Showing papers on "Fuzzy associative matrix published in 2003"

On relaxed LMI-based designs for fuzzy regulators and fuzzy observers

Abstract: Relaxed conditions for stability of nonlinear, continuous and discrete-time systems given by fuzzy models are presented. A theoretical analysis shows that the proposed methods provide better or at least the same results of the methods presented in the literature. Numerical results exemplify this fact. These results are also used for fuzzy regulators and observers designs. The nonlinear systems are represented by fuzzy models proposed by Takagi and Sugeno (1985). The stability analysis and the design of controllers are described by linear matrix inequalities, that can be solved efficiently using convex programming techniques. The specification of the decay rate, constrains on control input and output are also discussed.

Robust stability analysis and fuzzy-scheduling control for nonlinear systems subject to actuator saturation

Abstract: Takagi-Sugeno (TS) fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input-output submodels. In this paper, the TS fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation. The TS fuzzy representation of a nonlinear system subject to actuator saturation is presented. In our TS fuzzy representation, the modeling error is also captured by norm-bounded uncertainties. A set invariance condition for the system in the TS fuzzy representation is first established. Based on this set invariance condition, the problem of estimating the domain of attraction of a TS fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality (LMI) optimization problem. By viewing the state feedback gain as an extra free parameter in the LMI optimization problem, we arrive at a method for designing state feedback gain that maximizes the domain of attraction. A fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction. An inverted pendulum is used to show the effectiveness of the proposed fuzzy controller.

Fuzzy association rules: general model and applications

Abstract: The theory of fuzzy sets has been recognized as a suitable tool to model several kinds of patterns that can hold in data. In this paper, we are concerned with the development of a general model to discover association rules among items in a (crisp) set of fuzzy transactions. This general model can be particularized in several ways; each particular instance corresponds to a certain kind of pattern and/or repository of data. We describe some applications of this scheme, paying special attention to the discovery of fuzzy association rules in relational databases.

The WM method completed: a flexible fuzzy system approach to data mining

Abstract: In this paper, the so-called Wang-Mendel (WM) method for generating fuzzy rules from data is enhanced to make it a comprehensive and flexible fuzzy system approach to data description and prediction. In the description part, the core ideas of the WM method are used to develop three methods to extract fuzzy IF-THEN rules from data. The first method shows how to extract rules for the user-specified cases, the second method generates all the rules that can be generated directly from the data, and the third method extrapolates the rules generated by the second method over the entire domain of interest. In the prediction part, two fuzzy predictive models are constructed based on the fuzzy IF-THEN rules extracted by the methods of the description part. The first model gives a continuous output and is suitable for predicting continuous variables, and the second model gives a piecewise constant output and is suitable for predicting categorical variables. We show that by comparing the prediction accuracy of the fuzzy predictive models with different numbers of fuzzy sets covering the input variables, we can rank the importance of the input variables. We also propose an algorithm to optimize the fuzzy predictive models, and show how to use the models to solve pattern recognition problems. Throughout this paper, we use a set of real data from a steel rolling plant to demonstrate the ideas and test the models.

Learning fuzzy classification rules from labeled data

Abstract: The automatic design of fuzzy rule-based classification systems based on labeled data is considered. It is recognized that both classification performance and interpretability are of major importance and effort is made to keep the resulting rule bases small and comprehensible. For this purpose, an iterative approach for developing fuzzy classifiers is proposed. The initial model is derived from the data and subsequently, feature selection and rule-base simplification are applied to reduce the model, while a genetic algorithm is used for parameter optimization. An application to the Wine data classification problem is shown.

Fuzzy reasoning Petri nets

Abstract: This paper presents a fuzzy reasoning Petri net (FRPN) model to represent a fuzzy production rule-based system. The issues of how to represent and reason about rules containing negative literals are addressed in the proposed PN model. The execution rules based on the model are defined formally using the operators in max-algebra. Then, a fuzzy reasoning algorithm is proposed to perform fuzzy reasoning automatically. The algorithm is consistent with the matrix equation expression method in the traditional PNs and allows one to exploit the maximum parallel reasoning potential embedded in the model. The legitimacy and feasibility of the proposed approach are proved and validated through a turbine fault diagnosis expert system.

