, a new constrained convex optimization problem is introduced and solved. Afterward, the parameters of fuzzy rules are trained to reduce the error between the current rules’ outputs and the estimated desired ones. Therefore, the proposed learning method avoids direct output error backpropagation, which leads to vanishing gradient and consequently getting stuck in a local optimum. Therefore, the proposed method does not need any sophisticated initialization method. This learning method is successfully utilized to train a new Takagi–Sugeno-Kang (TSK) Fuzzy Neural Network with correlated fuzzy rules. The proposed paradigm, including the proposed TSK correlation-aware architecture along with the learning method, is successfully applied to six real-world time-series predictions, regression problems, and nonlinear system identification. According to the experimental results, the performance of our proposed method outperforms other methods with a more parsimonious structure.

Adaptive Multi-Agent Control Strategy in Heterogeneous Countermeasure Environments

In the rapidly changing air combat environment, it is quite difficult for pilots to make speedy and reasonable decisions in a very short period due to lack of experience and the uncertainty of perception situation. Hence, the authors propose an intelligent cognitive tactical strategy framework of air combat on multi-source information in uncertain air combat situations for decision support. A fuzzy inferring tree method is proposed to simulate human intellection. Then, to further improve the accuracy of the reasoning results, a genetic algorithm is introduced to optimize the structure and parameters of fuzzy rules. The simulation results show that the proposed model is reasonable, fast, accurate, repeatable, and fatigue-free, which lays a good foundation for future high-end unmanned combat explorations.

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.

Research on Flocculation and Sedimentation Characteristics of Extremely Fine Coal Slime Based on Computer PID Algorithm

Coal slime water treatment is a very important process in coal preparation plant, its treatment effect directly affects the reuse of washing water and closed-circuit circulation index, and on the other links of coal preparation plant such as separation efficiency, the number of product quality index has a great impact, and even restricts the economic and social benefits of an important system. Based on improved grey prediction fuzzy control principle, an improved slurry flocculating settling process of feed forward and feedback control strategy, the improvement is: using fuzzy algorithm to replace the current use of conventional fuzzy control algorithm, namely according to the online setting parameters of fuzzy rules, both to overcome the difficult to eliminate the steady-state error and fuzzy control to realize accurate control weaknesses, and overcome the difficulty of parameter setting, make them form a complementary advantages. Therefore, it is of great significance to study advanced control method and improve control effect in coal preparation plant.

Optimized Hybridization of Ant Colony Optimization and Genetic Algorithm (HACOGA) Based Interpretable Intuitive and Correlated-Contours Fuzzy Neural Network Classifier for Abalone

Classification generally assigns objects to enormous predefined categories and it is pervasive crisis that covers various application. Preparing the data for Classification and Prediction is the major problem in classification. In order to rectify this issue, an approximate function is proposed using Interpretable intuitive and Correlated-contours Fuzzy Neural Network (IC-FNN). For acquiring cor- related fuzzy rules and non-separable rules that comes under proper optimization problem. The extracted fuzzy rule’s parameter was fine-tuned sourced on hierarchical Levenberg Marquardt (LM) learning method for enhancing performance. But here parameters of fuzzy rules aren’t tuned per- fectly. Hybridization of Ant Colony Optimization Genetic Algorithm (HACOGA) is proposed here to rectify these issues. It tunes the parameters of the extracted fuzzy rules. Hybridization is enforced to certain factors and ACO and GA variables that share same characteristics in the computation. Experimental results shows that proposed HACOGA assist in enhancing the performance of FNN with recall, precision, accuracy and F -measure for the Abalone age prediction dataset.

Gravitational Search For Designing A Fuzzy Rule-Based Classifiers For Handwritten Signature Verification

Handwritten signatures are used in authentication systems as a universal biometric identifier. Signature authenticity verification requires building and training a classifier. This paper describes a new approach to the verification of handwritten signatures by dynamic characteristics with a fuzzy rule-based classifier. It is suggested to use the metaheuristic Gravitational Search Algorithm for the selection of the relevant features and tuning fuzzy rule parameters. The efficiency of the approach was tested with an original dataset; the type II errors in finding the signature authenticity did not exceed 0.5% for the worst model and 0.08% for the best model.

