Fuzzy Discrete Event Systems Research Articles

Decentralized prognosis of fuzzy discrete-event systems

This paper gives a decentralized approach to the problem of failure prognosis in the framework of fuzzy discrete event systems (FDES). A notion of co-predictability is formalized for decentralized prognosis of FDESs, where several local agents with fuzzy observability rather than crisp observability are used in the prognosis task. An FDES is said to be co-predictable if each faulty event can be predicted prior to its occurrence by at least one local agent using the observability of fuzzy events. The verification of the decentralized predictability is performed by constructing a fuzzy co-verifier from a given FDES. The complexity of the fuzzy co-verifier is polynomial with respect to the FDES being predicted, and is exponential with respect to the number of the local prognosis agents. Then, a necessary and sufficient condition for the co-predictability of FDESs is given. In addition, we show that the proposed method may be used to deal with the decentralized prognosis for both FDESs and crisp DESs. Finally, to illustrate the effectiveness of the approach, some examples are provided.

An integrative approach to simulation model discovery: Combining system theory, process mining and fuzzy logic

System inference, i.e., the building of system structure from system behavior, is widely recognized as a critical challenging issue. In System Theory, structure and behavior are at the extreme sides of the hierarchy that defines knowledge about the system. System inference is known as climbing the hierarchy from less to more knowledge. In addition, it is possible only under justifying conditions. In this paper, a new system inference method is proposed. The proposed method extends the process mining technique to extract knowledge from data and to represent complex systems. The modularity, frequency and timing aspects can be extracted from the data. They are integrated together to construct the Fuzzy Discrete Event System Specification (Fuzzy-DEVS) model. The proposed approach consists of three stages: (1) extraction of event logs from data by using the System Entity Structure method; (2) discovery of a transition system, using process discovery techniques; (3) integration of fuzzy methods to automatically generate a Fuzzy-DEVS model from the transition system. The last stage is implemented as a plugin in the Process Mining Framework (ProM) environment. A case study is presented in which Fuzzy-DEVS model is inferred from real life data, and the SimStudio tool is used for its simulation.

A Belief-Evolution-Based Approach for Online Control of Fuzzy Discrete-Event Systems Under Partial Observation

In this paper, we investigate the partially observed supervisor synthesis problem in the framework of fuzzy discrete-event systems (DESs). The goal is to synthesize a fuzzy supervisor such that the behavior of the closed-loop system is within a given fuzzy language. A new approach for solving this problem is proposed based on the idea of belief evolution. Specifically, we propose an algorithm that can be implemented in an online manner. We show that the proposed algorithm is both sound and complete, i.e., it effectively solves the supervisor synthesis problem. To the best of our knowledge, this is the first algorithm with such a property for fuzzy DESs, as previous works on this topic mostly focus on the supervisor existence condition rather than the supervisor synthesis problem.

Predictability of fuzzy discrete event systems

This paper studies the problem of predictability in fuzzy discrete event systems (FDESs). FDESs combine fuzzy set theory with discrete events systems (DESs). They are proposed in Lin and Ying (2001) to cope with vagueness, impreciseness, and subjectivity in real-world problems. In this work: (1) We propose a fuzzy approach for predictability by introducing fuzzy predictability functions to characterize the predictability degree of a prefix, a faulty trace as well as a faulty event in a fuzzy DES. These functions take values in the interval [0, 1]. The degree of predictability gives a valuable measure to refine the decision about fault predictability. (2) We show that the degree of predictability of a faulty event is always at most equal to its degree of diagnosability. This captures the idea that predictability is stronger than diagnosability. (3) For checking predictability in FDESs, we propose an approach based on the so-called verifier. This approach results in a polynomial (in the number of states) complexity test for the verification of predictability. Our results generalize those of predictability for crisp DESs and allow one to deal with the problem of predictability for both crisp DESs and FDESs.

State-Based Decentralized Diagnosis of Bi-Fuzzy Discrete Event Systems

Recently, we have introduced bi-fuzzy discrete event systems (BFDESs) and established their supervisory control theory under full observations and partial observations, respectively. Compared with the models of discrete event systems and fuzzy discrete event systems, BFDESs are more satisfactory models to characterize some high-uncertainty systems. In this paper, we study the fault diagnosis problems of BFDESs. First, the framework of state-based decentralized diagnosis is introduced. Then, the notion of state-based codiagnosability is defined and a necessary and sufficient condition for state-based codiagnosability is provided. In particular, a polynomial-time algorithm for state-based codiagnosability verification and an online decentralized diagnosis method are presented. In addition, a compact state-based decentralized diagnosis framework is introduced, and the notion of state-based jointly diagnosability and its verification algorithm are proposed. Finally, the implication relationships between the two diagnosabilities are investigated.

