Fuzzy clustering decomposes data into clusters using partial memberships by exploring the cluster structure information, which demonstrates comparable performance for knowledge exploitation under the circumstance of information incompleteness. In general, this scheme considers the memberships of objects to cluster centroids and applies to clusters with the spherical distribution. In addition, the noises and outliers may significantly influence the clustering process; a common mitigation measure is the application of separate noise processing algorithms, but this usually introduces multiple parameters which are challenging to be determined for different data types. This paper proposes a new fuzzy-rough intrigued harmonic discrepancy clustering (HDC) algorithm by noting that fuzzy-rough sets offer a higher degree of uncertainty modelling for both vagueness and imprecision present in real-valued datasets. The HDC is implemented by introducing a novel concept of harmonic discrepancy, which effectively indicates the dissimilarity between a data instance and foreign clusters with their distributions fully considered. The proposed HDC is thus featured by a powerful processing ability on complex data distribution leading to enhanced clustering performance, particularly on noisy datasets, without the use of explicit noise handling parameters. The experimental results confirm the effectiveness of the proposed HDC, which generally outperforms the popular representative clustering algorithms on both synthetic and benchmark datasets, demonstrating the superiority of the proposed algorithm.

As one of rapidly developing methodology for dealing with complex problems in line with human cognition, granular computing has made significant achievements in knowledge discovery. Neighborhood classifier, as a typical description of granular computing (GrC), is an effective method for classification of continuous data. However, in the phase of constructing neighborhood rules, the existing neighborhood classifiers are divided into the following two modes and both have defects: (1) The strategy driven by center: There are a lot of overlap and inclusion among neighborhood rules, that is, it need to spend much time to reduce redundancy rules; (2) The strategy driven by rule: There are many rules containing only one object, which cannot form an effective covering, and would affect knowledge acquisition in the incremental environment. Therefore, in this paper, fuzzy quotient space theory is introduced to construct neighborhood rules. Based on optimal granularity of fuzzy quotient space, a neighborhood covering classifier, which has no redundant rules and could form the effective covering, is proposed without any artificial parameter. Second, comprehensively considering the knowledge purity and complexity, the quality measure of granularity is proposed, which guides the optimal granularity selection of HQSS. Third, neighborhood rules are constructed in the optimal granularity. Then, the offset of center is introduced to describe the membership degree of the test object to different neighborhood rules, and the neighborhood allocation strategy is proposed accordingly. Next, an algorithm for the neighborhood covering classifier based on these theories is proposed. Finally, experiments on 13 UCI datasets and 3 real datasets are carried out to verify the performance of the proposed classifier from four common classification indexes.

A fuzzy-model-based approach is developed to investigate the reinforcement learning-based optimization for nonlinear Markov jump singularly perturbed systems. As the first attempt, an offline parallel iteration learning algorithm is presented to solve the coupled algebraic Riccati equations with singular perturbation and jumping parameters. Furthermore, based on the integral reinforcement learning approach, a novel online parallel learning algorithm is proposed by employing the slow and fast sampled data simultaneously, where the impacts of stochastic jumping and ill-conditioned numerical problems are avoided. Meanwhile, the convergence of the proposed learning algorithms is proved. Finally, we present a tunnel diode circuit model to demonstrate the efficacy of the proposed methods.

In this paper, the security-guaranteed fuzzy networked state estimation issue is investigated for a class of two-dimensional (2-D) systems with norm-bounded disturbances. Considering the structural specificity of the 2-D systems, the membership function in the Takagi-Sugeno fuzzy model is established to reflect the spatial information. Multiple sensor arrays are utilized to improve the observation diversity and overcome the measurement obstacle induced by geographical restrictions. The network-based deception attacks, occurring in a probabilistic fashion, are characterized by a set of Bernoulli distributed random variables. By resorting to the 2-D fuzzy blending and augmentation operations, the error dynamics of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$s$</tex-math></inline-formula> th 2-D fuzzy estimator is formulated and, subsequently, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">globally asymptotical stability</i> of the local error dynamics is studied in virtue of Lyapunov stability theory, fuzzy theory, and stochastic analysis technique. Then, sufficient conditions are derived to ensure the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><inline-formula><tex-math notation="LaTeX">$(\varrho _{1},\varrho _{2},\varrho _{3},\rho _{s})$</tex-math></inline-formula>-security</i> of the local error dynamics. Furthermore, the estimation fusion problem of the local fuzzy estimators is discussed and the corresponding <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><inline-formula><tex-math notation="LaTeX">$(\varrho _{1},\varrho _{2},\varrho _{3},\rho _{s})$</tex-math></inline-formula>-security</i> is also guaranteed. Finally, an illustrative example is provided to demonstrate the rationality and the effectiveness of the proposed state estimation algorithm.

