Fuzzy System

Fuzzy logic control was originally introduced and developed as a model free control design approach. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model-based fuzzy control systems that guarantee not only stability but also performance of closed-loop fuzzy control systems. This paper presents a survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems. Attention will be focused on stability analysis and controller design based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models. Perspectives of model based fuzzy control in future are also discussed.

Neural networks and fuzzy systems are different approaches to introducing human-like reasoning to intelligent information systems. This text is the first to combine the study of these two subjects, their basics and their use, along with the symbolic AI methods, the traditional statistical methods of data analysis, and the chaos theory, to build comprehensive artificial intelligence systems. All these techniques are applied to a set of simple prototype problems with applications in engineering, business and finance. AI problems that cover most of the application-oriented research in the field (speech recognition, image processing, classification, planning, optimisation, prediction, control, decision making, game simulation, chaos analysis) are discussed and illustrated with concrete examples. Intended both as a text for advanced undergraduate and postgraduate students as well as a reference for researchers in the f ield of knowledge engineering, " Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering" has chapters structured for various levels of teaching. Teaching materials, such as PowerPoint presentations, slides etc., are available free. An integrated software environment and other software that can be used to solve the problems and to do the exercises from the book, as well as data sets and Power Point lecture notes, are available from the WWW: http://www.kedri.info (books -> Foundations of NN,FS and KE).

Rendón, The fuzzy classifier system: motivations and first results, Proc. First Intl. Conf. on Parallel Problem Solving from Nature-PPSN I, Springer, Berlin, 1991, pp. 330-334 (scatter Mamdani fuzzy rules for control/modeling problems) M. Valenzuela-Rendón, Reinforcement learning in the fuzzy classifier system, Expert Systems with Applications 14 (1998) 237-247 (scatter Mamdani fuzzy rules for control/modeling problems) J.R. Velasco, Genetic-based on-line learning for fuzzy process control, IJIS 13 (10-11) (1998) 891-903 (scatter Mamdani fuzzy rules for control problems)

Intrusion detection based upon computational intelligence is currently attracting considerable interest from the research community. Characteristics of computational intelligence (CI) systems, such as adaptation, fault tolerance, high computational speed and error resilience in the face of noisy information, fit the requirements of building a good intrusion detection model. Here we want to provide an overview of the research progress in applying CI methods to the problem of intrusion detection. The scope of this review will encompass core methods of CI, including artificial neural networks, fuzzy systems, evolutionary computation, artificial immune systems, swarm intelligence, and soft computing. The research contributions in each field are systematically summarized and compared, allowing us to clearly define existing research challenges, and to highlight promising new research directions. The findings of this review should provide useful insights into the current IDS literature and be a good source for anyone who is interested in the application of CI approaches to IDSs or related fields.

In this state-of-the-art paper, important advances that have been made during the past five years for both general and interval type-2 fuzzy sets and systems are described. Interest in type-2 subjects is worldwide and touches on a broad range of applications and many interesting theoretical topics. The main focus of this paper is on the theoretical topics, with descriptions of what they are, what has been accomplished, and what remains to be done.

Stability and performance requirements in fuzzy control of Takagi-Sugeno systems are usually stated as fuzzy summations, i.e., sums of terms, related to Lyapunov functions, which are weighted by membership functions or products of them. This paper presents an application to fuzzy control of Polya's theorems on positive forms on the standard simplex. The result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations; such conditions are less and less conservative as a complexity parameter, n, increases. Particular cases of such conditions are those in [C.-H. Fang, Y.-S. Liu, S.-W. Kau, L. Hong, C.-H. Lee, A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems, IEEE Trans. Fuzzy Systems 14 (2006) 286-397; X. Liu, Q. Zhang, New approaches to H ∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI, Automatica 39 (9) (2003) 1571-1582]

Although fuzzy control was initially introduced as a model-free control design method based on the knowledge of a human operator, current research is almost exclusively devoted to model-based fuzzy control methods that can guarantee stability and robustness of the closed-loop system. State-of-the-art techniques for identifying fuzzy models and designing model-based controllers are reviewed in this article. Attention is also paid to the role of fuzzy systems in higher levels of the control hierarchy, such as expert control, supervision and diagnostic systems. Open issues are highlighted and an attempt is made to give some directions for future research.