Bifuzzy Discrete Event Systems and Their Supervisory Control Theory

It is well known that type-1 fuzzy sets (T1 FSs) have limited capabilities to handle some data uncertainties directly, and type-2 fuzzy sets (T2 FSs) can cover the shortcoming of T1 FSs to a certain extent. Fuzzy discrete event systems (FDESs) were proposed based on T1 FSs theory. Hence, FDES may not be a satisfactory model to characterize some high-uncertainty systems. In this paper, we propose a new model, called as bi-fuzzy discrete event systems (BFDESs), by combining classical DESs theory and T2 FSs theory. Then, we consider the supervisory control problem of BFDESs. The bi-fuzzy controllability theorem and nonblocking bi-fuzzy controllability theorem are demonstrated. Also, an algorithm for checking the bi-fuzzy controllability condition is presented. In addition, two controllable approximations to an uncontrollable language are investigated in detail. An illustrative example is provided to show the applicability and the advantages of BFDESs model.

Using Fuzzy Discrete Event Systems in Treatment Decision Making

Using Fuzzy Discrete Event Systems in Treatment Decision Making

Safe Diagnosability of Fuzzy Discrete-Event Systems and a Polynomial-Time Verification

Since fuzzy discrete-event systems (FDESs) were significantly brought forward, the study of FDESs has received increasing attention recently. This paper addresses the safe diagnosability under the framework of FDESs. The contributions are threefold. First, the notion of safe diagnosability for fuzzy systems is formalized. A safe diagnosable FDES means that not only each failure can be detected in terms of fuzziness, as well as the detection must be completed before any unsafe operation is executed. Then, a necessary and sufficient condition of safe diagnosability of FDESs is proposed by constructing the safe diagnoser. Finally, we present an algorithm for verifying the safe diagnosability of FDESs based on a constructive nondeterministic automaton, namely verifier. It is worth noting that both constructing the verifier and verifying the safe diagnosability of FDESs can be realized with a polynomial complexity.

An FDES-Based Shared Control Method for Asynchronous Brain-Actuated Robot.

The asynchronous brain-computer interface (BCI) offers more natural human-machine interaction. However, it is still considered insufficient to control rapid and complex sequences of movements for a robot without any advanced control method. This paper proposes a new shared controller based on the supervisory theory of fuzzy discrete event system (FDES) for brain-actuated robot control. The developed supervisory theory allows the more reliable control mode to play a dominant role in the robot control which is beneficial to reduce misoperation and improve the robustness of the system. The experimental procedures consist of real-time direct manual control and BCI control tests from ten volunteers. Both tests have shown that the proposed method significantly improves the performance and robustness of the robotic control. In an online BCI experiment, eight of the participants successfully controlled the robot to circumnavigate obstacles and reached the target with a three mental states asynchronous BCI while the other two participants failed in all the BCI control sessions. Furthermore, the FDES-based shared control method also helps to reduce the workload. It can be stated that the asynchronous BCI, in combination with FDES-based shared controller, is feasible for the real-time and robust control of robotics.

Supervisory Control of Fuzzy Discrete-Event Systems for Simulation Equivalence

The supervisory control theory of fuzzy discrete event systems (FDESs) for fuzzy language equivalence has been developed. However, in a way, language equivalence has limited expressiveness. So if the given specification can not be expressed by language equivalence, then the control for language equivalence does not work. In this paper, we further establish the supervisory control theory of FDESs for fuzzy simulation equivalence whose expressiveness is stronger than that of fuzzy language equivalence. First, we formalize the notions of fuzzy simulation and fuzzy simulation equivalence between two FDESs. Then we present a method for deciding whether there is a fuzzy simulation or not. In addition, we also show several basic properties of fuzzy simulation relations. Afterwards, we put forward the notion of fuzzy simulation-based controllability, and particularly show that it serves as a necessary and sufficient condition for the existence of the fuzzy supervisors of FDESs. Moreover, we study the "range" control problem of FDESs. Some examples are given to illustrate the main results obtained.

