Abstracts:This addresses one small error in [1]. Specifically, in the sentence just before (13), the word “ms” is incorrect. The correct words are “matrix of fuzzy coefficients.”

Abstracts:This article proposes a new result on mismatched double fuzzy summation inequality. The mismatched double fuzzy summation inequality usually originates from the control system design with using the Takagi–Sugeno (TS) fuzzy model, in which the controller and the system are with mismatched membership functions. Compared with the existing method to deal with the mismatched double fuzzy summation inequality, the proposed one is less conservative and does not introduce additional decision variables. Three examples including the mismatched membership functions of the TS fuzzy control system in the discrete-time case, the continuous-time case and the interval type-2 fuzzy system under state feedback control mechanism are used to show that the new result is less conservative than the existing one.

Abstracts:The concept of fuzzy domain adaptation (FDA) is focused on transferring a model trained in a source domain to a target domain, where intrinsic distribution discrepancies exist in nonstationary and nondeterministic environments. In this article, a novel drift decoupling-based variational adaptation network (DD-VAN) is proposed for FDA, allowing for the learning of intradomain evolutionary patterns and interdomain uncertainties. The DD-VAN algorithm is implemented in three main steps: 1) An intradomain evolutionary trend modeling module is first employed to capture unknown temporal variations through an autoencoder architecture with variational inference; 2) a prototype-assisted fuzzy clustering module is used to estimate the membership degree of the target data, characterizing the inherent uncertainty and imprecision present in real-world distributions; and 3) a membership-aware domain fuzzy matching module is utilized to learn the gradual transitions between category-related data pairs in the source and target domains by introducing uncertainties. Furthermore, it is theoretically demonstrated that the inferred posterior distributions of latent codes can be optimized to align with the corresponding prior distributions by minimizing the Kullback–Leibler divergence. Extensive experiments are conducted on cross-domain tasks involving both synthetic and real-world datasets, and the experimental results suggest that the DD-VAN algorithm outperforms existing state-of-the-art methods.

Abstracts:The three-way approximation of fuzzy sets represents membership values using a three-valued set $\lbrace \mathbf{1}, \mathbf{m}, \mathbf{0}\rbrace$, where 1 indicates total belongingness, 0 total nonbelongingness, and m an intermediate state. This approach elevates values of membership function above a threshold $\alpha$ to 1, reduces those below $\beta$ to 0, and assigns the remaining ones to an intermediate value m. A key challenge lies in determining the thresholds $\alpha$ and $\beta$ and selecting the value of m, as existing models often lack analytical solutions and fail to fully explore the relationship between m and membership structures. This study introduces an asymmetric three-way approximation model for fuzzy sets, removing the constraint $\alpha + \beta = 1$. Analytical formulas are derived for the thresholds $ \alpha $ and $ \beta $ by minimizing information loss, and the relationship between m and membership structures is thoroughly examined. An adaptive optimizer is proposed to learn the approximate optimal value of m by minimizing the information loss. The experimental results show that information loss decreases initially before increasing as m grows. Besides, our model achieves the best classification across most datasets.

Abstracts:Traditional stochastic configuration networks (SCNs)-based industrial soft sensors have the shortcomings of failing to account for “slowness” characteristic and struggling with processing rule-based information. The original slow feature extraction methods based on autoencoders with fixed structure are lack of flexibility and difficult to maintain a balance between efficiency and accuracy. To address these challenges, a framework of fuzzy hierarchical SCNs (FHSCNs) is proposed, which consists of a slow feature extraction block, a fuzzy inference block and an enhanced output block. The slow feature extraction block is designed, which utilizes a autoencoder based on two SCNs with shared-parameters and the incremental learning paradigm of SCNs to efficiently and adaptively extract the slow-varying latent features. The fuzzy inference block is proposed, which can process rule-based slow feature information. The fuzzy inference block can allow the model to have the fuzzy reasoning capabilities and improve the model interpretability. The enhanced output block with an enhancement layer and a direct-connect portion is presented, which enables the FHSCNs to have the ability of capturing both linearity and nonlinearity of the fuzzy rule-based features. The proposed framework is validated through comprehensive experiments to demonstrate its effectiveness in constructing industrial soft sensor model.

Abstracts:This study explores a novel interpretable Takagi–Sugeno–Kang (TSK) fuzzy ensemble classifier called MEI-TSK from a multiview learning perspective. Unlike most existing fuzzy ensemble classifiers where aggregation learning performs only after the training of multiple fuzzy subclassifiers, MEI-TSK first allows the determination of the antecedents of all fuzzy rules in an individual way for each of TSK fuzzy subclassifiers. It then employs the proposed misclassification-error-inspired learning to accomplish its ensemble learning by training the consequents of all fuzzy rules of each TSK fuzzy subclassifier in a multiview learning way with the simplest averaging aggregation. As a result, the misclassification error caused by such an ensemble learning of fuzzy subclassifiers is theoretically upper bounded. MEI-TSK also features the use of both Bernoulli random feature selection and random feature permutation. The permuted features can be conveniently useful for determining all the antecedents of fuzzy rules with diversity guarantee among all the subclassifiers, and accordingly, be discarded after ensemble learning, resulting in shorter fuzzy rules and improved generalization capability. The experimental results indicate the effectiveness of MEI-TSK in terms of classification performance and/or interpretability.