In this paper, a fast approach for automatically
generating fuzzy rules from sample patterns using generalized
dynamic fuzzy neural networks (GD-FNNs) is presented. The
GD-FNN is built based on ellipsoidal basis function and functionally
is equivalent to a Takagi–Sugeno–Kang fuzzy system. The
salient characteristics of the GD-FNN are: 1) structure identification
and parameters estimation are performed automatically
and simultaneously without partitioning input space and selecting
initial parameters a priori; 2) fuzzy rules can be recruited or
deleted dynamically; 3) fuzzy rules can be generated quickly
without resorting to the backpropagation (BP) iteration learning,
a common approach adopted by many existing methods. The
GD-FNN is employed in a wide range of applications ranging
from static function approximation and nonlinear system identification
to time-varying drug delivery system and multilink
robot control. Simulation results demonstrate that a compact and
high-performance fuzzy rule-base can be constructed. Comprehensive
comparisons with other latest approaches show that the
proposed approach is superior in terms of learning efficiency and
performance.

This paper proposes a fuzzy approach to classify single-site electromyograph (EMG) signals for multifunctional prosthesis control. While the classification problem is the focus of this paper, the ultimate goal is to improve myoelectric system control performance, and classification is an essential step in the control. Time segmented features are fed to a fuzzy system for training and classification. In order to obtain acceptable training speed and realistic fuzzy system structure, these features are clustered without supervision using the Basic Isodata algorithm at the beginning of the training phase, and the clustering results are used in initializing the fuzzy system parameters. Afterwards, fuzzy rules in the system are trained with the back-propagation algorithm. The fuzzy approach was compared with an artificial neural network (ANN) method on four subjects, and very similar classification results were obtained. It is superior to the latter in at least three points: slightly higher recognition rate; insensitivity to overtraining; and consistent outputs demonstrating higher reliability. Some potential advantages of the fuzzy approach over the ANN approach are also discussed.

The automatic diagnosis of breast cancer is an important, real-world medical problem. In this paper we focus on the Wisconsin breast cancer diagnosis (WBCD) problem, combining two methodologies-fuzzy systems and evolutionary algorithms -so as to automatically produce diagnostic systems. We find that our fuzzy-genetic approach produces systems exhibiting two prime characteristics: first, they attain high classification performance (the best shown to date), with the possibility of attributing a confidence measure to the output diagnosis; second, the resulting systems involve a few simple rules, and are therefore (human-) interpretable. (C.A. Peñ a-Reyes), moshe.sipper@di.epfl.ch (M. Sipper) 0933-3657/99/$ -see front matter © 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 3 3 -3 6 5 7 ( 9 9 ) 0 0 0 1 9 -6 C.A. Peña-Reyes, M. Sipper / Artificial Intelligence in Medicine 17 (1999) 131-155 132

This paper describes a general fuzzy min-max (GFMM) neural network which is a generalization and extension of the fuzzy min-max clustering and classification algorithms developed by Simpson. The GFMM method combines the supervised and unsupervised learning within a single training algorithm. The fusion of clustering and classification resulted in an algorithm that can be used as pure clustering, pure classification, or hybrid clustering classification. This hybrid system exhibits an interesting property of finding decision boundaries between classes while clustering patterns that cannot be said to belong to any of existing classes. Similarly to the original algorithms, the hyperbox fuzzy sets are used as a representation of clusters and classes. Learning is usually completed in a few passes through the data and consists of placing and adjusting the hyperboxes in the pattern space which is referred to as an expansion-contraction process. The classification results can be crisp or fuzzy. New data can be included without the need for retraining. While retaining all the interesting features of the original algorithms, a number of modifications to their definition have been made in order to accommodate fuzzy input patterns in the form of lower and upper bounds, combine the supervised and unsupervised learning, and improve the effectiveness of operations.

