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Given a discrete event system, it is said to be opaque if an intruder who can partially observe system behavior cannot infer that the system is necessarily in a predefined secret. A discrete event system is current-state opaque if an intruder is never able to verify whether the current state of the system is within the secret states. This article addresses the verification of current-state opacity of a discrete event system modeled with Petri nets, where the secret is defined as a set of states. The existing methods cannot deal with large-sized systems due to the curse of dimensionality. Multi-valued decision diagrams (MDDs) are widely accepted as an efficient and compact data structure for representing the extremely large reachability sets of Petri nets. We show that MDDs can be used in Petri nets with partial observable transitions and propose an approach for the verification of current-state opacity for bounded Petri nets. It is shown by experimental studies that the symbolic approach is practically more efficient than traditional techniques such as basis reachability graphs (BRGs). [ABSTRACT FROM AUTHOR]

Nowadays, high-throughput screening (HTS) systems are widely used in pharmaceutical industries and laboratories for the discovery of new drugs and biomedical substances. It is important to efficiently schedule them so as to reduce the cost. In the operation of an HTS system, a microplate may visit some resources more than once and complex time window constraints are imposed on some activities and activity sequences. Moreover, with the consistency requirement, a one-microplate cyclic schedule is necessary. Thus, its scheduling problem is very challenging. This article studies the scheduling problem of an HTS system for an enzymatic assay, a typical application of HTSs, from the perspective of control theory. The system is modeled by resource-oriented Petri nets (ROPNs). With the model, necessary and sufficient conditions under which a feasible cyclic schedule exists are established. Then, we determine how many microplates should be in the system for concurrent processing and the transition firing sequence to obtain the activity sequence for an optimal and feasible schedule. In this way, a feasible and optimal cyclic schedule can be found by very simple computations, which shows that polynomial algorithms for an optimal schedule exist, while the existing studies apply mathematical programming with exponential computation complexity. Also, its efficient implementation is given. [ABSTRACT FROM AUTHOR]

This article proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimal-maximal basis reachability graph (min-max-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its min-max-BRG is unobstructed, which can be verified by solving a set of integer constraints and then examining the min-max-BRG. For Petri nets that are not deadlock-free, one needs to determine the set of dead markings. This can be done with an approach based on the computation of maximal implicit firing sequences enabled by the markings in the min-max-BRG. The approach we developed does not require the construction of the reachability graph and has wide applicability. [ABSTRACT FROM AUTHOR]

In this article, we elaborate on a design and realization of fuzzy rule-based model in the horizontal federated learning framework. Traditional machine learning in distributed environment often involves sharing sensitive information with other sites or transferring data to a central server on which a global model is trained. These situations increase the communication overhead and pose serious threats to the privacy of sensitive data. Federated learning opens up the possibility for collaboratively training a global model on a basis of distributed on-site data without sacrificing data privacy. While fuzzy rule-based models have been used in system modeling due to their substantial modeling abilities and good interpretability, the implementation of fuzzy rule-based models in a distributed environment without compromising data privacy still requires careful consideration. This article proposes a two-step federated learning approach to train a global model on a basis of private data located across different sites without their centralization. The first step concerns the determination of the structure of the data through federated collaborative clustering. Subsequently, a shared global model is trained jointly by all the participating clients. An advantage of the proposed method is that it achieves high accuracy without violating data privacy. A series of experimental studies are conducted to gain a detailed insight into the realization steps and demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we elaborate on a Kullback–Leibler (KL) divergence-based Fuzzy ${C}$ -Means (FCM) algorithm by incorporating a tight wavelet frame transform and morphological reconstruction (MR). To make membership degrees of each image pixel closer to those of its neighbors, a KL divergence term on the partition matrix is introduced as a part of FCM, thus resulting in KL divergence-based FCM. To make the proposed FCM robust, a filtered term is augmented in its objective function, where MR is used for image filtering. Since tight wavelet frames provide redundant representations of images, the proposed FCM is performed in a feature space constructed by tight wavelet frame decomposition. To further improve its segmentation accuracy (SA), a segmented feature set is reconstructed by minimizing the inverse process of its objective function. Each reconstructed feature is reassigned to the closest prototype, thus modifying abnormal features produced in the reconstruction process. Moreover, a segmented image is reconstructed by using tight wavelet frame reconstruction. Finally, supporting experiments coping with synthetic, medical, and real-world images are reported. The experimental results exhibit that the proposed algorithm works well and comes with better segmentation performance than other peers. In a quantitative fashion, its average SA improvements over its peers are 4.06%, 3.94%, and 4.41%, respectively, when segmenting synthetic, medical, and real-world images. Moreover, the proposed algorithm requires less time than most of the FCM-related algorithms. [ABSTRACT FROM AUTHOR]