Abstracts:Inverse reinforcement learning optimal control is under the framework of learner–expert, the learner system can learn expert system's trajectory and optimal control policy via a reinforcement learning algorithm and does not need the predefined cost function, so it can solve optimal control problem effectively. This article develops a fuzzy inverse reinforcement learning optimal control scheme with inverse reinforcement learning algorithm for Takagi–Sugeno (T–S) fuzzy systems with disturbances. Since the controlled fuzzy systems (learner systems) desire to learn or imitate expert system's behavior trajectories, a learner–expert structure is established, where the learner only know the expert system's optimal control policy. To reconstruct expert system's cost function, we develop a model-free inverse Q-learning algorithm that consists of two learning stages: an inner Q-learning iteration loop and an outer inverse optimal iteration loop. The inner loop aims to find fuzzy optimal control policy and the worst-case disturbance input via learner system's cost function by employing zero-sum differential game theory. The outer one is to update learner system's state-penalty weight via only observing expert systems' optimal control policy. The model-free algorithm does not require that the controlled system dynamics are known. It is proved that the designed algorithm is convergent and also the developed inverse reinforcement learning optimal control policy can ensure T–S fuzzy learner system to obtain Nash equilibrium solution. Finally, we apply the presented fuzzy inverse Q-learning optimal control method to nonlinear unmanned surface vehicle system and the computer simulation results verified the effectiveness of the developed scheme.

Abstracts:Large-scale group decision making provides an effective way to obtain desirable group decision outcomes. Many studies have neglected the effect of opinion dynamics on the consensus reaching process (CRP) in the social trust network (STN) with a hybrid mesoscale structure. In addition, the application of communication theory to the CRP has rarely been considered. This article is devoted to building a fuzzy opinion dynamics-driven consensus model through the detection of hybrid mesoscale structures. First, this article proposes a novel mesoscale structure detection method that can detect both overlapping community structures and core–periphery structures in the STN. Then, to capture the opinion dynamics process under hybrid mesoscale structures, this article improves the opinion dynamics model by delineating five categories of nodes. Considering the dynamic changes of the CRP, a consensus feedback mechanism driven by opinion dynamics is proposed. In addition, the opinion adjustment is based on the “Spiral of Silence Theory.” Finally, the practicality of the proposed model is illustrated through an example. The superiority of the new detection algorithm and the efficiency of the novel consensus model are demonstrated through comparative analysis.

Abstracts:Traditional partition-based fuzzy clustering algorithms are widely used for revealing possible hidden structures in data. However, high computational cost limits their applications in large-scale and high-dimensional data. Moreover, most fuzzy clustering algorithms are sensitive to noise. To tackle these issues, a robust jointly sparse fast fuzzy clustering algorithm via anchor graph (RSFCAG) is proposed and analyzed in this article. Specifically, we first propose a fast k-means method integrated shadowed set and balanced ternary tree, which serves as a fast hierarchical clustering approach by partitioning every cluster into three subclusters at each layer (3KHK). 3KHK can quickly obtain the anchor set and its optimization is solved fast by the simplex method, which also captures the ambiguity and uncertainty between clusters in large-scale clustering tasks. Second, a similarity matrix learning approach based on possibilistic neighbors is further proposed to get a robust similarity graph, which strengthens the ability of fuzzy clustering to handle large-scale data. Furthermore, the orthogonal projection matrix is integrated into the RSFCAG framework to transform the original high-dimensional space into low-dimensional space. Finally, the $L_{2,1}$-norm loss and regularization are integrated into the joint algorithm RSFCAG, which is solved optimally by block coordinate technique, to enhance the robustness and interpretability of the fuzzy clustering process. The experimental results demonstrate the effectiveness and efficiency of our proposed method in most of benchmark datasets.

Abstracts:To address the problem of robust stability analysis for interval type-2 fuzzy systems (IT2FSs), this article proposes an innovative analysis approach based on model transformation. First, a classical piecewise linear approximation method is utilized to process the upper boundary membership functions and lower boundary membership functions of the footprint of uncertainty in IT2FSs, resulting in linear boundary membership functions (MFs) that are more convenient for analysis, along with the corresponding approximation error functions. Subsequently, a novel error model transformation method is introduced to handle these error terms. By constructing new fuzzy rules and MFs, the boundary error terms are converted into a new fuzzy model, thereby incorporating more information about the error functions into the stability analysis. Based on this model, a robust stability condition in the form of linear matrix inequalities are derived, achieving improved robustness. Finally, the effectiveness of the proposed method is validated through simulations on real-world systems, and its superiority is demonstrated by comparison with existing methods.