Self-organising interval type-2 fuzzy neural network with asymmetric membership functions and its application

For the identification and modelling problems of a nonlinear system with complex uncertainties, a self-organising interval type-2 fuzzy neural network structure with asymmetric membership functions (SIT2FNN-AMF) is developed. First, a fuzzy c-means algorithm with four fuzzifier parameters is used to partition the input data to obtain the uncertainty means and widths of the fuzzy rule antecedent; then, according to the cluster validity criterion, the number of fuzzy rules is determined. Thus, identifications of the structure and rule antecedent parameters are automatically completed. The consequent part uses the Mamdani model, and the initial value of the consequent parameter is an interval random number. The fuzzy rule parameters are tuned by the gradient descent method. Finally, the proposed SIT2FNN-AMF is applied to simulations of nonlinear system identification and soft-sensing model for ethylene cracking furnace yield. The comparison of simulation results obtained with a conventional fuzzy neural network and interval type-2 fuzzy neural network verifies the performance of the proposed SIT2FNN-AMF.

Bayesian Takagi–Sugeno–Kang Fuzzy Classifier

In this paper, the Takagi–Sugeno–Kang (TSK) fuzzy classifier is casted into the Bayesian inference framework and a new fuzzy classifier called Bayesian TSK fuzzy classifier (B-TSK-FC) is proposed accordingly. The proposed classifier can be constructed by learning both the antecedent and consequent parameters of the involved fuzzy rules simultaneously. As a result of the introduction of Bayesian inference, the proposed B-TSK-FC can be distinguished as follows. 1) Unlike most existing TSK fuzzy classifiers where the antecedent and consequent parameters of fuzzy rules are learnt in a decoupled manner and the antecedent parameters are learnt only in the input space, the antecedent parameters of the fuzzy rules in B-TSK-FC are learnt by developing a fuzzy clustering method in the input–output space, and the consequent parameters of fuzzy rules are learnt in accordance with the maximum margin of separation principle, thereby resulting to form an intrinsic link between the input and output spaces to achieve improved classification performance and better interpretability. 2) With a Dirichlet prior assumption about fuzzy memberships in fuzzy clustering, a Markov-Chain Monte-Carlo technique is employed to estimate the parameters of the proposed classifier from a sampling perspective. 3) Rather than being rivals, fuzziness and probability in B-TSK-FC are collaboratively modeled to enhance the performance of TSK fuzzy classifier, in terms of classification and interpretability. Our experimental results in synthetic datasets as well as several real-world datasets confirm such merits of the proposed fuzzy classifier.

Imbalanced TSK Fuzzy Classifier by Cross-Class Bayesian Fuzzy Clustering and Imbalance Learning

In this paper, a novel construction algorithm called imbalanced Takagi–Sugeno–Kang fuzzy classifier (IB-TSK-FC) for the TSK fuzzy classifier is presented to improve the classification performance and rule-based interpretability for imbalanced datasets. IB-TSK-FC consists of two components: 1) a cross-class Bayesian fuzzy clustering algorithm (BF3C) and 2) an imbalance learning algorithm. In order to achieve high interpretability, BF3C is developed to determine an appropriate number of fuzzy rules and identify antecedent parameters of fuzzy rules from the perspective of the probabilistic model. In addition to inheriting the distinctive advantage of Bayesian fuzzy clustering that the number of clusters can be estimated in the framework of Bayesian inference, BF3C considers repulsion forces between cluster centers belonging to different classes, and uses an alternating iterative strategy to obtain more interpretable antecedent parameters for imbalanced datasets. In order to improve the classification performance for imbalanced datasets, an imbalance learning algorithm is derived to estimate consequent parameters of fuzzy rules on the basis of the weighted average misclassification error. Comprehensive experiments on synthetic and UCI datasets demonstrate the effectiveness of the proposed IB-TSK-FC algorithm.

Adaptive Self-Learning Fuzzy Autopilot Design for Uncertain Bank-to-Turn Missiles

This paper proposes an adaptive self-learning fuzzy autopilot design for uncertain bank-to-turn (BTT) missiles due to external disturbances and system errors from the variations of the aerodynamic coefficients and control surface loss. The self-learning fuzzy systems called extended sequential adaptive fuzzy inference systems (ESAFISs) are utilized to compensate for these uncertainties in an adaptive backstepping architecture. ESAFIS is a real‐time self-learning fuzzy system with simultaneous structure identification and parameter learning. The fuzzy rules of the ESAFIS can be added or deleted based on the input data. Based on the Lyapunov stability theory, adaptation laws are derived to update the consequent parameters of fuzzy rules, which guarantees both tracking performance and stability. The robust control terms with the adaptive bound-estimation schemes are also designed to compensate for modeling errors of the ESAFISs by augmenting the self-learning fuzzy autopilot control laws. The proposed autopilot is validated under the control surface loss, aerodynamic parameter perturbations, and external disturbances. Simulation study is also compared with a conventional backstepping autopilot and a neural autopilot in terms of the tracking ability. The results illustrate that the designed fuzzy autopilot can obtain better steady‐state and transient performance with the dynamically self-learning ability.