This article provides a solution to tube-based output feedback robust model predictive control (RMPC) for discrete-time linear parameter varying (LPV) systems with bounded disturbances and noises. The proposed approach synthesizes an offline optimization problem to design a look-up table and an online tube-based output feedback RMPC with tightened constraints and scaled terminal constraint sets. In the offline optimization problem, a sequence of nested robust positively invariant (RPI) sets and robust control invariant (RCI) sets, respectively, for estimation errors and control errors is optimized and stored in the look-up table. In the online optimization problem, real-time control parameters are searched based on the bounds of time-varying estimation error sets. Considering the characteristics of the uncertain scheduling parameter in LPV systems, the online tube-based output feedback RMPC scheme adopts one-step nominal system prediction with scaled terminal constraint sets. The formulated simple and efficient online optimization problem with fewer decision variables and constraints has a lower online computational burden. Recursive feasibility of the optimization problem and robust stability of the controlled LPV system are guaranteed by ensuring that the nominal system converges to the terminal constraint set, and uncertain state trajectories are constrained within robust tubes with the center of the nominal system. A numerical example is given to verify the approach. [ABSTRACT FROM AUTHOR]

Deadlocks are a highly undesirable situation in flexible manufacturing systems (FMSs). This article presents a direct and novel method to detect such markings by constructing the resource flow graph of a Petri net that models an FMS and to recover such markings by adding a set of recovery transitions. First, an algorithm is developed to build a new kind of directed graph called the resource flow graph of a Petri net. Resource flow graphs can well represent the competition for shared resources by different processes. Second, based on the resource flow graph, loop graphs can be found. Furthermore, partial deadlock markings can be easily detected due to their relationship with loop graphs. Then, we propose an algorithm to design a set of recovery transitions for loop graphs that are enabled at partial deadlock markings. The proposed approach can detect partial deadlock markings without generating a complete reachability graph of a Petri net and the resulting net is deadlock-free with all reachable markings by adding the obtained recovery transitions. Finally, some widely used examples are provided to demonstrate the proposed approach. Note to Practitioners—The occurrence of deadlocks in an FMS tends to cause unnecessary productivity costs and even catastrophic results. In the framework of Petri nets, reachability graph analysis can usually obtain a maximally permissive supervisor of a plant. However, it is rather inefficient since it suffers from the state explosion problem. In this particular research, we develop an off-line deadlock detection and recovery policy by setting a group of virtual events that are not present in a physical model. The proposed approach is computationally efficient since it does not require to generate a reachability graph. It guarantees that the resulted system is deadlock-free with its all original reachable markings. [ABSTRACT FROM AUTHOR]

Rule-based fuzzy models play a dominant role in fuzzy modeling and come with extensive applications in the system modeling area. Due to the presence of system modeling error, it is impossible to construct a model that fits exactly the experimental evidence and, at the same time, exhibits high generalization capabilities. To alleviate these problems, in this study, we elaborate on a realization of granular outputs for rule-based fuzzy models with the aim of effectively quantifying the associated modeling errors. Through analyzing the characteristics of modeling errors, an error model is constructed to characterize deviations among the estimated outputs and the expected ones. The resulting granular model comes into play as an aggregation of the regression model and the error model. Information granularity plays a central role in the construction of granular outputs (intervals). The quality of the produced interval estimates is quantified in terms of the coverage and specificity criteria. The optimal allocation of information granularity is determined through a combined index involving these two criteria pertinent to the evaluation of interval outputs. A series of experimental studies is provided to demonstrate the effectiveness of the proposed approach and show its superiority over the traditional statistical-based method. [ABSTRACT FROM AUTHOR]

With integer linear programming problems (ILPPs) being formulated and solved, the existing approaches design optimal Petri-net supervisors via nonpure net structures, including self-loops and data inhibitor arcs. Nonpure net structures are powerful for control of Petri-net-modeled discrete-event systems. However, in the existing work, the formulated ILPPs contain a large number of constraints, which is computationally inefficient. In this article, we propose approaches that formulate ILPPs with fewer constraints such that the computational efficiency is significantly improved. To do so, in formulating ILPPs for optimal Petri-net controllers by using self-loops and data inhibitor arcs, we remove the reachability conditions for legal markings. By doing so, an obtained solution may result in some legal markings unreachable. To solve this problem, a novel technique is developed to design an optimal controller by modifying the initial marking and structure of the obtained supervisor. It is shown that, by the reduced ILPPs, one can find the same feasible solutions as that obtained by the existing work. Finally, the proposed approaches are demonstrated by examples. [ABSTRACT FROM AUTHOR]