This paper shows how a small number of linguistically interpretable fuzzy rules can be extracted from numerical data for high-dimensional pattern classification problems. One difficulty in the handling of high-dimensional problems by fuzzy rule-based systems is the exponential increase in the number of fuzzy rules with the number of input variables. Another difficulty is the deterioration in the comprehensibility of fuzzy rules when they involve many antecedent conditions. Our task is to design comprehensible fuzzy rule-based systems with high classification ability. This task is formulated as a combinatorial optimization problem with three objectives: to maximize the number of correctly classified training patterns, to minimize the number of fuzzy rules, and to minimize the total number of antecedent conditions. We show two genetic-algorithm-based approaches. One is rule selection where a small number of linguistically interpretable fuzzy rules are selected from a large number of prespecified candidate rules. The other is fuzzy genetics-based machine learning where rule sets are evolved by genetic operations. These two approaches search for non-dominated rule sets with respect to the three objectives.

The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multimodel approach in which simple submodels (typically linear models) are combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance (i.e., the model is capable of approximating the given system with arbitrary accuracy, provided that sufficient rules are used and sufficient training data are available), they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior, which is difficult to interpret. Since one of the important motivations of using the TSK model (also other fuzzy models) is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. In this paper, we propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user's preference, generating models with good tradeoff in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example.

This paper presents a genetic algorithm for the Resource Constrained Multi-Project Scheduling Problem (RCMPSP). The chromosome representation of the problem is based on random keys. The schedules are constructed using a heuristic that builds parameterized active schedules based on priorities, delay times, and release dates defined by the genetic algorithm. The approach is tested on a set of randomly generated problems. The computational results validate the effectiveness of the proposed algorithm.

This article is a reaction to recent publications on rulebased modeling using fuzzy set theory and fuzzy logic. The interest in fuzzy systems has recently shifted from the seminal ideas about complexity reduction toward data-driven construction of fuzzy systems. Many algorithms have been introduced that aim at numerical approximation of functions by rules, but pay little attention to the interpretability of the resulting rule base. We show that fuzzy rule-based models acquired from measurements can be both accurate and transparent by using a low number of rules. The rules are generated by product-space clustering and describe the system in terms of the characteristic local behavior of the system in regions identified by the clustering algorithm. The fuzzy transition between rules makes it possible to achieve precision along with a good qualitative description in linguistic terms. The latter is useful for expert evaluation, rule-base maintenance, operator training, control systems design, user interfacing, etc. We demonstrate the approach on a modeling problem from a recently published article.

This paper is concerned with the problem of the robust stability of nonlinear delayed Hopfield neural networks (HNNs) with Markovian jumping parameters by Takagi-Sugeno (T-S) fuzzy model. The nonlinear delayed HNNs are first established as a modified T-S fuzzy model in which the consequent parts are composed of a set of Markovian jumping HNNs with interval delays. Time delays here are assumed to be time-varying and belong to the given intervals. Based on Lyapunov-Krasovskii stability theory and linear matrix inequality approach, stability conditions are proposed in terms of the upper and lower bounds of the delays. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.

Most processes in industry are characterized by nonlinear and time-varying behavior. Nonlinear system identification is becoming an important tool which can be used to improve control performance and achieve robust fault-tolerant behavior. Among the different nonlinear identification techniques, methods based on neuro-fuzzy models are gradually becoming established not only in the academia but also in industrial applications. Neuro-fuzzy modeling can be regarded as a gray-box technique on the boundary between neural networks and qualitative fuzzy models. The tools for building neuro-fuzzy models are based on combinations of algorithms from the fields of neural networks, pattern recognition and regression analysis. In this paper, an overview of neuro-fuzzy modeling methods for nonlinear system identification is given, with an emphasis on the tradeoff between accuracy and interpretability.

This paper proposs a systematic methodology of fuzzy logic modeling as a generic tool for modeling of complex systems. The methodology conveys three distinct features: 1) a unified parameterized reasoning formulation; 2) an improved fuzzy clustering algorithm; and 3) an efficient strategy of selecting significant system inputs and their membership functions. The reasoning mechanism introduces four parameters whose variation provides a continuous range of inference operation. As a result, we are no longer restricted to standard extremes in any step of reasoning. Unlike traditional approach of selecting the inference mechanism a priori, the fuzzy model itself can then adjust the reasoning process by optimizing the inference parameters based on input-output data. The fuzzy rules are generated through fuzzy c-means (FCM) clustering algorithm. Major bottlenecks of the algorithm are addressed and analytical solutions are suggested. Furthermore, we also address the classification process in fuzzy modelng to extend the derived fuzzy partition to the entire output space. This issue remains unattained in the current literature. In order to select suitable input variables among a finite number of candidates (unlike traditional approaches) we suggest a new strategy through which dominant input parameters are assigned in one step and no iteration process is required. Furthermore, a clustering technique called fuzzy line clustering is introduced to assign the input membership functions. In order to evaluate the proposed methodology, two examples-a nonlinear function and a gas furnace dynamic procedure-are investigated in detail. The significant improvement of the model is concluded compared to other fuzzy modeling approaches.

