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We introduce two novel concepts: fuzzy weak (bi)simulations and their approximations, breadth-first fuzzy (bi)simulations , for fuzzy automata with membership values in an arbitrary complete residuated lattice. They offer improved approximations of the subsethood degree (equivalence degree) of fuzzy automata compared to previously established notions. Fuzzy weak (bi)simulations are defined as fuzzy relations, whereas breadth-first fuzzy (bi)simulations are characterized by decreasing sequences of fuzzy relations, where each component is a solution to a finite and linear system of fuzzy relation inequalities. Such systems consist of fuzzy sets that are nodes of the trees constructed in the classic breadth-first search manner. We provide an algorithm that computes the proposed simulations and bisimulations, along with a modified version that computes the subsethood/equality degree for given fuzzy automata. Both algorithms run in the exponential time complexity, reflecting the trade-off for achieving more precise approximations. • We introduce fuzzy weak bisimulations and their approximations, breadth-first fuzzy bisimulations, for fuzzy automata. • Both concepts provide better approximations of the equivalence degree for fuzzy automata compared to previous approaches. • Breadth-first fuzzy bisimulations are sequences of fuzzy relations where each component solves a system of fuzzy relation inequalities. • We calculate the fuzzy sets of these systems by constructing two complete m -ary trees in the classic breadth-first search manner. • The computation for the proposed bisimulations has a higher cost, as a trade-off for achieving greater precision. [ABSTRACT FROM AUTHOR]

This paper presents a fuzzy-based assessment model to evaluate system reliability of a labour-intensive manufacturing system with repair actions. Due to the uncertainty in human performance, labour-intensive manufacturing systems must determine the capacity of each labourer in order to accurately characterise the performance of the systems. Therefore, we model such a manufacturing system as a fuzzy multi-state network in order to characterise the labourers’ influence on workstation performance. First, the workstation reliability is defined according to the loading state by three fuzzy membership functions, namely ‘under loading’, ‘normal loading’ and ‘over loading’, respectively. The system reliability is subsequently evaluated with fuzzy intersection operations in terms of these workstation reliabilities. Thus, the system reliability is defined as a fuzzy membership function to assess whether the manufacturing system performance is sufficient to satisfy the demand reliably. A case study of a footwear manufacturing system is illustrated to explain the proposed model. Furthermore, we apply the proposed model to a non-labour-intensive manufacturing network in order to validate the applicability to this class of systems. [ABSTRACT FROM PUBLISHER]

Since fuzzy discrete-event systems (FDESs) modeled by fuzzy automata were put forward, extensive research on FDESs has been successfully conducted from different perspectives. Recently, the safe codiagnosability of decentralized FDESs was introduced and an approach of constructing the safe codiagnoser to verify the safe codiagnosability was proposed. However, the complexity of constructing the safe codiagnoser of decentralized FDESs is exponential. In this paper, we present a polynomial verification. Firstly, the recognizer and the safe coverifier are constructed to recognize the prohibited strings in the illegal language and carry out safe diagnosis of decentralized FDESs, respectively. Then the necessary and sufficient condition for safe codiagnosability of decentralized FDESs is presented. In particular, an algorithm for verifying the safe codiagnosability of decentralized FDESs is proposed based on the safe coverifier. Notably, both complexities of constructing the safe coverifier and verifying the safe codiagnosability are polynomial in the numbers of fuzzy events and fuzzy states of FDESs. Finally, two examples are provided to illustrate the proposed algorithm and the derived results. [ABSTRACT FROM AUTHOR]

Refinement relations, such as trace containment, simulation preorder, and their alternating versions, have been successfully applied in formal verification of concurrent systems. Recently, trace containment and simulation preorder have been adopted and developed in fuzzy systems, but the generalization of their alternating versions to fuzzy systems has not been investigated. To satisfy the need for modeling and analyzing fuzzy systems, this article proposes two types of refinement relations called fuzzy alternating trace containment and fuzzy alternating simulation preorder, based on fuzzy concurrent game structures (FCGSs) under the Gödel semantics. These two fuzzy notions inherit properties from the corresponding classical setting. For example, fuzzy alternating simulation preorder for finite-state FCGSs can be computed in polynomial time; fuzzy alternating simulation preorder is a fuzzy subset of fuzzy alternating trace containment, and both relations can be logically characterized in terms of fuzzy version of alternating-time temporal logic. These properties make the theory developed here suitable for the modeling and verification of fuzzy systems. [ABSTRACT FROM AUTHOR]