Information granulation and degranulation play a fundamental role in granular computing (GrC). Given a collection of information granules (referred to as reference information granules), the essence of the granulation process (encoding) is to represent each data (either numeric or granular) in terms of these reference information granules. The degranulation process (decoding) that realizes the reconstruction of original data is associated with a certain level of reconstruction error. An important issue is how to reduce the reconstruction error such that the data could be reconstructed more accurately. In this study, the granulation process is realized by involving fuzzy clustering. A novel neural network is leveraged in the consecutive degranulation process, which could help significantly reduce the reconstruction error. We show that the proposed degranulation architecture exhibits improved capabilities in reconstructing original data in comparison with other methods. A series of experiments with the use of synthetic data and publicly available datasets coming from the machine-learning repository demonstrates the superiority of the proposed method over some existing alternatives. [ABSTRACT FROM AUTHOR]

In an automated manufacturing system (AMS), resources are, in general, subject to unpredictable failures, which invalidate many existing deadlock control strategies. In this article, we propose an adaptive deadlock control policy for an AMS with multiple types of unreliable resources. The considered AMS is modeled with a system of simple sequential processes with resources. First, based on an elementary siphon control method, monitors are added for elementary siphons and some particular dependent siphons to ensure the liveness of a system if there are no resource failures. By considering the fact that an unreliable resource may fail in a system, recovery subnets are added to describe the resource failures and recoveries. Since a monitor added for a siphon may not be able to guarantee that the corresponding siphon is always marked if the failure of a resource in the siphon occurs, the concept of switch controllers is presented so as to make the siphon always remarked if it is emptied by resource failures. It is verified that the adaptive controller proposed in this article can guarantee the liveness of the controlled system no matter whether unreliable resources break down or not. More importantly, if there is no resource failure, the system can maintain predefined production without degrading planned system performance. Finally, examples are presented to illustrate the validity of the proposed method. [ABSTRACT FROM AUTHOR]

This article focuses on the issue of checking critical observability for labeled Petri nets. Critical observability is a property related to the safety concern of cyber-physical systems. With the aim of checking this property of a net system, it is required to detect whether a set of markings consistent with any observed word of the net system is a subset of a set of critical states representing undesirable operations or a set of noncritical states. In this work, we prove a necessary and sufficient condition to check critical observability when the critical state set is described by an arbitrary subset of reachable markings. Then, the result is extended to the case when a critical state set is modeled by all the reachable markings that satisfy disjunctions of generalized mutual exclusion constraints. The proposed method is derived from the solutions of integer linear programming problems and is applicable to net systems with liveness and boundness. Several case studies show the performance of the presented methodology for discrete-event systems. [ABSTRACT FROM AUTHOR]

For Takagi–Sugeno fuzzy systems subject to inexact membership functions, bounded disturbances, and noises, an output feedback robust model predictive control (RMPC) approach with time-varying robust tubes is investigated. The membership functions errors are bounded within convex sets via the properties of zonotopes and interval matrices. An offline table stores a series of structures that include nested robust positive invariant sets with the corresponding nominal feedback controller gains, ancillary controller gains, and observer gains. According to bounds of real-time estimation error sets, the time-varying structures in the offlined table are searched. Then, the output feedback RMPC problem with time-varying tightened constraints on inputs and states is optimized to stabilize the nominal system. The output feedback RMPC approach can not only update bounds of the estimation errors and uncertain terms resulting from inexact membership functions, but also reduce the computational burden. The proposed RMPC algorithm with recursive feasibility guarantees the robust stability of the controlled systems. [ABSTRACT FROM AUTHOR]

In this article, we are concerned with the formation of type-2 information granules in a two-stage approach. We present a comprehensive algorithmic framework which gives rise to information granules of a higher type (type-2, to be specific) such that the key structure of the local granular data, their topologies, and their diversities become fully reflected and quantified. In contrast to traditional collaborative clustering where local structures (information granules) are obtained by running algorithms on the local datasets and communicating findings across sites, we propose a way of characterizing granular data (formed) by forming a suite of higher type information granules to reveal an overall structure of a collection of locally available datasets. Information granules built at the lower level on a basis of local sources of data are weighted by the number of data they represent while the information granules formed at the higher level of hierarchy are more abstract and general, thus facilitating a formation of a hierarchical description of data realized at different levels of detail. The construction of information granules is completed by resorting to fuzzy clustering algorithms (more specifically, the well-known Fuzzy C-Means). In the formation of information granules, we follow the fundamental principle of granular computing, viz., the principle of justifiable granularity. Experimental studies concerning selected publicly available machine-learning datasets are reported. [ABSTRACT FROM AUTHOR]

