Showing papers on "Fuzzy logic published in 2001"

Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions

Abstract: (NOTE: Each chapter concludes with Exercises.) I: PRELIMINARIES. 1. Introduction. Rule-Based FLSs. A New Direction for FLSs. New Concepts and Their Historical Background. Fundamental Design Requirement. The Flow of Uncertainties. Existing Literature on Type-2 Fuzzy Sets. Coverage. Applicability Outside of Rule-Based FLSs. Computation. Supplementary Material: Short Primers on Fuzzy Sets and Fuzzy Logic. Primer on Fuzzy Sets. Primer on FL. Remarks. 2. Sources of Uncertainty. Uncertainties in a FLS. Words Mean Different Things to Different People. 3. Membership Functions and Uncertainty. Introduction. Type-1 Membership Functions. Type-2 Membership Functions. Returning to Linguistic Labels. Multivariable Membership Functions. Computation. 4. Case Studies. Introduction. Forecasting of Time-Series. Knowledge Mining Using Surveys. II: TYPE-1 FUZZY LOGIC SYSTEMS. 5. Singleton Type-1 Fuzzy Logic Systems: No Uncertainties. Introduction. Rules. Fuzzy Inference Engine. Fuzzification and Its Effect on Inference. Defuzzification. Possibilities. Fuzzy Basis Functions. FLSs Are Universal Approximators. Designing FLSs. Case Study: Forecasting of Time-Series. Case Study: Knowledge Mining Using Surveys. A Final Remark. Computation. 6. Non-Singleton Type-1 Fuzzy Logic Systems. Introduction. Fuzzification and Its Effect on Inference. Possibilities. FBFs. Non-Singleton FLSs Are Universal Approximators. Designing Non-Singleton FLSs. Case Study: Forecasting of Time-Series. A Final Remark. Computation. III: TYPE-2 FUZZY SETS. 7. Operations on and Properties of Type-2 Fuzzy Sets. Introduction. Extension Principle. Operations on General Type-2 Fuzzy Sets. Operations on Interval Type-2 Fuzzy Sets. Summary of Operations. Properties of Type-2 Fuzzy Sets. Computation. 8. Type-2 Relations and Compositions. Introduction. Relations in General. Relations and Compositions on the Same Product Space. Relations and Compositions on Different Product Spaces. Composition of a Set with a Relation. Cartesian Product of Fuzzy Sets. Implications. 9. Centroid of a Type-2 Fuzzy Set: Type-Reduction. Introduction. General Results for the Centroid. Generalized Centroid for Interval Type-2 Fuzzy Sets. Centroid of an Interval Type-2 Fuzzy Set. Type-Reduction: General Results. Type-Reduction: Interval Sets. Concluding Remark. Computation. IV: TYPE-2 FUZZY LOGIC SYSTEMS. 10. Singleton Type-2 Fuzzy Logic Systems. Introduction. Rules. Fuzzy Inference Engine. Fuzzification and Its Effect on Inference. Type-Reduction. Defuzzification. Possibilities. FBFs: The Lack Thereof. Interval Type-2 FLSs. Designing Interval Singleton Type-2 FLSs. Case Study: Forecasting of Time-Series. Case Study: Knowledge Mining Using Surveys. Computation. 11. Type-1 Non-Singleton Type-2 Fuzzy Logic Systems. Introduction. Fuzzification and Its Effect on Inference. Interval Type-1 Non-Singleton Type-2 FLSs. Designing Interval Type-1 Non-Singleton Type-2 FLSs. Case Study: Forecasting of Time-Series. Final Remark. Computation. 12. Type-2 Non-Singleton Type-2 Fuzzy Logic Systems. Introduction. Fuzzification and Its Effect on Inference. Interval Type-2 Non-Singleton Type-2 FLSs. Designing Interval Type-2 Non-Singleton Type-2 FLSs. Case Study: Forecasting of Time-Series. Computation. 13. TSK Fuzzy Logic Systems. Introduction. Type-1 TSK FLSs. Type-2 TSK FLSs. Example: Forecasting of Compressed Video Traffic. Final Remark. Computation. 14. Epilogue. Introduction. Type-2 Versus Type-1 FLSs. Appropriate Applications for a Type-2 FLS. Rule-Based Classification of Video Traffic. Equalization of Time-Varying Non-linear Digital Communication Channels. Overcoming CCI and ISI for Digital Communication Channels. Connection Admission Control for ATM Networks. Potential Application Areas for a Type-2 FLS. A. Join, Meet, and Negation Operations For Non-Interval Type-2 Fuzzy Sets. Introduction. Join Under Minimum or Product t-Norms. Meet Under Minimum t-Norm. Meet Under Product t-Norm. Negation. Computation. B. Properties of Type-1 and Type-2 Fuzzy Sets. Introduction. Type-1 Fuzzy Sets. Type-2 Fuzzy Sets. C. Computation. Type-1 FLSs. General Type-2 FLSs. Interval Type-2 FLSs. References. Index.