The fuzzy discrete event system theory is unique in that it is capable of modeling a class of event-driven systems as fuzzy automata with states and event-invoked state transitions being ambiguous. At present, the theory lacks a self-learning component, an important topic that has hardly been touched in the literature. In this article, we use stochastic gradient descent to develop online learning algorithms for the fuzzy automata. We uncover an inherent obstacle in the initial derived algorithms that fundamentally restricts their learning capability owing to dependences of the model parameters to be learned. We develop a novel mechanism to not only overcome the obstacle but also make the learning adaptive. Our final algorithms can learn an event transition matrix based on automaton's states before and after the occurrence of a fuzzy event, and learn the transition matrix and multidimensional Gaussian fuzzy sets yielding initial automaton states from relevant input variables and target states. Computer simulation results are presented to show learning performance of the final algorithms. [ABSTRACT FROM AUTHOR]

The ability to build lean and agile supply chains has not developed as rapidly as anticipated, because the development of technology to manage such concepts of lean/agile for integrated supply chains is still under way. Also, due to ill-defined and vague indicators, which exist within leanness/agility assessment, many measures are described subjectively by linguistic terms, which are characterized by vagueness and multi-possibility, and the conventional assessment approaches cannot suitably or effectively handle such dynamic situations. In this paper, we propose a novel approach to model agility (which includes leanness) and introduce dynamic agility level index (DALi) through fuzzy intelligent agents. Generally, it is difficult to emulate human decision making if the recommendations of the agents are provided as crisp, numerical values. The multiple intelligent agents used in this study communicate their recommendation as fuzzy numbers to accommodate ambiguity in the opinion and the data used for modelling agility attributes for integrated supply chains. Moreover, when agents operate based on different criteria pertaining to agility like flexibility, profitability, quality, innovativeness, pro-activity, speed of response, cost, robustness, etc., for integrated supply chains, the ranking and aggregation of these fuzzy opinions to arrive at a consensus is complex. The proposed fuzzy intelligent agents approach provides a unique and unprecedented attempt to determine consensus in these fuzzy opinions and effectively model dynamic agility. The efficacy of the proposed approach is demonstrated with the help of an illustrative example. [ABSTRACT FROM AUTHOR]

