Consequent Parameters Of Fuzzy Rules Research Articles

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.

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.

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.

The design of neuro-fuzzy networks using particle swarm optimization and recursive singular value decomposition

In this paper, a neuro-fuzzy network with novel hybrid learning algorithm is proposed. The novel hybrid learning algorithm is based on the fuzzy entropy clustering (FEC), the modified particle swarm optimization (MPSO), and the recursive singular value decomposition (RSVD). The FEC is used to partition the input data for performing structure learning. Then, we adopt the MPSO to adjust the antecedent parameters of fuzzy rules. Two strategies in the MPSO, called the effective local approximation method (ELAM) and the multi-elites strategy (MES), are proposed to improve the performance of the traditional PSO. Moreover, we will apply RSVD to obtain the optimal consequent parameters of fuzzy rules. The proposed hybrid learning algorithm achieves superior performance in learning speed and learning accuracy than those of some traditional genetic methods.