We describe a novel life-long learning approach for intelligent agents that are embedded in intelligent environments. The agents aim to realize the vision of ambient intelligence in intelligent inhabited environments (IIE) by providing ubiquitous computing intelligence in the environment supporting the activities of the user. An unsupervised, data-driven, fuzzy technique is proposed for extracting fuzzy membership functions and rules that represent the user's particularized behaviors in the environment. The user's learned behaviors can then be adapted online in a life-long mode to satisfy the different user and system objectives. We have performed unique experiments in which the intelligent agent has learned and adapted to the user's behavior, during a stay of five consecutive days in the intelligent dormitory (iDorm), which is a real ubiquitous computing environment test bed. Both offline and online experimental results are presented comparing the performance of our technique with other approaches. The results show that our proposed system has outperformed the other approaches, while operating online in a life-long mode to realize the ambient intelligence vision.

A method for designing optimal interval type-2 fuzzy logic controllers using evolutionary algorithms is presented in this paper. Interval type-2 fuzzy controllers can outperform conventional type-1 fuzzy controllers when the problem has a high degree of uncertainty. However, designing interval type-2 fuzzy controllers is more difficult because there are more parameters involved. In this paper, interval type-2 fuzzy systems are approximated with the average of two type-1 fuzzy systems, which has been shown to give good results in control if the type-1 fuzzy systems can be obtained appropriately. An evolutionary algorithm is applied to find the optimal interval type-2 fuzzy system as mentioned above. The human evolutionary model is applied for optimizing the interval type-2 fuzzy controller for a particular non-linear plant and results are compared against an optimal type-1 fuzzy controller. A comparative study of simulation results of the type-2 and type-1 fuzzy controllers, under different noise levels, is also presented. Simulation results show that interval type-2 fuzzy controllers obtained with the evolutionary algorithm outperform type-1 fuzzy controllers.

This paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for Takagi-Sugeno (TS) systems. This approach is based on the idea of multiple Lyapunov functions together with simple techniques for introducing slack matrices. Unlike some previous approaches based on multiple Lyapunov functions, both the stability and the stabilization conditions are written as linear matrix inequality (LMI) problems. The proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the LMI problems. Numeric examples illustrate the effectiveness of this method. assumptions ensure that this combination guarantees global stability. In , certain boundary conditions are applied due to the discontinuities of the function across the subspace boundaries. On the other hand, proposes extra LMI constraints to ensure the continuity of the function at the boundaries. In , some methods ensure that the function decreases when leaving one subspace for another closer to the equilibrium, relaxing the continuity assumption. Even so, designing controllers with piecewise Lyapunov functions generally results in nonconvex optimization problems .

This paper proposes various methods for constructing a compact fuzzy classification system consisting of a small number of linguistic classification rules. First we formulate a rule selection problem of linguistic classification rules with two objectives: to maximize the number of correctly classified training patterns and to minimize the number of selected rules. Next we propose three methods for finding a set of non-dominated solutions of the rule selection problem. These three methods are based on a single-objective genetic algorithm. We also propose a method based on a multi-objective genetic algorithm for finding a set of non-dominated solutions. We examine the performance of the proposed methods by applying them to the well-known iris data. Finally we propose a hybrid algorithm by combining a learning method of linguistic classification rules with the multi-objective genetic algorithm. High performance of the hybrid algorithm is demonstrated by computer simulations on the iris data. © 1997 Elsevier Science B.V.