The present research work outlines a fuzzified approach using fuzzy linear programming (FLP) using a suitably designed smooth logistic membership function (MF) for finding fuzziness patterns at disparate levels of satisfaction for theory of constraints-based (TOC) product-mix decision problems. The objective of the present work is to find fuzziness patterns of product-mix decisions with disparate levels of satisfaction of the decision-maker (DM). Another objective is to provide a robust, quantified monitor of the level of satisfaction among DMs and to calibrate these levels of satisfaction against DM expectations. Product-mix decision should take into account considerations such as the DM's level of satisfaction (sometimes called 'emotions') in order to make the decision a robust one. Sensitivity of the decision has been focused on a bottleneck-free, optimal product-mix solution of a TOC problem. The inefficiency of traditional linear programming (LP) in handling multiple-bottleneck problems using TOC is discussed using an illustrative example. Relationships among the degree of fuzziness, level of satisfaction and the throughput of modified TOC guide decision-makers (DM) under tripartite fuzzy environment in obtaining their product-mix choice trading-off with a pre-determined allowable fuzziness. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The computational study on finite/infinite-state systems, probabilistic systems, and finite-state fuzzy systems, has received much attention recently. In contrast, there are very few results for algorithmic analysis of infinite-state fuzzy systems. In this paper, we introduce fuzzy pushdown termination games (FPDTGs), which are an extension of fuzzy pushdown automata with a game feature and can serve as a formal model of infinite-state fuzzy systems. We investigate some computational issues of the games under termination objectives for two players: the goal of player-1 is to maximize the truth value of eventually terminating at some given configurations with the empty stack, while player-2 aims at the opposite. Some interesting results are obtained. For example, we show that both players have optimal memoryless strategies and the same value. The problem of computing the value can be solved in exponential time when the triangular norm is chosen as the minimum one. Furthermore, we present efficient algorithms for computing the values of two special subclasses of FPDTGs. The potential for practical use of our model is demonstrated by a case study on a manufacturing system. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the tracking control problem for the non-Gaussian stochastic distribution sampled-data fuzzy systems. First, by constructing an augmented system, an asynchronous proportional-integral (PI) controller is designed such that the probability density functions (PDFs) of the system output can track the target one. Second, by introducing two sets (the extension reachable set and the ellipsoid set), the state trajectories of the augmented system with persistent reference input signal can be restricted in a given local region, namely, the state constrained problem can be addressed. Furthermore, in some existing asynchronous controller strategies, it is required that the derivative of the membership function of the system not explicitly depends on the system input. However, in this paper, by restricting the state into a specified region, a new asynchronous scheme is proposed so as to the above-mentioned requirement is removed. Finally, an example is given to demonstrate the efficiency of the presented method. [ABSTRACT FROM AUTHOR]

In this paper, for an ultra-metric D on the unit interval and a small positive real number ϵ, we firstly define the concept of approximate bisimulation relations between two fuzzy automata and prove that the behavior of a fuzzy automaton A1 differs by ϵ from the behavior of a fuzzy automaton A2 under an approximate bisimulation relation between them. Then we put forward the notion of surjective functional approximate bisimulation relations between two fuzzy automata. A connection between surjective functional approximate bisimulation relations between two fuzzy automata A1 and A2 and approximate bisimulation relations for A1 is also discussed. Finally, we give a method to construct the greatest approximate bisimulation relation for a fuzzy automaton and point out that bisimulation relations for a fuzzy automaton are also approximate bisimulation relations. [ABSTRACT FROM AUTHOR]

This paper studies the fault detection problem for T–S fuzzy systems with partly unmeasurable premise variables. By using measurable premise variables and estimations of unmeasurable premise variables of fuzzy models as the premise variables of observers, a novel fuzzy fault detection observer scheme is constructed and the corresponding design condition is proposed via a set-theoretic description. Different from the conventional fault detection observer schemes, where all premise variables of the observer are the estimations of the premise variables in the fuzzy systems, the proposed method can take full advantage of the partly measurable premise variables for achieving a better fault detection performance. A numerical example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fuzzy unknown input observer (FUIO)-based fault estimation for discrete-time Takagi–Sugeno fuzzy systems. Firstly, an augmented system description is given. Then a FUIO is proposed to achieve fault estimation, which is robust against the effect of the external disturbance. Furthermore, a less conservative FUIO design method is proposed by using a finite-frequency range technique instead of an entire-frequency method. The gain matrices of the FUIO are obtained by solving linear matrix inequalities. Finally, simulation results of a discrete-time nonlinear system are presented to illustrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

Inspired by the applications of fuzzy automata and parallel regular expressions, we propose a new mathematical concept of parallel fuzzy regular expressions. In this paper, we investigate the equivalence between parallel fuzzy regular expressions and parallel fuzzy finite automata. An algorithm is proposed for carrying out the conversion of parallel fuzzy regular expressions to ϵ-free non-deterministic fuzzy automata. Furthermore, an analysis of the number of states obtained in the fuzzy automaton will be carried out using the proposed algorithm. Finally, the proposed algorithm is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