Fuzzy Logic for Embedded Systems Applications

Abstract: Fuzzy Logic for Embedded Systems Applications, by a recognized expert in the field, covers all the basic theory relevant to electronics design, with particular emphasis on embedded systems, and shows how the techniques can be applied to shorten design cycles and handle logic problems that are tough to solve using conventional linear techniques. All the latest advances in the field aree discussed and practical circuit design examples presented.Fuzzy logic has been found to be particularly suitable for many embedded control applications. The intuitive nature of the fuzzy-based system design saves engineers time and reduces costs by shortening product development cycles and making system maintenance and adjustments easier. Yet despite its wide acceptance—and perhaps because of its name—it is still misunderstood and feared by many engineers. There is a need for embedded systems designers—both hardware and software—to get up to speed on the principles and applications of fuzzy logic in order to ascertain when and how to use them appropriately.Fuzzy Logic for Embedded Systems Applications provides practical guidelines for designing electronic circuits and devices for embedded systems using fuzzy-based logic. It covers both theory and applications with design examples.

Hoops and Fuzzy Logic

Abstract: Hajek acknowledges partial support by the grant No.A1030004/00 of the Grant Agency of the Academy of Sciences of the Czech Republic. Esteva and Godo acknowledge partial support by the Spanish CICYT project LOFAG TIC2001-1577-C03-01.

An Approach to Improving Consistency of Fuzzy Preference Matrix

Abstract: Based on the transfer formulas of fuzzy preference matrix and multiplicative preference matrix, this paper presents an approach to improving consistency of fuzzy preference matrix and gives a practical iterative algorithm to derive a modified fuzzy preference matrix with acceptable consistency. By using two criteria, we can judge whether the modification is acceptable or not. Finally, a numerical example is given to show the feasibility and effectiveness of the algorithm.

Fuzzy Output Feedback Control Design for Nonlinear Systems: An LMI Approach

Abstract: This paper addresses the problem of stabilizing a class of nonlinear systems by using an fuzzy output feedback controller. First, a class of nonlinear systems is approximated by a Takagi-Sugeno (TS) fuzzy model. Then, based on a well-known Lyapunov functional approach, we develop a technique for designing an fuzzy output feedback control law which guarantees the gain from an exogenous input to a regulated output is less or equal to a prescribed value. A design algorithm for constructing an fuzzy output feedback controller is given. In contrast to the existing results, the premise variables of the fuzzy output feedback controller are not necessarily to be the same as the premise variables of the TS fuzzy model of the plant. A numerical simulation example is presented to illustrate the theory development.

Smarandache Fuzzy Algebra

Abstract: The author studies the Smarandache Fuzzy Algebra, which, like its predecessor Fuzzy Algebra, arose from the need to define structures that were more compatible with the real world where the grey areas mattered, not only black or white. This book has seven chapters, which are divided into two parts. Part I contains the first chapter, and Part II encloses the remaining six chapters. In the first chapter (which also forms the first part), which is subdivided into twelve sections, we deal with eleven distinct fuzzy algebraic concepts and in the concluding section list the miscellaneous properties of fuzzy algebra. The eleven fuzzy algebraic concepts which we analyze are fuzzy sets, fuzzy subgroups, fuzzy sub-bigroups, fuzzy rings, fuzzy birings, fuzzy fields, fuzzy semirings, fuzzy near-rings, fuzzy vector spaces, fuzzy semigroups and fuzzy half-groupoids. The results used in these sections are extensive and we have succeeded in presenting new concepts defined by several researchers.