Learning and Soft Computing: Support Vector Machines, Neural Networks, and Fuzzy Logic Models

Abstract: This textbook provides a thorough introduction to the field of learning from experimental data and soft computing. Support vector machines (SVM) and neural networks (NN) are the mathematical structures, or models, that underlie learning, while fuzzy logic systems (FLS) enable us to embed structured human knowledge into workable algorithms. The book assumes that it is not only useful, but necessary, to treat SVM, NN, and FLS as parts of a connected whole. Throughout, the theory and algorithms are illustrated by practical examples, as well as by problem sets and simulated experiments. This approach enables the reader to develop SVM, NN, and FLS in addition to understanding them. The book also presents three case studies: on NN-based control, financial time series analysis, and computer graphics. A solutions manual and all of the MATLAB programs needed for the simulated experiments are available.

Designing fuzzy inference systems from data: An interpretability-oriented review

Abstract: Fuzzy inference systems (FIS) are widely used for process simulation or control. They can be designed either from expert knowledge or from data. For complex systems, FIS based on expert knowledge only may suffer from a loss of accuracy. This is the main incentive for using fuzzy rules inferred from data. Designing a FIS from data can be decomposed into two main phases: automatic rule generation and system optimization. Rule generation leads to a basic system with a given space partitioning and the corresponding set of rules. System optimization can be done at various levels. Variable selection can be an overall selection or it can be managed rule by rule. Rule base optimization aims to select the most useful rules and to optimize rule conclusions. Space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters. Structure optimization is of a major importance: selecting variables, reducing the rule base and optimizing the number of fuzzy sets. Over the years, many methods have become available for designing FIS from data. Their efficiency is usually characterized by a numerical performance index. However, for human-computer cooperation another criterion is needed: the rule interpretability. An implicit assumption states that fuzzy rules are by nature easy to be interpreted. This could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts. The paper analyzes the main methods for automatic rule generation and structure optimization. They are grouped into several families and compared according to the rule interpretability criterion. For this purpose, three conditions for a set of rules to be interpretable are defined.

Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model

Abstract: This study introduces a fuzzy control design method for nonlinear systems with a guaranteed H/sub /spl infin// model reference tracking performance. First, the Takagi and Sugeno (TS) fuzzy model is employed to represent a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based fuzzy controller is developed to reduce the tracking error as small as possible for all bounded reference inputs. The advantage of proposed tracking control design is that only a simple fuzzy controller is used in our approach without feedback linearization technique and complicated adaptive scheme. By the proposed method, the fuzzy tracking control design problem is parameterized in terms of a linear matrix inequality problem (LMIP). The LMIP can be solved very efficiently using the convex optimization techniques. Simulation example is given to illustrate the design procedures and tracking performance of the proposed method.

Reasoning within fuzzy description logics

Abstract: Description Logics (DLs) are suitable, well-known, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e. set of individuals with common properties. The experience in using DLs in applications has shown that in many cases we would like to extend their capabilities. In particular, their use in the context of Multimedia Information Retrieval (MIR) leads to the convincement that such DLs should allow the treatment of the inherent imprecision in multimedia object content representation and retrieval. In this paper we will present a fuzzy extension of ALC, combining Zadeh's fuzzy logic with a classical DL. In particular, concepts becomes fuzzy and, thus, reasoning about imprecise concepts is supported. We will define its syntax, its semantics, describe its properties and present a constraint propagation calculus for reasoning in it.

ECG beat recognition using fuzzy hybrid neural network

Abstract: Presents the application of the fuzzy neural network for electrocardiographic (ECG) beat recognition and classification. The new classification algorithm of the ECG beats, applying the fuzzy hybrid neural network and the features drawn from the higher order statistics has been proposed in the paper. The cumulants of the second, third, and fourth orders have been used for the feature selection. The hybrid fuzzy neural network applied in the solution consists of the fuzzy self-organizing subnetwork connected in cascade with the multilayer perceptron, working as the final classifier. The c-means and Gustafson-Kessel algorithms for the self-organization of the neural network have been applied. The results of experiments of recognition of different types of beats on the basis of the ECG waveforms have confirmed good efficiency of the proposed solution. The investigations show that the method may find practical application in the recognition and classification of different type heart beats.