This paper presents two indirect adaptive fuzzy control schemes for a class of uncertain continuous-time multiinput multi-output nonlinear dynamic systems. Within these schemes, fuzzy systems are employed to approximate the plant's unknown nonlinear functions and robustifying control terms are used to compensate for approximation errors. By using a regularized matrix inverse, a stable well-defined adaptive controller is firstly investigated. Then, in order to obtain an adaptive controller not depending upon any parameter initialization conditions and to relax the requirement of bounding parameter values, a second adaptive controller is proposed. All parameter adaptive laws and robustifying control terms are derived based on Lyapunov stability analysis so that, under appropriate assumptions, semi-global stability and asymptotic convergence to zero of tracking errors can be guaranteed. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.

We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observers analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state.

Since accurate regional load forecasting is very important for improvement of the management performance of the electric industry, various regional load forecasting methods have been developed. The purpose of this study is to apply the adaptive network based fuzzy inference system (ANFIS) model to forecast the regional electricity loads in Taiwan and demonstrate the forecasting performance of this model. Based on the mean absolute percentage errors and statistical results, we can see that the ANFIS model has better forecasting performance than the regression model, artificial neural network (ANN) model, support vector machines with genetic algorithms (SVMG) model, recurrent support vector machines with genetic algorithms (RSVMG) model and hybrid ellipsoidal fuzzy systems for time series forecasting (HEFST) model. Thus, the ANFIS model is a promising alternative for forecasting regional electricity loads.

We propose a new general method for segmenting brain tumors in 3D magnetic resonance images. Our method is applicable to different types of tumors. First, the brain is segmented using a new approach, robust to the presence of tumors. Then a first tumor detection is performed, based on selecting asymmetric areas with respect to the approximate brain symmetry plane and fuzzy classification. Its result constitutes the initialization of a segmentation method based on a combination of a deformable model and spatial relations, leading to a precise segmentation of the tumors. Imprecision and variability are taken into account at all levels, using appropriate fuzzy models. The results obtained on different types of tumors have been evaluated by comparison with manual segmentations.

This paper aims at providing an in-depth overview of designing interpretable fuzzy inference models from data within a unified framework. The objective of complex system modelling is to develop reliable and understandable models for human being to get insights into complex real-world systems whose first-principle models are unknown. Because system behaviour can be described naturally as a series of linguistic rules, data-driven fuzzy modelling becomes an attractive and widely used paradigm for this purpose. However, fuzzy models constructed from data by adaptive learning algorithms usually suffer from the loss of model interpretability. Model accuracy and interpretability are two conflicting objectives, so interpretation preservation during adaptation in data-driven fuzzy system modelling is a challenging task, which has received much attention in fuzzy system modelling community. In order to clearly discriminate the different roles of fuzzy sets, input variables, and other components in achieving an interpretable fuzzy model, a taxonomy of fuzzy model interpretability is first proposed in terms of low-level interpretability and high-level interpretability in this paper. The low-level interpretability of fuzzy models refers to fuzzy model interpretability achieved by optimizing the membership functions in terms of semantic criteria on fuzzy set level, while the high-level interpretability refers to fuzzy model interpretability obtained by dealing with the coverage, completeness, and consistency of the rules in terms of the criteria on fuzzy rule level. Some criteria for low-level interpretability and high-level interpretability are identified, respectively. Different data-driven fuzzy modelling techniques in the literature focusing on the interpretability issues are reviewed and discussed from the perspective of low-level interpretability and high-level interpretability. Furthermore, some open problems about interpretable fuzzy models are identified and some potential new research directions on fuzzy model interpretability are also suggested. Crown

Generally, how to satisfy the deadline constraint is the major issue in solving real-time scheduling. Recently, neural network using competitive learning rule provides a highly effective method and deriving a sound solution for scheduling problem with less network complexity. However, due to the availability of resources, the machines may not reach full utilization. To facilitate the problem the extra neuron is introduced to the competitive neural network (CHNN). This study tries to impose slack neuron on CHNN with respect to process time and deadline constraints. Simulation results reveal that the competitive neural network imposed on the proposed energy function with slack neurons integrated ensures an appropriate approach of solving this class of scheduling problems of single or multiple identical machines.