Bayesian zero-order TSK fuzzy system modeling

Different from the existing TSK fuzzy system modeling methods, a novel zero-order TSK fuzzy modeling method called Bayesian zero-order TSK fuzzy system (B-ZTSK-FS) is proposed from the perspective of Bayesian inference in this paper. The proposed method B-ZTSK-FS constructs zero-order TSK fuzzy system by using the maximum a posteriori (MAP) framework to maximize the corresponding posteriori probability. First, a joint likelihood model about zero-order TSK fuzzy system is defined to derive a new objective function which can assure that both antecedents and consequents of fuzzy rules rather than only their antecedents of the most existing TSK fuzzy systems become interpretable. The defined likelihood model is composed of three aspects: clustering on the training set for antecedents of fuzzy rules, the least squares (LS) error for consequent parameters of fuzzy rules, and a Dirichlet prior distribution for fuzzy cluster memberships which is considered to not only automatically match the “sum-to-one” constraints on fuzzy cluster memberships, but also make the proposed method B-ZTSK-FS scalable for large-scale datasets by appropriately setting the Dirichlet index. This likelihood model indeed indicates that antecedent and consequent parameters of fuzzy rules can be linguistically interpreted and simultaneously optimized by the proposed method B-ZTSK-FS which is based on the MAP framework with the iterative sampling algorithm, which in fact implies that fuzziness and probability can co-jointly work for TSK fuzzy system modeling in a collaborative rather than repulsive way. Finally, experimental results on 28 synthetic and real-world datasets are reported to demonstrate the effectiveness of the proposed method B-ZTSK-FS in the sense of approximation accuracy, interpretability and scalability.

Indirect adaptive hierarchical fuzzy sliding mode controller for a class of nonlinear systems

This study presents a novel indirect adaptive hierarchical fuzzy sliding mode controller for a class of high-order SISO nonlinear systems with unknown function in the presence of bounded disturbance. The hierarchical fuzzy system is able to reduce the number of rules and parameters with respect to ordinary fuzzy systems. On-line tuning algorithm for consequent part parameters of fuzzy rules in different layer of hierarchical fuzzy system is derived using defined Lyapunov function. It is proved that the suggested adaptive scheme can achieve asymptotically stable tracking of a reference input with guarantee of the bounded system signals. To show the effectiveness of the proposed method, control of flexible joint robot system is considered in simulations. The simulation results demonstrate the validity, efficiency and feasibility of the proposed approach to control of nonlinear dynamic system.

Optimal Tuning Strategy for MIMO Fuzzy Predictive Controllers

This paper describes the development of a method to optimally tune constrained MPC algorithms for a nonlinear process. The T-S model is firstly established for nonlinear systems and its sequence parameters of fuzzy rules are identified by local recursive least square method. The proposed method is obtained by minimizing performance criteria in the worst-case conditions to control the process system, thus assuring robustness to the set of optimum tuning parameters. The resulting constrained mixed-integer nonlinear optimization problem is solved on the basis of a version of the particle swarm optimization technique. The practicality and effectiveness of the identification and control scheme is demonstrated by simulation results.

AN EFFICIENT EVOLUTIONARY NEURAL FUZZY CONTROLLER FOR THE INVERTED PENDULUM SYSTEM

In this article we propose an evolutionary neural fuzzy controller for the planetary train–type inverted pendulum system (IPS) and verify its effectiveness. The novel hybrid particle swarm optimization (HPSO) learning algorithm of the proposed controller is based on approaches of the fuzzy entropy clustering (FEC), the modified PSO (MPSO), and recursive singular value decomposition (RSVD). The FEC is applied to generate base particles and the MPSO is proposed to effectively improve the performance of the traditional PSO. There are mainly two different characteristics between the MPSO and its original version; that is, the initial parameters of the MPSO are calculated by an effective local approximation method (ELAM), and the global optimum is chosen by the multi-elites strategy (MES). In addition, we use the RSVD to determine the optimal consequent parameters of fuzzy rules, in order to reduce requirements of the computational time and space. Experimental results show that the proposed approach outperforms the proportional–integral–derivative (PID), PSO, and MPSO in terms of better abilities of tracking and noise rejection for planetary train–type IPS.