Nonlinear internal model control: application of inverse model based fuzzy control

Abstract: This paper investigates the possible applications of dynamical fuzzy systems to control nonlinear plants with asymptotically stable zero dynamics using a fuzzy nonlinear internal model control strategy. The developed strategy consists in including a dynamical Takagi-Sugeno fuzzy model of the plant within the control structure. In this way, the controller design simply results in a fuzzy model inversion. In this framework, the originality of the presented work lies in the use of a dynamical fuzzy model and its inversion. In order to be able to implement the control structure, two crucial points have to be addressed in the considered fuzzy context, on the one hand the model representation and identification, on the other, the model inversion. As the fuzzy system can be viewed as a collection of elementary subsystems, its inversion is approached here in a local way, i.e., on the elementary subsystems capable to provide an inverse solution. In this case, the inversion of the global fuzzy system is thus tackled by inversion of some of its components. By doing so, exact inversion is obtained and offset-free performances are ensured. In order to guarantee a desired regulation behavior and robustness of stability of the control system, the fuzzy controller is connected in series with a robustness filter. The potential of the proposed method is demonstrated with simulation examples.

Extracting Interpretable Fuzzy Rules from RBF Networks

Abstract: Radial basis function networks and fuzzy rule systems are functionally equivalent under some mild conditions. Therefore, the learning algorithms developed in the field of artificial neural networks can be used to adapt the parameters of fuzzy systems. Unfortunately, after the neural network learning, the structure of the original fuzzy system is changed and interpretability, which is considered to be one of the most important features of fuzzy systems, is usually impaired. This Letter discusses the differences between RBF networks and interpretable fuzzy systems. Based on these discussions, a method for extracting interpretable fuzzy rules from RBF networks is suggested. Simulation examples are given to embody the idea of this paper.

Data-driven linguistic modeling using relational fuzzy rules

Abstract: This paper presents a new approach to fuzzy rule-based modeling of nonlinear systems from numerical data. The novelty of the approach lies in the way of input partitioning and in the syntax of the rules. This paper introduces interpretable relational antecedents that incorporate local linear interactions between the input variables into the inference process. This modification improves the approximation quality and allows for limiting the number of rules. Additionally, the resulting linguistic description better captures the system characteristics by exposing the interactions between the input variables.

A note on quality measures for fuzzy association rules

Abstract: Several approaches generalizing association rules to fuzzy association rules have been proposed so far While the formal specification of fuzzy associations is more or less straightforward, the evaluation of such rules by means of appropriate quality measures assumes an understanding of the semantic meaning of a fuzzy rule In this respect, most existing proposals can be considered ad-hoc to some extent In this paper, we suggest a theoretical basis of fuzzy association rules by generalizing the classification of the data stored in a database into positive, negative, and irrelevant examples of a rule

Discovering fuzzy association rules using fuzzy partition methods

Abstract: Fuzzy association rules described by the natural language are well suited for the thinking of human subjects and will help to increase the flexibility for supporting users in making decisions or designing the fuzzy systems. In this paper, a new algorithm named fuzzy grids based rules mining algorithm (FGBRMA) is proposed to generate fuzzy association rules from a relational database. The proposed algorithm consists of two phases: one to generate the large fuzzy grids, and the other to generate the fuzzy association rules. A numerical example is presented to illustrate a detailed process for finding the fuzzy association rules from a specified database, demonstrating the effectiveness of the proposed algorithm.

Fuzzy logic applications

Abstract: Fuzzy logic is a modeling method well suited for the control of complex and non-linear systems. This paper illustrates some of the power of fuzzy logic through a simple control example. For the analytical chemist, fuzzy logic incorporates imprecision from measurement noise as well as from linguistic process descriptions to produce operational control systems.