Machine prognosis is a significant part of Condition-Based Maintenance (CBM) and intends to monitor and track the time evolution of the fault so that maintenance can be performed or the task be terminated to avoid a catastrophic failure. A new prognostic method is developed in this paper using adaptive neuro-fuzzy inference systems (ANFIS) and high-order particle filtering. The ANFIS is trained via machine historical failure data. The trained ANFIS and its modeling noise constitute an m th -order hidden Markov model to describe the fault propagation process. The high-order particle filter uses this Markov model to predict the time evolution of the fault indicator in the form of a probability density function (pdf). An on-line update scheme is developed to adapt the Markov model to various machine dynamics quickly. The performance of the proposed method is evaluated by using the testing data from a cracked carrier plate and a faulty bearing. The results show that it outperforms classical condition predictors.

Since many real-world engineering systems are too complex to be defined in precise terms, imprecision is often involved in any engineering design process. Fuzzy systems have an essential role in this fuzzy modelling, which can formulate uncertainty in actual environment. In addition, this is an important sub-process in determining inverse, eigenvalue and some other useful matrix computations, too. One of the most practicable subjects in recent studies is based on LR fuzzy numbers, which are defined and used by Dubois and Prade with some useful and easy approximation arithmetic operators on them. Recently Dehghan et al. [M. Dehghan, M. Ghatee, B. Hashemi, Some computations on fuzzy matrices, submitted for publication.] extended some matrix computations on fuzzy matrices, where a fuzzy matrix appears as a rectangular array of fuzzy numbers. In continuation to our previous work, we focus on fuzzy systems in this paper. It is proved that finding all of the real solutions which satisfy in a system with interval coefficients is NP-hard. The same result can similarly be derived for fuzzy systems. So we employ some heuristics based methods on Dubois and Prade's approach, finding some positive fuzzy vectorx which satisfiesÃx ¼b, whereà andb are a fuzzy matrix and a fuzzy vector respectively. We propose some new methods to solve this system that are comparable to the well known methods such as the Cramer's rule, Gaussian elimination, LU decomposition method (Doolittle algorithm) and its simplification. Finally we extend a new method employing Linear Programming (LP) for solving square and non-square (over-determined) fuzzy systems. Some numerical examples clarify the ability of our heuristics. (M. Ghatee).

In this paper, we are concerned with the problem of stability analysis and stabilization control design for Takagi-Sugeno (T-S) fuzzy systems with probabilistic interval delay. By employing the information of probability distribution of the time delay, the original system is transformed into a T-S fuzzy model with stochastic parameter matrices. Based on the new type of T-S fuzzy model, the delay-distribution-dependent criteria for the mean-square exponential stability of the considered systems are derived by using the Lyapunov-Krasovskii functional method, parallel distributed compensation approach, and the convexity of some matrix equations. The solvability of the derived criteria depends not only on the size of the delay but also on the probability distribution of the delay taking values in some intervals. The revisions of the main criteria in this paper can also be used to deal with the case when only the information of variation range of the delay is considered. It is shown by practical examples that our method can lead to very less conservative results than those by other existing methods.

In this paper, we consider a fundamental theoretical question: Is it always possible to design a fuzzy system able of approximating any real continuous function on a compact set with arbitrary accuracy? Moreover, we will research whether the answer to the above question is positive when we restrict to a fixed (but arbitrary) type of fuzzy reasoning and to a subclass of fuzzy relations. This result can be viewed as an existence theorem of an optimal fuzzy system for a wide variety of problems.

Grid computing is a computing framework to meet the growing computational demands. Essential grid services contain more intelligent functions for resource management, security, grid service marketing, collaboration and so on. The load sharing of computational jobs is the major task of computational grids. Grid resource manager provides functional mechanism for discovery, publishing of resources as well as scheduling, submission and monitoring of jobs. In this paper, we introduce a novel approach based on Particle Swarm Optimization (PSO) for scheduling jobs on computational grids. The representations of the position and velocity of the particles in the conventional PSO is extended from the real vectors to fuzzy matrices. Our approach is to dynamically generate an optimal schedule so as to complete the tasks in a minimum period of time as well as utilizing the resources in an efficient way. We evaluate the performance of our proposed approach with a direct Genetic Algorithm (GA) and Simulated Annealing (SA) approach.