In this paper first, we introduce three fuzzy approximation operators denoted C, C, C on an arbitrary set X, and then we use these operators to associate various topologies to a given finite state machine. Also, we obtain some basic properties of these topological spaces. Finally, for a given fuzzy finite state automata M = (Q, ∑,μ), these results allows us to obtain (fuzzy) topology on Q, in terms of the source and successors Kuratowski closure operators on Q. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an implementation of a fuzzy system whose parameters are mutable according to the context. The construction of the system is done via two steps. First, we build a based type-1 Takagi–Sugeno–Kang (TSK) fuzzy system whose membership functions will be later adjusted to the situation by means of contextual transformation to reflect the influence of context in the interpretation of fuzzy sets. Second, an iterative algorithm is performed to identify the transformation matrix, which is used to scale the membership functions of the reference-based fuzzy sets in each of the contexts. The identification of the premise part of the based fuzzy system is performed via a combination of an island model parallel genetic algorithm and a space search memetic algorithm, while the identification of the consequent parameters of the system is done via an improved QR Householder least-squares method. The proposed system is evaluated using the well-known Mackey–Glass time-series prediction benchmark dataset and has shown better accuracy than any other previous works concerning the same problem. [ABSTRACT FROM AUTHOR]

The importance of semigroups and their fuzzy subsystems is evident from their applications and significant role in several applied dis- ciplines like computer sciences, control engineering, error-correcting codes and fuzzy automata theory. In this paper, we give generalizations of intuitionistic fuzzy interior ideals of semigroups and introduced the notions of intuitionistic fuzzy interior ideals of type ((∊̅,∊̅ V q̅k) and ((∊̅,∊̅) of semigroups. The important mile stone of the present paper is to link ordinary intuitionistic fuzzy interior ideals, ((∊̅,∊̅)-intuitionistic fuzzy interior ideals and (∊̅,∊̅ V q̅k)-intuitionistic fuzzy interior ideals. Moreover semigroups are characterized by the properties of these notions. [ABSTRACT FROM AUTHOR]

In this note first by considering the notion of general fuzzy automata (for simplicity GFA), we define the notions of direct product, restricted direct product and join of two GFA. Also, we introduce some operations on (Fuzzy) sets and then prove some related theorems. Finally we construct the general fuzzy recognizers and recognizable sets and give the notion of (trim) reversal of a given GFA. In particular, we define the notion of the language of a given general fuzzy E-recognizer and we show that the language of direct product of two ∑-recognizer is equal to direct product of their languages. [ABSTRACT FROM AUTHOR]

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In contrast with the existing approaches to exact bisimulation for fuzzy systems, we introduce a robust notion of behavioral distance to measure the behavioral similarity of nondeterministic fuzzy-transition systems which are a generalization of fuzzy automata. This behavioral distance provides a quantitative analogue of bisimilarity and is defined as the greatest fixed point of a suitable monotonic function. The behavioral distance has the important property that two systems are at zero distance if and only if they are bisimilar. Moreover, for any given threshold, we find that systems with behavioral distances bounded by the threshold are equivalent. In addition, we show that two system combinators—parallel composition and product—are nonexpansive with respect to our behavioral distance, which makes compositional verification possible. The theory developed here is applicable to the quantitative verification, approximate reduction, and reliability analysis of fuzzy-transition systems. [ABSTRACT FROM AUTHOR]

Because the number of transmission control protocol sessions usually varies from time to time, a perturbed Takagi-Sugeno fuzzy model is used in this paper to represent the dynamic transmission control protocol network systems. According to the proposed perturbed Takagi-Sugeno fuzzy model, a robust fuzzy controller design approach is investigated to achieve the congestion avoidance for the transmission control protocol network systems. In order to accomplish the above mission, some sufficient conditions are derived based on the Lyapunov stability theory. By solving these sufficient stability conditions, an active queue management router can be obtained via the proposed robust fuzzy congestion control technique. [ABSTRACT FROM AUTHOR]