Robust fuzzy control of nonlinear systems with parametric uncertainties

Abstract: Addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties. The Takagi-Sugeno (T-S) fuzzy model is adopted for fuzzy modeling of the nonlinear system. Two cases of the T-S fuzzy system with parametric uncertainties, both continuous-time and discrete-time cases are considered. In both continuous-time and discrete-time cases, sufficient conditions are derived for robust stabilization in the sense of Lyapunov asymptotic stability, for the T-S fuzzy system with parametric uncertainties. The sufficient conditions are formulated in the format of linear matrix inequalities. The T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. The effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic Lorenz system.

Evolving fuzzy neural networks for supervised/unsupervised online knowledge-based learning

Abstract: This paper introduces evolving fuzzy neural networks (EFuNNs) as a means for the implementation of the evolving connectionist systems (ECOS) paradigm that is aimed at building online, adaptive intelligent systems that have both their structure and functionality evolving in time. EFuNNs evolve their structure and parameter values through incremental, hybrid supervised/unsupervised, online learning. They can accommodate new input data, including new features, new classes, etc., through local element tuning. New connections and new neurons are created during the operation of the system. EFuNNs can learn spatial-temporal sequences in an adaptive way through one pass learning and automatically adapt their parameter values as they operate. Fuzzy or crisp rules can be inserted and extracted at any time of the EFuNN operation. The characteristics of EFuNNs are illustrated on several case study data sets for time series prediction and spoken word classification. Their performance is compared with traditional connectionist methods and systems. The applicability of EFuNNs as general purpose online learning machines, what concerns systems that learn from large databases, life-long learning systems, and online adaptive systems in different areas of engineering are discussed.

Fuzzy Modeling and Control

Abstract: In the last ten years, a true explosion of investigations into fuzzy modeling and its applications in control, diagnostics, decision making, optimization, pattern recognition, robotics, etc. has been observed. The attraction of fuzzy modeling results from its intelligibility and the high effectiveness of the models obtained. Owing to this the modeling can be applied for the solution of problems which could not be solved till now with any known conventional methods. The book provides the reader with an advanced introduction to the problems of fuzzy modeling and to one of its most important applications: fuzzy control. It is based on the latest and most significant knowledge of the subject and can be used not only by control specialists but also by specialists working in any field requiring plant modeling, process modeling, and systems modeling, e.g. economics, business, medicine, agriculture,and meteorology.

Fuzzy c-means clustering of incomplete data

Abstract: The problem of clustering a real s-dimensional data set X={x/sub 1/,...,x/sub n/} /spl sub/ R/sup s/ is considered. Usually, each observation (or datum) consists of numerical values for all s features (such as height, length, etc.), but sometimes data sets can contain vectors that are missing one or more of the feature values. For example, a particular datum x/sub k/ might be incomplete, having the form x/sub k/=(254.3, ?, 333.2, 47.45, ?)/sup T/, where the second and fifth feature values are missing. The fuzzy c-means (FCM) algorithm is a useful tool for clustering real s-dimensional data, but it is not directly applicable to the case of incomplete data. Four strategies for doing FCM clustering of incomplete data sets are given, three of which involve modified versions of the FCM algorithm. Numerical convergence properties of the new algorithms are discussed, and all approaches are tested using real and artificially generated incomplete data sets.

An optimal fuzzy PID controller

Abstract: This paper introduces an optimal fuzzy proportional-integral-derivative (PID) controller. The fuzzy PID controller is a discrete-time version of the conventional PID controller, which preserves the same linear structure of the proportional, integral, and derivative parts but has constant coefficient yet self-tuned control gains. Fuzzy logic is employed only for the design; the resulting controller does not need to execute any fuzzy rule base, and is actually a conventional PID controller with analytical formulae. The main improvement is in endowing the classical controller with a certain adaptive control capability. The constant PID control gains are optimized by using the multiobjective genetic algorithm (MOGA), thereby yielding an optimal fuzzy PID controller. Computer simulations are shown to demonstrate its improvement over the fuzzy PID controller without MOGA optimization.

A fast approach for automatic generation of fuzzy rules by generalized dynamic fuzzy neural networks

Abstract: 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 functions 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.