While granular computing has experienced rapid growth in the past decades and some milestones have been reached, a comprehensive study of the representation capabilities delivered by numeric prototypes and granular prototypes produced by different techniques still calls for comprehensive research and a comparative analysis. Well-constructed information granules are reflective of the nature of the numeric evidence and serve as backbones of granular classifiers and granular models. The objective of this study is to review a number of clustering paradigms aimed at the construction of information granules, discuss the development of granular prototypes, and conduct a comprehensive evaluation of quality of numeric prototypes and their corresponding augmentations coming in the form of granular prototypes. We have been witnessing many studies devoted to the construction of information granules, but a comparative analysis of the quality of information granules constructed on a basis of prototypes produced by different clustering algorithms is still lacking. In this regard, the review of the clustering algorithms supporting the formation of information granules and the comprehensive comparative study of their usefulness in classification and modeling tasks offered in this study make sense. This will promote the usage of information granules in various future works, especially classification problem and system modeling. [ABSTRACT FROM AUTHOR]

This article is concerned with a problem of relational factorization which engages fuzzy relational calculus. It forms an interesting alternative to the method of nonnegative matrix factorization that has been commonly discussed and found in numerous applications. The relational factorization takes original n-dimensional data located in the unit hypercube and factorizes it into data of lower dimensionality and some fuzzy relations. Owing to the logic nature of processing delivered by relational calculus, the dimensionality reduction exhibits transparency as the reduction mechanism itself is described in terms of logic expressions. Two types of factorizations mechanisms are investigated by using s–t and t–s composition operators where t and s are triangular norms and conorms, respectively. A two-level process of factorization is designed. A gradient-based learning scheme is developed. The quantification of the performance of the factorization process is realized by bringing a concept of information granularity: The obtained fuzzy relations are formed based on granular constructs and the quality of the produced factorization is assessed in terms of the coverage and specificity of the obtained granular results. A collection of experiments is included to present the performance of factorization and its parametric analysis. In addition, the proposed algorithm comes with sound interpretability in terms of both the structure of the model and an intuitive meaning of the fuzzy relations being the result of factorization. [ABSTRACT FROM AUTHOR]

This article proposes a risk assessment method based on interval intuitionistic integrated cloud Petri net (IIICPN). The cloud model is widely used in data mining and knowledge discovery, especially in risk assessment problems with linguistic variables. However, the cloud models proposed in the literature do not express interval-valued intuitionistic linguistic satisfactorily, and the reasoning methods based on the cloud models cannot perform risk assessment well. The work in this article includes the definition of IIIC and IIICPN, the method of converting the interval-valued intuitionistic uncertain linguistic numbers into IIIC, and the reasoning method of IIICPN. As proofs, a subway fire accident model is adopted to confirm the feasibility of the proposed method, and comparison experiments between the IIICPN with general fuzzy Petri net and the trapezium cloud model are conducted to verify the superiority of the proposed model. Note to Practitioners—This work deals with the subway fire risk assessment problem. It proposes a cloud model based on interval-valued intuitionistic uncertain linguistic and builds a cloud-based Petri net model. The methods of fire risk assessment use the existing fault trees or aggregation operators to combine all the factors into consideration, but they do not take the interaction of factors. The goal of this work is to assess the risk of subway fire accident of subway, using fuzzy linguistic decision variables. The simulation results indicate that the proposed method is highly effective. The obtained results can help assessors better determine which factors may cause the disaster. [ABSTRACT FROM AUTHOR]

Transportation services play an increasingly significant role for people’s daily lives and bring a lot of benefits to individuals and economic development. The randomness and volatility of traffic flows, however, constrains the effective provision of transportation services to a certain extent. Precise traffic flow forecasting becomes the key and primary task to realize the stability of intelligent transport systems and ensure efficient scheduling of traffic. This paper investigates the application of an ensemble approach based on deep belief networks for short-term traffic flow forecasting. Traffic flow data, collected from the real world, is decomposed into several Intrinsic Mode Functions (IMFs) and a residue with EEMD (Ensemble Empirical Mode Decomposition). Then, for each component, the essential feature subset is extracted by the mRMR (minimum Redundancy Maximum Relevance Feature Selection) method considering weather conditions and day properties. Furthermore, each component is trained by DBN (Deep belief networks) and their forecasting results are summed up as the output of the ensemble model at last. Results indicate that the proposed approach achieves significant performance improvement over the single DBN and other selected methods. [ABSTRACT FROM AUTHOR]