In this paper, a fuzzy neural network (FNN) based discrete adaptive iterative learning controller (AILC) is proposed for a class of discrete-time uncertain nonlinear plants which can repeat a given task over a finite time sequence. Compared with the existing discrete AILC schemes, the proposed strategy can be applied to the discrete-time uncertain nonlinear plants with not only initial resetting errors and iteration- varying desired trajectory, but also random bounded disturbances and unknown non-Lipschitz plant nonlinearities. Two FNNs are used as approximators to compensate for the unknown plant nonlinearities. To overcome the function approximation error and possibly large random bounded disturbance, a time-varying boundary layer is introduced to design an auxiliary error function. The auxiliary error function is then utilized to derive the adaptive laws since the optimal FNN parameters for a good function approximation and the optimal width of time-varying boundary layer are unavailable. By using a Lyapunov like analysis, we show that the closed-loop is stable in the sense that the adjustable parameters and internal signals are bounded for all the iterations. Furthermore, learning performance is guaranteed in the sense that the norm of output tracking error vector will asymptotically converge to a residual set which is bounded by the width of boundary layer. [ABSTRACT FROM AUTHOR]

This paper aims to propose an efficient control algorithm for the mobile robot path control. A supervisory fuzzy-Gaussian-neural-network (SFGNN) controller is proposed. This controller includes a fuzzy-Gaussian-neural-network (FGNN) controller and a supervisory controller. The FGNN controller is constructed in a form of neural network with a Gaussian-type fuzzy membership function; and the parameters of the membership function are on-line tuned by the derived adaptive laws. The supervisory controller is designed to compensate for the approximation error between the FGNN controller and an ideal controller. This combination of FGNN controller and supervisory controller can achieve favorable control performance and can reduce the required neurons and tuned-weights of the SFGNN control system. The path control of mobile robot for two paths, a circular path and a square path, are used to test the effectiveness of the proposed design method. Simulation results demonstrate that the proposed SFGNN controller can achieve better control performance than an FGNN controller and a PID controller for the mobile robot path control. [ABSTRACT FROM AUTHOR]

Abstract: The target searching problem is a situation where a formation of multi-robot systems is set to search for a target and converge towards it when it is found. This problem lies in the fact that the target is initially absent and the formation must search for it in the environment. During the target search, false targets may appear dragging the formation towards it. Therefore, in order to avoid the formation following a false target, this paper presents a new methodology using the Takagi–Sugeno type fuzzy automaton (TS-TFA) in the area of formation control to solve the target searching problem. The TS fuzzy system is used to change the formation through the modifications in the states of the automaton. This change does not only switch the rules and therefore the state of each robot, but also the controllers and cost functions. This approach amplifies the versatility of the formation of mobile robots in the target searching problem. In this paper, the TS-TFA is presented and its implications in the formation are explained. Simulations and results with real robot are presented where it can be noticed that the formation is broken to maximize the perception range based on each robot’s observation of a possible target. Finally this work is concluded in the last section. [Copyright &y& Elsevier]

Abstract: In this paper we study subsystems, reverse subsystems and double subsystems of a fuzzy transition system. We characterize them in terms of fuzzy relation inequalities and equations, as eigen fuzzy sets of the fuzzy quasi-order Q δ and the fuzzy equivalence E δ generated by fuzzy transition relations, and as linear combinations of aftersets and foresets of Q δ and equivalence classes of E δ . We also show that subsystems, reverse subsystems and double subsystems of a fuzzy transition system form both closure and opening systems in the lattice of fuzzy subsets of A, where A is the set of states of , and we provide efficient procedures for computing related closures and openings of an arbitrary fuzzy subset of A. These procedures boil down to computing the fuzzy quasi-order Q δ or the fuzzy equivalence E δ , which can be efficiently computed using the well-known algorithms for computing the transitive closure of a fuzzy relation. [Copyright &y& Elsevier]

Abstract: Automata theory based on complete residuated lattice-valued logic has been first established by Qiu, and then has been systematically studied by Qiu and others. The definition of -valued Chomsky Normal Form in Xing and Qiu [Automata theory based on complete residuated lattice-valued logic: pushdown automata, Fuzzy Sets and Systems 160 (2009) 1125–1140] is somewhat different from that in Xing and Qiu [Pumping lemma in context-free grammar theory based on complete residuated lattice-valued logic, Fuzzy Sets and Systems 160 (2009) 1141–1151]. In this note, we give a more general -valued Chomsky Normal Form to unify the two definitions. We mainly show that, for an -valued context-free grammar, an -valued Greibach Normal Form can be equivalently constructed. [Copyright &y& Elsevier]