Possibility Theory, Probability Theory and Multiple-Valued Logics: A Clarification

Abstract: There has been a long-lasting misunderstanding in the literature of artificial intelligence and uncertainty modeling, regarding the role of fuzzy set theory and many-valued logics. The recurring question is that of the mathematical and pragmatic meaningfulness of a compositional calculus and the validity of the excluded middle law. This confusion pervades the early developments of probabilistic logic, despite early warnings of some philosophers of probability. This paper tries to clarify this situation. It emphasizes three main points. First, it suggests that the root of the controversies lies in the unfortunate confusion between degrees of belief and what logicians call “degrees of truth”. The latter are usually compositional, while the former cannot be so. This claim is first illustrated by laying bare the non-compositional belief representation embedded in the standard propositional calculus. It turns out to be an all-or-nothing version of possibility theory. This framework is then extended to discuss the case of fuzzy logic versus graded possibility theory. Next, it is demonstrated that any belief representation where compositionality is taken for granted is bound to at worst collapse to a Boolean truth assignment and at best to a poorly expressive tool. Lastly, some claims pertaining to an alleged compositionality of possibility theory are refuted, thus clarifying a pervasive confusion between possibility theory axioms and fuzzy set basic connectives.

Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems

Abstract: This paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction, rule reduction, and robust compensation for nonlinear systems. The model construction part replaces the nonlinear dynamics of a system with a generalized form of Takagi-Sugeno fuzzy systems, which is newly developed by us. The generalized form has a decomposed structure for each element of A/sub i/ and B/sub i/ matrices in consequent parts. The key feature of this structure is that it is suitable for constructing IF-THEN rules and reducing the number of IF-THEN rules. The rule reduction part provides a successive procedure to reduce the number of IF-THEN rules. Furthermore, we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models. The robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties. Finally, two examples demonstrate the utility of the systematic procedure developed.

Low-complexity fuzzy relational clustering algorithms for Web mining

Abstract: This paper presents new algorithms-fuzzy c-medoids (FCMdd) and robust fuzzy c-medoids (RFCMdd)-for fuzzy clustering of relational data. The objective functions are based on selecting c representative objects (medoids) from the data set in such a way that the total fuzzy dissimilarity within each cluster is minimized. A comparison of FCMdd with the well-known relational fuzzy c-means algorithm (RFCM) shows that FCMdd is more efficient. We present several applications of these algorithms to Web mining, including Web document clustering, snippet clustering, and Web access log analysis.

Tuning of PID controllers with fuzzy logic

Abstract: The paper presents a comparison between different methods, based on fuzzy logic, for the tuning of PID controllers. Specifically considered are different control structures in which a fuzzy mechanism is adopted to improve the performances given by Ziegler-Nichols parameters. To verify the full capabilities of each controller, genetic algorithms are used to tune the parameters of the fuzzy inference systems (scaling coefficients, shape of the membership functions, etc.). Furthermore, a discussion about the practical implementation issue of the controllers is provided, and comparisons made with a typical PID-like fuzzy controller and a standard nonlinear PID controller. The results show the superiority of the fuzzy set-point weighting methodology over the other methods.

Super-resolution target identification from remotely sensed images using a Hopfield neural network

Abstract: Fuzzy classification techniques have been developed recently to estimate the class composition of image pixels, but their output provides no indication of how these classes are distributed spatially within the instantaneous field of view represented by the pixel. As such, while the accuracy of land cover target identification has been improved using fuzzy classification, it remains for robust techniques that provide better spatial representation of land cover to be developed. Such techniques could provide more accurate land cover metrics for determining social or environmental policy, for example. The use of a Hopfield neural network to map the spatial distribution of classes more reliably using prior information of pixel composition determined from fuzzy classification was investigated. An approach was adopted that used the output from a fuzzy classification to constrain a Hopfield neural network formulated as an energy minimization tool. The network converges to a minimum of an energy function, defined as a goal and several constraints. Extracting the spatial distribution of target class components within each pixel was, therefore, formulated as a constraint satisfaction problem with an optimal solution determined by the minimum of the energy function. This energy minimum represents a "best guess" map of the spatial distribution of class components in each pixel. The technique was applied to both synthetic and simulated Landsat TM imagery, and the resultant maps provided an accurate and improved representation of the land covers studied, with root mean square errors (RMSEs) for Landsat imagery of the order of 0.09 pixels in the new fine resolution image recorded.