Zhiwu Li

Yingying Liu, Kai Cai, Zhiwu Li

In this paper we study multi-agent discrete-event systems where the agents can be divided into several groups, and within each group the agents have similar or identical state transition structures. We employ a relabeling map to generate a "template structure" for each group, and synthesize a scalable supervisor whose state size and computational process are independent of the number of agents. This scalability allows the supervisor to remain invariant (no recomputation or reconfiguration needed) if and when there are agents removed due to failure or added for increasing productivity. The constant computational effort for synthesizing the scalable supervisor also makes our method promising for handling large-scale multi-agent systems. Moreover, based on the scalable supervisor we design scalable local controllers, one for each component agent, to establish a purely distributed control architecture. Three examples are provided to illustrate our proposed scalable supervisory synthesis and the resulting scalable supervisors as well as local controllers.

Chunwei Tian, Menghua Zheng, Chia-Wen Lin et al.

Deep networks can usually depend on extracting more structural information to improve denoising results. However, they may ignore correlation between pixels from an image to pursue better denoising performance. Window transformer can use long- and short-distance modeling to interact pixels to address mentioned problem. To make a tradeoff between distance modeling and denoising time, we propose a heterogeneous window transformer (HWformer) for image denoising. HWformer first designs heterogeneous global windows to capture global context information for improving denoising effects. To build a bridge between long and short-distance modeling, global windows are horizontally and vertically shifted to facilitate diversified information without increasing denoising time. To prevent the information loss phenomenon of independent patches, sparse idea is guided a feed-forward network to extract local information of neighboring patches. The proposed HWformer only takes 30% of popular Restormer in terms of denoising time.

Chunwei Tian, Chengyuan Zhang, Bob Zhang et al.

Deep convolutional neural networks can use hierarchical information to progressively extract structural information to recover high-quality images. However, preserving the effectiveness of the obtained structural information is important in image super-resolution. In this paper, we propose a cosine network for image super-resolution (CSRNet) by improving a network architecture and optimizing the training strategy. To extract complementary homologous structural information, odd and even heterogeneous blocks are designed to enlarge the architectural differences and improve the performance of image super-resolution. Combining linear and non-linear structural information can overcome the drawback of homologous information and enhance the robustness of the obtained structural information in image super-resolution. Taking into account the local minimum of gradient descent, a cosine annealing mechanism is used to optimize the training procedure by performing warm restarts and adjusting the learning rate. Experimental results illustrate that the proposed CSRNet is competitive with state-of-the-art methods in image super-resolution.

Sichen Ding, Zhiwu Li

Classical opacity theory for discrete-event systems relies strictly on observable event sequences, fundamentally failing to capture security breaches in hybrid architectures where an attacker exploits both classical traces and localized quantum correlations. To address this gap, we formalize current-state opacity within the framework of safe partially observed quantum Petri nets by introducing a true-concurrency semantics that represents classical observations as partially ordered multisets via unfolding configurations. Building upon this, we define quantitative posterior-state leakage as the trace distance between the attacker's localized quantum states, evaluated conditionally on whether the underlying system has reached a secret or non-secret marking. This formulation strictly preserves classical opacity definitions. To achieve computational tractability, we apply the stabilizer formalism and develop an exact symbolic verification algorithm. By combining targeted unfolding exploration, state aggregation exclusively at maximal unobservable reach, and stabilizer-tableau propagation, this procedure circumvents both concurrent interleaving explosions and exponential density-matrix overhead. Finally, an entanglement-swapping case study validates the exact leakage evaluation, demonstrates substantial computational gains, and establishes a rigorous interface for counterexample-guided leakage enforcement.

Xiaoguang Han, Kuize Zhang, Jiahui Zhang et al.