Theory of Generalized Fuzzy Discrete-Event Systems

There exist a large number of systems whose state variables are continuous signals, and transit based on event-driven mechanisms. To model the transitions of these state variables, the theory of extended fuzzy discrete-event systems (EFDESs) was developed by extending the fuzzy discrete-event system (FDES) theory. However, the EFDES theory remains limited in modeling these event-driven systems. A primary reason for this is that the EFDES theory allows every event to be characterized by one variable only, and thus every event can be modeled by a fuzzy set (FS) only. Although the EFDES theory provides the steps for computing the next states of the state variables, how to compute their next states remains unknown when any event is modeled by multiple FSs. To overcome this limitation, this paper will present the theory of generalized fuzzy discrete-event systems (GFDESs) by generalizing the EFDES theory. In the proposed GFDES theory, events are characterized by their multiple attributes which may determine the transitions of the state variables, and are modeled by representing each of their attributes using one FS. To establish the GFDES theory, models for GFDESs will be presented by extending the concepts of EFDESs. To make this theory complete, the procedures for computing the next states of the state variables will also be provided. In addition, numerical examples will be presented to further illustrate the proposed GFDES theory.

Nonblocking check in fuzzy discrete event systems based on observation equivalence

In this paper, we deal with the synthesis about nonblocking check in fuzzy discrete event systems (FDESs) by using abstraction and observation equivalence of fuzzy finite automaton (FFA). In FDESs, such a check imposes a great computational challenge because of the complexity incurred by the composition of plants and the supervisors. With respect to ideas in modeling control system, we present procedure based on FFA abstractions, which removes internal transitions of irrelevant transitions, allowing the nonblocking check to be performed on relatively small automata.

Learning Diagnosis Based on Evolving Fuzzy Finite State Automaton


 
 
 Nowadays, determining faults (or critical situations) in non- stationary environment is a challenging task in complex systems such as Nuclear center, or multi-collaboration such as crisis management. A discrete event system or a fuzzy discrete event system approach with a fuzzy role-base may re- solve the ambiguity in a fault diagnosis problem especially in the case of multiple faults (or multiple critical situations). The main advantage of fuzzy finite state automaton is that their fuzziness allows them to handle imprecise and uncertain data, which is inherent to real-world phenomena, in the form of fuzzy states and transitions. Thus, most of approaches proposed for fault diagnosis of discrete event systems require a complete and accurate model of the system to be diagnosed. However, in non-stationary environment it is hard or impossible to obtain the complete model of the system. The focus of this work is to propose an evolving fuzzy discrete event system whose an activate degree is associated to each active state and to develop a fuzzy learning diagnosis for incomplete model. Our approach use the fuzzy set of output events of the model as input events of the diagnoser and the output of a fuzzy system should be defuzzified in an appropriate way to be usable by the environment.
 
 

Polynomial-time verification of diagnosability of fuzzy discrete event systems

A fuzzy approach to perform diagnosis of fuzzy discrete event systems (FDESs) is proposed by constructing diagnosers, which may more effectively cope with the problems of vagueness and fuzziness arising from failure diagnosis of fuzzy systems. However, the complexity of constructing this kind of diagnosers is exponential in the state space and the number of fuzzy events of the system. In this paper, we present an algorithm for verifying the diagnosability of FDESs based on the construction of a nondeterministic automaton called F-verifier instead of diagnosers. Both the construction of F-verifiers and the verification of diagnosability of FDESs can be realized with a polynomial-time complexity.

Reduction of fuzzy automata by means of fuzzy quasi-orders

In our recent paper we have established close relationships between state reduction of a fuzzy automaton and resolution of a particular system of fuzzy relation equations. In that paper we have also studied reductions by means of those solutions which are fuzzy equivalences. In this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi-orders. Generally, fuzzy quasi-orders and fuzzy equivalences are equally good in the state reduction, but we show that right and left invariant fuzzy quasi-orders give better reductions than right and left invariant fuzzy equivalences. We also show that alternate reductions by means of fuzzy quasi-orders give better results than alternate reductions by means of fuzzy equivalences. Furthermore we study a more general type of fuzzy quasi-orders, weakly right and left invariant ones, and we show that they are closely related to determinization of fuzzy automatons. We also demonstrate some applications of weakly left invariant fuzzy quasi-orders in conflict analysis of fuzzy discrete event systems.