Modelling and long-term simulation of a heat recovery steam generator

Developing accurate non-linear dynamical models for heat recovery steam generator (HRSG) units is presented in this article. The common non-linear autoregressive with exogenous input (NARX) system topology was employed to develop the neuro-fuzzy models based on the experimental data taken during field experiments. In this structure, the non-linear behaviours of the HRSG unit can be characterized through interpolation of local linear models associated with different operating regions via fuzzy inference mechanism. The operating regimes were recognized by applying a genetic algorithm-based fuzzy clustering technique to the prepared data sets. The structures of the fuzzy models are defined with respect to the obtained optimal cluster centres and the corresponding membership functions. The parameters of fuzzy rules were adjusted by recursive least-squares estimation method to fit the model responses to real data. The performances of developed models were evaluated by performing a comparison between the model responses and the responses of the real plant. In addition, the stability of the developed models was assessed by perturbing the model inputs from the nominal values. This guarantees the long-term simulation capabilities of the developed models. A comparison between the responses of the corresponding models and the models obtained from some recent modelling approaches was performed to show the advantages of the developed models. The results show the accuracy and reliability of the developed models at transient and steady-state conditions.

Evolutionary Tuning of Fuzzy Rule Base Systems for Nonlinear System Modelling and Control

Fuzzy systems generally works based on expert knowledge base. Fuzzy Expert knowledge base derived from the heuristic knowledge of experts or experience operators in the form of fuzzy control rules and membership functions (MFs). The major difficulties for design ing a fuzzy models and controllers are identify the optimized fuzzy rules and their corresponding shape, type and distribution of MFs. Moreover, the numbers of fuzzy control rules increases exponentially with the number of input output variables related to the control system. For this reason it is very difficult and time consuming for an expert to identify the complete rule set and shape of MFs for a complex control system having large number of input and output variables. In this paper, we propose a methodcalled evolutionary fuzzy system for tuning the parameters of fuzzy rules and adjust the shape of MFs through evolutionary algorithms in order to design a suitable and flexible fuzzy models and controller for complex systems. This paper also presents new flexible encoding method methods for evolutionary algorithms. In evolutionary fuzzy system, the evolutionary algorithms is adapted in two different ways Firstly, generating the optimal fuzzy rule sets including the number of rules inside it and secondly, selecting the optimum shape and distribution of MFs for the fuzzy control rules. In order to evaluate the validity and performance of the proposed approach we have designed a test strategy for the modeling and control of nonlinear systems. The simulation re sults show the effectiveness of our method and give better performance than existing fuzzy expert systems.

Design of an adaptive self-organizing fuzzy neural network controller for uncertain nonlinear chaotic systems

Though the control performances of the fuzzy neural network controller are acceptable in many previous published papers, the applications are only parameter learning in which the parameters of fuzzy rules are adjusted but the number of fuzzy rules should be determined by some trials. In this paper, a Takagi–Sugeno-Kang (TSK)-type self-organizing fuzzy neural network (TSK-SOFNN) is studied. The learning algorithm of the proposed TSK-SOFNN not only automatically generates and prunes the fuzzy rules of TSK-SOFNN but also adjusts the parameters of existing fuzzy rules in TSK-SOFNN. Then, an adaptive self-organizing fuzzy neural network controller (ASOFNNC) system composed of a neural controller and a smooth compensator is proposed. The neural controller using the TSK-SOFNN is designed to approximate an ideal controller, and the smooth compensator is designed to dispel the approximation error between the ideal controller and the neural controller. Moreover, a proportional-integral (PI) type parameter tuning mechanism is derived based on the Lyapunov stability theory, thus not only the system stability can be achieved but also the convergence of tracking error can be speeded up. Finally, the proposed ASOFNNC system is applied to a chaotic system. The simulation results verify the system stabilization, favorable tracking performance, and no chattering phenomena can be achieved using the proposed ASOFNNC system.