This paper studies a nonlinear disturbance observer (NDO) based finite-time fuzzy adaptive dynamic surface control (DSC) of nonlinear systems (NSs) with external disturbances and preassigned performance indices. By constructing a type of finite-time preassigned-performance function (FTPF), the tracking error variable is confined within the boundaries of the FTPF such that the performance metrics, for instance, steady state error, and convergence time, could be satisfied. Incorporating fuzzy adaptive control with the NDO technique, an effective composite NDO (CNDO) scheme is built to reckon the unknown composite disturbances, including unknown external disturbances and fuzzy approximation errors, which implies that fuzzy approaching errors can be further cut down. It is confirmed that the closed-loop system is semi-globally practically finite-time stable (SPFTS), as well as the tracking error and convergence time satisfies the predefined performance indices. In the end, the validity of the CNDO-based finite-time adaptive DSC scheme has been evidenced by a practical example model.

This paper addresses the problem of fault-tolerant output tracking control for a class of Takagi-Sugeno (T-S) fuzzy systems with unmeasurable premise variables subject to additive and multiplicative actuator faults and external disturbances. In nominal conditions, utilizing a quadratic Lyapunov function and non-parallel distributed compensation (non-PDC) technique, the suggested strategy delivers linear matrix inequality (LMI)-based constraints. Simultaneously design of the proportional-integral (PI)-like state feedback controller and fuzzy anti-windup compensator is achieved with the aim of output tracking. In the faulty case, by considering the nominal system as a reference model, a direct adaptive projection-based approach is developed using the T-S fuzzy modeling and control techniques to supply the adaptive fault-tolerant controller components. An enhanced proportional-integral (PI) state/fault observer with unmeasurable premise variables is introduced only to provide the estimation of states to be used in the proposed controller. The overall closed-loop system ensures the uniformly ultimately bounded (u.u.b) solutions for error dynamics. Two examples, subsuming an inverted pendulum and a chaotic power system, have been used to present the merits and efficiency of the suggested approach persuasively.

This study focuses on the problem of adaptive fuzzy dynamic surface output feedback control for a class of uncertain nonlinear systems subjected to unknown input hysteresis. A Prandtl–Ishlinskii (PI) model is applied to the uncertain nonlinear system for describing the unknown input hysteresis, making the controller design feasible. In addition, a nonlinear extended state observer (NESO) is designed for simultaneously estimating the unmeasurable states and generalized disturbances, including the nonlinear hysteresis term of the PI model and external disturbances. In addition, a novel nonlinear function is designed to replace the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$fal(\cdot)$</tex-math></inline-formula> function of the general NESO to address a modification that increases the convergence speed. Considering the incorporation of the improved nonlinear extended state observer (INESO), an adaptive output feedback control scheme is proposed based on fuzzy logic system and dynamic surface techniques. A command filter is employed to avoid the “explosion of complexity” problem inherent in the backstepping technique, while compensating the filtering error caused by adopting the filter. The Lyapunov approach is used to demonstrate the stability of the entire closed-loop system. Experiments regarding a piezoelectric micro–positioning stage are conducted, the results of which illustrate that the proposed adaptive fuzzy output feedback control method can guarantee a satisfactory tracking performance.

This paper studies the fixed-time consensus tracking control of nonlinear multi-agent systems (NNMASs) suffering from non-affine faults. A fixed-time command filter is constructed to solve the “explosion of complexity” issue, and a novel fixed-time error compensation mechanism is designed to eliminate filtering errors. The adaptive fuzzy control technique is introduced to deal with the unknown nonlinear terms containing non-affine fault functions. A new fixed-time fault-tolerant control scheme based on the modified prescribed performance technology is proposed for the NNMASs, which ensures that the closed-loop system satisfies the practical fixed-time stability. In addition, the consensus tracking errors of the NNMASs converge to a given range within a prescribed performance bound in a fixed time. Finally, comparative simulation results show the effectiveness of the proposed method.

We introduce a neural network model for regression in which prediction uncertainty is quantified by Gaussian random fuzzy numbers (GRFNs), a newly introduced family of random fuzzy subsets of the real line that generalizes both Gaussian random variables and Gaussian possibility distributions. The output GRFN is constructed by combining GRFNs induced by prototypes using a combination operator that generalizes Dempster's rule of Evidence Theory. The three output units indicate the most plausible value of the response variable, variability around this value, and epistemic uncertainty. The network is trained by minimizing a loss function that generalizes the negative log-likelihood. Comparative experiments show that this method is competitive, both in terms of prediction accuracy and calibration error, with state-of-the-art techniques such as random forests or deep learning with Monte Carlo dropout. In addition, the model outputs a predictive belief function that can be shown to be calibrated, in the sense that it allows us to compute conservative prediction intervals with specified belief degree.