Abstract: Li and Pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice-ordered monoid, and generalize the well-known results of the classical theory of formal languages. In particular, they have shown that a fuzzy language over an integral lattice-ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton. However, they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression. In this paper we provide such an efficient method. Transforming scalars appearing in a fuzzy regular expression αinto letters of the new extended alphabet, we convert the fuzzy regular expression αto an ordinary regular expression . Then, starting from an arbitrary nondeterministic finite automaton that recognizes the language represented by the regular expression , we construct fuzzy finite automata and with the same or even less number of states than the automaton , which recognize the fuzzy language ‖α‖represented by the fuzzy regular expression α. The starting nondeterministic finite automaton can be obtained from using any of the well-known constructions for converting regular expressions to nondeterministic finite automata, such as Glushkov–McNaughton–Yamada''s position automaton, Brzozowski''s derivative automaton, Antimirov''s partial derivative automaton, or Ilie–Yu''s follow automaton. [Copyright &y& Elsevier]

Abstract: Bisimulations have been widely used in many areas of computer science to model equivalence between various systems, and to reduce the number of states of these systems, whereas uniform fuzzy relations have recently been introduced as a means to model the fuzzy equivalence between elements of two possible different sets. Here we use the conjunction of these two concepts as a powerful tool in the study of equivalence between fuzzy automata. We prove that a uniform fuzzy relation between fuzzy automata and is a forward bisimulation if and only if its kernel and co-kernel are forward bisimulation fuzzy equivalence relations on and and there is a special isomorphism between factor fuzzy automata with respect to these fuzzy equivalence relations. As a consequence we get that fuzzy automata and are UFB-equivalent, i.e., there is a uniform forward bisimulation between them, if and only if there is a special isomorphism between the factor fuzzy automata of and with respect to their greatest forward bisimulation fuzzy equivalence relations. This result reduces the problem of testing UFB-equivalence to the problem of testing isomorphism of fuzzy automata, which is closely related to the well-known graph isomorphism problem. We prove some similar results for backward–forward bisimulations, and we point to fundamental differences. Because of the duality with the studied concepts, backward and forward–backward bisimulations are not considered separately. Finally, we give a comprehensive overview of various concepts on deterministic, nondeterministic, fuzzy, and weighted automata, which are related to bisimulations. [Copyright &y& Elsevier]

This paper presents the analysis of Load Frequency Control (LFC) of a two-area hydrothermal system under deregulated environment by considering Adaptive Neuro-Fuzzy Inference System (ANFIS). Fixed gain controllers for LFC are designed at nominal operating conditions and fail to provide best control performance over a wide range of operating conditions. So, in order to keep system performance near its optimum, it is desirable to track the operating conditions and use updated parameters to compute control gains. Open transmission access and the evolving of more socialized companies for generation, transmission and distribution affects the formulation of AGC problem. So the traditional LFC two-area system is modified to take into account the effect of bilateral contracts on the dynamics. A control scheme based on ANFIS, which is trained by the results of off-line studies obtained using genetic algorithm, is proposed in this paper to optimize and update control gains in real-time according to load variations. The efficiency of the proposed method is demonstrated through computer simulations. [ABSTRACT FROM AUTHOR]

Although much progress has been made in developing seat belts and mandating their use, the injuries related to seat belts during frontal crashes are still widespread. This paper proposes an approach to control the seat belt restraint system force during a frontal crash to reduce thoracic injuries. A fuzzy logic controller based on moving the attachment point of the seat belt is proposed, and the simulation results with this controller are presented. Also, robustness to parameter variations is investigated. The results show that the proposed controller is very effective in reducing all critical values that lead to possible thoracic injuries during a frontal crash. The controller is also demonstrated to be robust with respect to varying impact conditions and parameters. [ABSTRACT FROM AUTHOR]