Linear programming problems with trapezoidal fuzzy variables (FVLP) have recently attracted some interest. Some methods have been developed for solving these problems by introducing and solving certain auxiliary problems. Here, we apply a linear ranking function to order trapezoidal fuzzy numbers. Then, we establish the dual problem of the linear programming problem with trapezoidal fuzzy variables and hence deduce some duality results. In particular, we prove that the auxiliary problem is indeed the dual of the FVLP problem. Having established the dual problem, the results will then follow as natural extensions of duality results for linear programming problems with crisp data. Finally, using the results, we develop a new dual algorithm for solving the FVLP problem directly, making use of the primal simplex tableau. This algorithm will be useful for sensitivity (or post optimality) analysis when using primal simplex tableaus.

A novel fuzzy-observer-design approach is presented for Takagi-Sugeno fuzzy models with unknown output disturbances. In order to decouple the unknown output disturbance, an augmented fuzzy descriptor model is constructed by supposing the disturbance to be an auxiliary state vector. A fuzzy state-space observer is next designed for the augmented fuzzy descriptor system, and the simultaneous estimates of the original state and disturbance are thus obtained. The proposed observer technique is further applied to estimate sensor faults. Finally, a numerical example is given to illustrate the design procedure, and the simulation results show the desired tracking performance. The preknowledge of the disturbance and fault is not necessary for our design. Moreover, the considered disturbance and sensor fault can be in any form.

A fuzzy rule can have the shape of an ellipsoid in the input-output state space of a system. Then an additive fuzzy system approximates a function by covering its graph with ellipsoidal rule patches. It averages rule patches that overlap. The best fuzzy rules cover the extrema or bumps in the function. Neural or statistical clustering systems can approximate the unknown fuzzy rules from training data. Neural systems can then both tune these rules and add rules to improve the function approximation. We use a hybrid neural system that combines unsupervised and supervised learning to find and tune the rules in the form of ellipsoids. Unsupervised competitive learning finds the first-order and second-order statistics of clusters in the training data. The covariance matrix of each cluster gives an ellipsoid centered at the vector or centroid of the data cluster. The supervised neural system learns with gradient descent. It locally minimizes the mean-squared error of the fuzzy function approximation. In the hybrid system unsupervised learning initializes the gradient descent. The hybrid system tends to give a more accurate function approximation than does the lone unsupervised or supervised system. We found a closed-form model for the optimal rules when only the centroids of the ellipsoids change. We used numerical techniques to find the optimal rules in the general case.

Motor fault detection and diagnosis involves processing a large amount of information of the motor system. With the combined synergy of fuzzy logic and neural networks, a better understanding of the heuristics underlying the motor fault detection/diagnosis process and successful fault detection/diagnosis schemes can be achieved. This paper presents two neural fuzzy (NN/FZ) inference systems, namely, Fuzzy Adaptive Learning Control/Decision Network (FALCON) and Adaptive Network Based Fuzzy Inference System (ANFIS), with applications to induction motor fault detection/diagnosis problems. The general specifications of the NN/FZ systems are discussed. In addition, the fault detection/diagnosis structures are analyzed and compared with regard to their learning algorithms, initial knowledge requirements, extracted knowledge types, domain partitioning, rule structuring and modifications. Simulated experimental results are presented in terms of motor fault detection accuracy and knowledge extraction feasibility. Results suggest new and promising research areas for using NN/FZ inference systems for incipient fault detection and diagnosis in induction motors.

This paper deals with a fuzzy-based intelligent robotic system that requires various capabilities normally associated with intelligence. It acquires skills and knowledge through interaction with a dynamic environment. Recently, subsumption architectures, behavior-based artificial intelligence, and behavioral engineering for robotic systems have been discussed as new technologies for intelligent robotic systems. This paper proposes a robotic system with "structured intelligence." We focus on a mobile robotic system with a fuzzy controller and propose a sensory network that allows the robot to perceive its environment. An evolutionary approach improves the robot's performance. Furthermore, we discuss the effectiveness of the proposed method through computer simulations of collision avoidance and path-planning problems.

In this paper the Gauss-Sidel iterative method in Allahviranloo [Appl. Math. Comput., in press], for solving Fuzzy system of linear equations (FSLE) is transformed to the successive over relaxation (SOR) method. This method is discussed in detail and followed by convergence theorem. Algorithm is compared with the Gauss-Sidel method by solving a numerical example.