Opacity, as an important property in information-flow security, characterizes the ability of a system to keep some secret information from an intruder. In discrete-event systems, based on a standard setting in which an intruder has the complete knowledge of the system's structure, the standard versions of current-state opacity and initial-state opacity cannot perfectly characterize high-level privacy requirements. To overcome such a limitation, in this paper we propose two stronger versions of opacity in partially-observed discrete-event systems, called \emph{strong current-state opacity} and \emph{strong initial-state opacity}. Strong current-state opacity describes that an intruder never makes for sure whether a system is in a secret state at the current time, that is, if a system satisfies this property, then for each run of the system ended by a secret state, there exists a non-secret run whose observation is the same as that of the previous run. Strong initial-state opacity captures that the visit of a secret state at the initial time cannot be inferred by an intruder at any instant. Specifically, a system is said to be strongly initial-state opaque if for each run starting from a secret state, there exists a non-secret run of the system that has the same observation as the previous run has. To verify these two properties, we propose two information structures using a novel concurrent-composition technique, which has exponential-time complexity $O(|X|^4|Σ_o||Σ_{uo}||Σ|2^{|X|})$, where $|X|$ (resp., $|Σ|$, $|Σ_o|$, $|Σ_{uo}|$) is the number of states (resp., events, observable events, unobservable events) of a system.

Cong Wang, Witold Pedrycz, ZhiWu Li et al.

G-images refer to image data defined on irregular graph domains. This work elaborates a similarity-preserving Fuzzy C-Means (FCM) algorithm for G-image segmentation and aims to develop techniques and tools for segmenting G-images. To preserve the membership similarity between an arbitrary image pixel and its neighbors, a Kullback-Leibler divergence term on membership partition is introduced as a part of FCM. As a result, similarity-preserving FCM is developed by considering spatial information of image pixels for its robustness enhancement. Due to superior characteristics of a wavelet space, the proposed FCM is performed in this space rather than Euclidean one used in conventional FCM to secure its high robustness. Experiments on synthetic and real-world G-images demonstrate that it indeed achieves higher robustness and performance than the state-of-the-art FCM algorithms. Moreover, it requires less computation than most of them.

Kaijie Xu, Witold Pedrycz, Zhiwu Li et al.

Traditional clustering methods are limited when dealing with huge and heterogeneous groups of gene expression data, which motivates the development of bi-clustering methods. Bi-clustering methods are used to mine bi-clusters whose subsets of samples (genes) are co-regulated under their test conditions. Studies show that mining bi-clusters of consistent trends and trends with similar degrees of fluctuations from the gene expression data is essential in bioinformatics research. Unfortunately, traditional bi-clustering methods are not fully effective in discovering such bi-clusters. Therefore, we propose a novel bi-clustering method by involving here the theory of Granular Computing. In the proposed scheme, the gene data matrix, considered as a group of time series, is transformed into a series of ordered information granules. With the information granules we build a characteristic matrix of the gene data to capture the fluctuation trend of the expression value between consecutive conditions to mine the ideal bi-clusters. The experimental results are in agreement with the theoretical analysis, and show the excellent performance of the proposed method.

Qi Zhang, Carla Seatzu, Zhiwu Li et al.

This paper focuses on the problem of cyber attacks for discrete event systems under supervisory control. In more detail, the goal of the supervisor, who has a partial observation of the system evolution, is that of preventing the system from reaching a set of unsafe states. An attacker may act in two different ways: he can corrupt the observation of the supervisor editing the sensor readings, and can enable events that are disabled by the supervisor. This is done with the aim of leading the plant to an unsafe state, and keeping the supervisor unaware of that before the unsafe state is reached. A special automaton, called attack structure is constructed as the parallel composition of two special structures. Such an automaton can be used by the attacker to select appropriate actions (if any) to reach the above goal, or equivalently by the supervisor, to validate its robustness with respect to such attacks.

Cong Wang, Witold Pedrycz, ZhiWu Li et al.