Robust adaptive fuzzy controller for non‐affine nonlinear systems with dynamic rule activation

Abstract: This paper describes the design of a robust adaptive fuzzy controller for an uncertain single-input single-output nonlinear dynamical systems. While most recent results on fuzzy controllers considers affine systems with fixed rule-base fuzzy systems, we propose a control scheme for non-affine nonlinear systems and a dynamic fuzzy rule activation scheme in which an appropriate number of the fuzzy rules are chosen on-line. By using the proposed scheme, we can reduce the computation time, storage space, and dynamic order of the adaptive fuzzy system without significant performance degradation. The Lyapunov synthesis approach is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as for all other signals in the closed loop. No a priori knowledge of an upper bounds on the uncertainties is required. The theoretical results are illustrated through a simulation example. Copyright © 2002 John Wiley & Sons, Ltd.

Rapid design of fuzzy systems with Xfuzzy

Abstract: The crecient use of fuzzy systems in complex applications has motivated us to develop a new version of Xfuzzy, the design environment for fuzzy system created at the IMSE (Instituto de Microelectronica de Sevilla). This new version, Xfuzzy 3.0, offers the advantages of being enterely programmed in Java, and allows designing hierarchical rule bases that can interchange fuzzy or non fuzzy values as well as employ user-defined fuzzy connectives, linguistic hedges, membership functions, and defuzzification methods. Xfuzzy 3.0 integrates tools that facilitate the description, tuning, verification, and synthesis of complex fuzzy systems. This is illustrated in this paper with the design of a fuzzy controller to solve a parking problem.

Reinforcement learning for high-level fuzzy Petri nets

Abstract: The author has developed a reinforcement learning algorithm for the high-level fuzzy Petri net (HLFPN) models in order to perform structure and parameter learning simultaneously. In addition to the HLFPN itself, the difference and similarity among a variety of subclasses concerning Petri nets are also discussed. As compared with the fuzzy adaptive learning control network (FALCON), the HLFPN model preserves the advantages that: 1) it offers more flexible learning capability because it is able to model both IF-THEN and IF-THEN-ELSE rules; 2) it allows multiple heterogeneous outputs to be drawn if they exist; 3) it offers a more compact data structure for fuzzy production rules so as to save information storage; and 4) it is able to learn faster due to its structural reduction. Finally, main results are presented in the form of seven propositions and supported by some experiments.

Generation of fuzzy membership function using information theory measures and genetic algorithm

Abstract: One of the most challenging issues in fuzzy systems design is generating suitable membership functions for fuzzy variables. This paper proposes a paradigm of applying an information theoretic model to generate fuzzy membership functions. After modeling fuzzy membership function by fuzzy partitions, a genetic algorithm based optimization technique is presented to find sub optimal fuzzy partitions. To generate fuzzy membership function based on fuzzy partitions, a heuristic criterion is also defined. Extensive numerical results and evaluation procedure are provided to demonstrate the effectiveness of the proposed paradigm.

Apparatus and method for monitoring system health based on fuzzy metric data ranges and fuzzy rules

Abstract: A method and apparatus for determining the status of a computer system and software applications running on that system and displaying the status to a system administrator are provided. With the apparatus and method, metrics related to a particular application or subsystem are identified and then collected over a predetermined period of time using a data monitoring or collection facility to generate metric history data. Once collected, the metric history data is analyzed by computing a set of parameters representing statistical measures of the metric history data. A set of fuzzy rules are used to define the relationships between metrics and the ultimate application or subsystem status. This metric history analysis phase may be performed periodically such that the fuzzy sets are dynamically redefined at periodic intervals. The fuzzy rules are then evaluated using a fuzzy reasoning process and an overall status indication is generated. As system performance or status changes, the monitoring system can adapt by changing the shape of the “normal” fuzzy set based on the distribution of metric values. The rules may remain the same but the fuzzy set may change dynamically. This greatly reduces maintenance costs since the monitoring rule set can be slowly tuned over time, while the underlying “normal” fuzzy sets could be adjusted as often as needed. Thus, the method and apparatus provide a mechanism to express the knowledge about the key underlying relationships as fuzzy rules and then to automatically tailor the fuzzy sets that are referenced in the fuzzy rules using statistical data mining techniques.