Wind power curve modeling has important applications in many fields, such as wind turbine condition monitoring and wind power forecasting. There are various studies on wind power curve construction though, the relation between wind speed and errors is not taken into account when constructing wind power curves. To fill this gap, a hybrid copula-based wind power curve model (HCCM) is proposed in this paper. The independent distribution of wind speed is modeled by a Weibull distribution, and the independent distribution of errors is modeled by a mixture of asymmetric gaussian models. Then a hybrid copula model, including four copula functions, is designed to construct the joint distribution. Finally, a grey wolf optimization algorithm is applied to optimize the regression parameters of wind power curves by taking the log-likelihood function of the joint distribution as the fitness function. The proposed model is compared with ten benchmark models on four wind farms and two wind turbines. Experiments show that in terms of RMSE the HCCM achieves 99.3131%, 99.1197%, 99.1715% and 98.9339% on four wind farms, respectively, and around 80% improvement in RMSE on two wind turbines. [ABSTRACT FROM AUTHOR]

G-images refer to image data defined on irregular graph domains. This article elaborates on 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 partition matrix 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 the 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 segmentation algorithms. Moreover, it requires less computation than most of them. [ABSTRACT FROM AUTHOR]

In this article, we elaborate on a design methodology and the detailed realization of hierarchically structured granular models by engaging the fundamental principles and concepts of granular computing. The existing models are elevated to a more abstract (general) level by allocating a certain level of information granularity throughout the parameter space. In a concise way, the essence of the overall architecture of the proposed modeling mechanism could be generalized as follows: Numeric model (granular model of type-0)→granular model of type-1→granular model of type-2→…→granular model of higher type. The results of the granular models come in the form of type-0, type-1, or higher type information granules, which are decided by the overall level of hierarchy of the corresponding granular model. The specificity of granular outputs becomes a more comprehensive and sound quantification of the prediction accuracy and precision of the model and the quality of the specific prediction outputs. The proposed method facilitates effective communication with humans, who could get actively involved in the modeling process and determine the suitable level of abstraction depending upon the requirements of the problem. The determination of a suitable level of information granularity is realized with the guidance of the principle of justifiable granularity. A number of experimental studies concerning publicly available datasets are presented to illustrate the development methodology and show the effectiveness of the approach to form hierarchically structured solutions (reflecting different levels of abstraction) to the problem. [ABSTRACT FROM AUTHOR]

In this article, we develop a residual-sparse Fuzzy C-Means (FCM) algorithm for image segmentation, which furthers FCM's robustness by realizing the favorable estimation of the residual (e.g., unknown noise) between an observed image and its ideal version (noise-free image). To achieve a sound tradeoff between detail preservation and noise suppression, morphological reconstruction is used to filter the observed image. By combining the observed and filtered images, a weighted sum image is generated. Tight wavelet frame decomposition is used to transform the weighted sum image into its corresponding feature set. Taking such feature set as data for clustering, we impose an $\ell _0$ regularization term on residual to FCM's objective function, thus resulting in residual-sparse FCM, where spatial information is introduced for improving its robustness and making residual estimation more reliable. To further enhance segmentation accuracy of the proposed FCM, we employ morphological reconstruction to smoothen the labels generated by clustering. Finally, based on the prototypes and smoothed labels, a segmented image is reconstructed by using tight wavelet frame reconstruction. Experimental results regarding synthetic, medical, and real-world images show that the proposed algorithm is effective and efficient, and outperforms its peers. [ABSTRACT FROM AUTHOR]

A kind of facilities for wafer fabrication, cluster tools (CTs) need to close down to an idle state from time to time because of periodical maintenance and switches from one type of lots to another, which is called a normal close-down process (NCDP). It is crucial to optimize such a transient process since it tends to occur more and more frequently due to customization. Also, process modules (PMs) in CTs are known to be failure-prone. Once a PM failure occurs, a tool needs to close down to an idle state as well, which is different from NCDP and is called a failure close-down process (FCDP). With wafer residency time constraints (WRTCs) being imposed, close-down process optimization for such a tool is challenging, since one needs to not only finish this process as soon as possible but also meet WRTCs during this transient process. In order to tackle this problem, this article first introduces steady state scheduling problems. Then, with a presented backward robot task sequence, a linear programming model is first proposed to optimize NCDP. To deal with the PM failures, efficient PM failure response policies are formulated for the cases in which a PM fails. Then, four linear programs are proposed to optimize an FCDP. Finally, industrial case studies are given to show the usefulness of the proposed approaches. [ABSTRACT FROM AUTHOR]