Due to its inferior characteristics, an observed (noisy) image's direct use gives rise to poor segmentation results. Intuitively, using its noise-free image can favorably impact image segmentation. Hence, the accurate estimation of the residual between observed and noise-free images is an important task. To do so, we elaborate on residual-driven Fuzzy C-Means (FCM) for image segmentation, which is the first approach that realizes accurate residual estimation and leads noise-free image to participate in clustering. We propose a residual-driven FCM framework by integrating into FCM a residual-related fidelity term derived from the distribution of different types of noise. Built on this framework, we present a weighted $\ell_{2}$-norm fidelity term by weighting mixed noise distribution, thus resulting in a universal residual-driven FCM algorithm in presence of mixed or unknown noise. Besides, with the constraint of spatial information, the residual estimation becomes more reliable than that only considering an observed image itself. Supporting experiments on synthetic, medical, and real-world images are conducted. The results demonstrate the superior effectiveness and efficiency of the proposed algorithm over existing FCM-related algorithms.

Kaijie Xu, Witold Pedrycz, Zhiwu Li

Information granules have been considered to be the fundamental constructs of Granular Computing (GrC). As a useful unsupervised learning technique, Fuzzy C-Means (FCM) is one of the most frequently used methods to construct information granules. The FCM-based granulation-degranulation mechanism plays a pivotal role in GrC. In this paper, to enhance the quality of the degranulation (reconstruction) process, we augment the FCM-based degranulation mechanism by introducing a vector of fuzzification factors (fuzzification factor vector) and setting up an adjustment mechanism to modify the prototypes and the partition matrix. The design is regarded as an optimization problem, which is guided by a reconstruction criterion. In the proposed scheme, the initial partition matrix and prototypes are generated by the FCM. Then a fuzzification factor vector is introduced to form an appropriate fuzzification factor for each cluster to build up an adjustment scheme of modifying the prototypes and the partition matrix. With the supervised learning mode of the granulation-degranulation process, we construct a composite objective function of the fuzzification factor vector, the prototypes and the partition matrix. Subsequently, the particle swarm optimization (PSO) is employed to optimize the fuzzification factor vector to refine the prototypes and develop the optimal partition matrix. Finally, the reconstruction performance of the FCM algorithm is enhanced. We offer a thorough analysis of the developed scheme. In particular, we show that the classical FCM algorithm forms a special case of the proposed scheme. Experiments completed for both synthetic and publicly available datasets show that the proposed approach outperforms the generic data reconstruction approach.

Kaijie Xu, Witold Pedrycz, Zhiwu Li et al.

As an important technology in artificial intelligence Granular Computing (GrC) has emerged as a new multi-disciplinary paradigm and received much attention in recent years. Information granules forming an abstract and efficient characterization of large volumes of numeric data have been considered as the fundamental constructs of GrC. By generating prototypes and partition matrix, fuzzy clustering is a commonly encountered way of information granulation. Degranulation involves data reconstruction completed on a basis of the granular representatives. Previous studies have shown that there is a relationship between the reconstruction error and the performance of the granulation process. Typically, the lower the degranulation error is, the better performance of granulation is. However, the existing methods of degranulation usually cannot restore the original numeric data, which is one of the important reasons behind the occurrence of the reconstruction error. To enhance the quality of degranulation, in this study, we develop an augmented scheme through modifying the partition matrix. By proposing the augmented scheme, we dwell on a novel collection of granulation-degranulation mechanisms. In the constructed approach, the prototypes can be expressed as the product of the dataset matrix and the partition matrix. Then, in the degranulation process, the reconstructed numeric data can be decomposed into the product of the partition matrix and the matrix of prototypes. Both the granulation and degranulation are regarded as generalized rotation between the data subspace and the prototype subspace with the partition matrix and the fuzzification factor. By modifying the partition matrix, the new partition matrix is constructed through a series of matrix operations. We offer a thorough analysis of the developed scheme. The experimental results are in agreement with the underlying conceptual framework

Cong Wang, Witold Pedrycz, ZhiWu Li et al.