Fuzzy Discrete Event Systems for Multiobjective Control: Framework and Application to Mobile Robot Navigation

Fuzzy discrete event systems (FDESs) have been introduced in recent years to model systems whose discrete states or discrete state transitions can be uncertain and are, hence, determined by a possibility degree. This paper develops an FDES framework for the control of sampled data systems that have to fulfill multiple objectives. The choice of a fuzzy system representation is justified by the assumption of a controller realization that depends on various potentially imprecise sensor measurements. The proposed framework consists of three basic steps that are performed at each sampling instant. First, the current fuzzy state of the system is determined by a sensor evaluation. Second, the fuzzy state in the future sampling instant is predicted for all possible control actions of the system. Finally, an original multiobjective weighting strategy is proposed to determine the control action to be applied in the current sampling instant. The features of the proposed approach are demonstrated by a detailed mobile robot example, which includes a simulation study.

Generalizing the Decentralized Control of Fuzzy Discrete Event Systems

The main objective of this paper is to establish a general architecture for decentralized supervision of fuzzy discrete event systems (FDES). First, two different types of decentralized supervisory control architectures of FDES are presented, which fuse the locally enabled degrees of fuzzy events using the fuzzy-intersection operator and the fuzzy-union operator, respectively. Both of these architectures possess limitations in information association. Second, to overcome the aforementioned drawbacks, a general architecture for decentralized supervisory control of FDES is introduced, in which the decisions of local supervisors are fused by using both fuzzy-union and fuzzy-intersection operators. The proposed general architecture is then implemented to control a tightly coupled multirobot object manipulation task in simulation. A performance evaluation is performed to quantitatively estimate the validity of the proposed architecture compared with centralized FDES-based and decentralized crisp DES-based approaches.

Reliable Decentralized Control of Fuzzy Discrete-Event Systems and a Test Algorithm

A framework for decentralized control of fuzzy discrete-event systems (FDESs) has been recently presented to guarantee the achievement of a given specification under the joint control of all local fuzzy supervisors. As a continuation, this paper addresses the reliable decentralized control of FDESs in face of possible failures of some local fuzzy supervisors. Roughly speaking, for an FDES equipped with n local fuzzy supervisors, a decentralized supervisor is called k-reliable (1 ≤ k ≤ n) provided that the control performance will not be degraded even when n - k local fuzzy supervisors fail. A necessary and sufficient condition for the existence of k-reliable decentralized supervisors of FDESs is proposed by introducing the notions of M̃uc-controllability and k-reliable coobservability of fuzzy language. In particular, a polynomial-time algorithm to test the k-reliable coobservability is developed by a constructive methodology, which indicates that the existence of k-reliable decentralized supervisors of FDESs can be checked with a polynomial complexity.

Analysis and control of fuzzy discrete event systems using bisimulation equivalence

In order to more effectively cope with the real-world problems of vagueness, impreciseness, and subjectivity, fuzzy discrete event systems (FDESs) were proposed recently. In this paper, we deal with the analysis and control of fuzzy discrete event systems by using bisimulation equivalence. In practice, we design a supervisor such that the controlled system is bisimilar to the specification. Also, a model theorem showing that a supervisor exists over a certain finite fuzzy state space is obtained. Furthermore, the notion of fuzzy state controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor.

Modular Supervisory Control and Hierarchical Supervisory Control of Fuzzy Discrete-Event Systems

This paper establishes modular and hierarchical supervisory control theories of Fuzzy Discrete-Event Systems (FDES). It aims to resolve the horizontal and vertical complexities present in large-scale event-driven systems, which are affected by uncertainties in their event and state representations. The modular supervisory control architecture composed of a set of noncommunicating local supervisors, in which one supervisor is assigned for each module having its own sensing and acting capabilities. The notion of separability for languages in FDES is introduced and the property of a language specification of FDES, termed as separably-controllable-observability, is proposed to determine the existence of modular supervisors to the control problem. The hierarchical supervisory control architecture consists of multilevel supervisors assigned to detailed low-level and abstract high-level models of the plant. The notion of output-control-consistency is introduced for languages in FDES. Then, the property called strictly-output-control-consistency is defined for FDES in order to maintain the hierarchical consistency between low-level and high-level FDES modules. The property of H-fuzzy observability is introduced to ensure the hierarchical consistency under the partial observation of low-level FDES. Finally, using the established hierarchical supervisory control theory of FDES, a behavior-based mobile robot navigation example is discussed.