Although spatial information of images usually enhance the robustness of the Fuzzy C-Means (FCM) algorithm, it greatly increases the computational costs for image segmentation. To achieve a sound trade-off between the segmentation performance and the speed of clustering, we come up with a Kullback-Leibler (KL) divergence-based FCM algorithm by incorporating a tight wavelet frame transform and a morphological reconstruction operation. To enhance FCM's robustness, an observed image is first filtered by using the morphological reconstruction. A tight wavelet frame system is employed to decompose the observed and filtered images so as to form their feature sets. Considering these feature sets as data of clustering, an modified FCM algorithm is proposed, which introduces a KL divergence term in the partition matrix into its objective function. The KL divergence term aims to make membership degrees of each image pixel closer to those of its neighbors, which brings that the membership partition becomes more suitable and the parameter setting of FCM becomes simplified. On the basis of the obtained partition matrix and prototypes, the segmented feature set is reconstructed by minimizing the inverse process of the modified objective function. To modify abnormal features produced in the reconstruction process, each reconstructed feature is reassigned to the closest prototype. As a result, the segmentation accuracy of KL divergence-based FCM is further improved. What's more, the segmented image is reconstructed by using a tight wavelet frame reconstruction operation. Finally, supporting experiments coping with synthetic, medical and color images are reported. Experimental results exhibit that the proposed algorithm works well and comes with better segmentation performance than other comparative algorithms. Moreover, the proposed algorithm requires less time than most of the FCM-related algorithms.

Cong Wang, Witold Pedrycz, ZhiWu Li et al.

Instead of directly utilizing an observed image including some outliers, noise or intensity inhomogeneity, the use of its ideal value (e.g. noise-free image) has a favorable impact on clustering. Hence, the accurate estimation of the residual (e.g. unknown noise) between the observed image and its ideal value is an important task. To do so, we propose an $\ell_0$ regularization-based Fuzzy $C$-Means (FCM) algorithm incorporating a morphological reconstruction operation and a tight wavelet frame transform. To achieve a sound trade-off between detail preservation and noise suppression, morphological reconstruction is used to filter an observed image. By combining the observed and filtered images, a weighted sum image is generated. Since a tight wavelet frame system has sparse representations of an image, it is employed to decompose the weighted sum image, thus forming its corresponding feature set. Taking it as data for clustering, we present an improved FCM algorithm by imposing an $\ell_0$ regularization term on the residual between the feature set and its ideal value, which implies that the favorable estimation of the residual is obtained and the ideal value participates in clustering. Spatial information is also introduced into clustering since it is naturally encountered in image segmentation. Furthermore, it makes the estimation of the residual more reliable. To further enhance the segmentation effects of the improved FCM algorithm, we also employ the morphological reconstruction to smoothen the labels generated by clustering. Finally, based on the prototypes and smoothed labels, the segmented image is reconstructed by using a tight wavelet frame reconstruction operation. Experimental results reported for synthetic, medical, and color images show that the proposed algorithm is effective and efficient, and outperforms other algorithms.

Qi Zhang, Carla Seatzu, Zhiwu Li et al.

The problem of state estimation in the setting of partially-observed discrete event systems subject to cyber attacks is considered. An operator observes a plant through a natural projection that hides the occurrence of certain events. The objective of the operator is that of estimating the current state of the system. The observation is corrupted by an attacker which can tamper with the readings of a set of sensors thus inserting some fake events or erasing some observations. The aim of the attacker is that of altering the state estimation of the operator. An automaton, called joint estimator, is defined to describe the set of all possible attacks. In more details, an unbounded joint estimator is obtained by concurrent composition of two state observers, the attacker observer and the operator observer. The joint estimator shows, for each possible corrupted observation, the joint state estimation, i.e., the set of states consistent with the uncorrupted observation and the set of states consistent with the corrupted observation. Such a structure can be used to establish if an attack function is harmful w.r.t. a misleading relation. Our approach is also extended to the case in which the attacker may insert at most n events between two consecutive observations.