Showing papers on "Fuzzy logic published in 2000"

Fuzzy-Set Social Science

Abstract: In this innovative approach to the practice of social science, Charles Ragin explores the use of fuzzy sets to bridge the divide between quantitative and qualitative methods. Paradoxically, the fuzzy set is a powerful tool because it replaces an unwieldy, "fuzzy" instrument (the variable, which establishes only the positions of cases relative to each other) with a precise one (degree of membership in a well-defined set). Ragin argues that fuzzy sets allow a far richer dialogue between ideas and evidence in social research than previously possible. They let quantitative researchers abandon "homogenizing assumptions" about cases and causes, they extend diversity-oriented research strategies, and they provide a powerful connection between theory and data analysis. Most important, fuzzy sets can be carefully tailored to fit evolving theoretical concepts, sharpening quantitative tools with in-depth knowledge gained through qualitative, case-oriented inquiry. This book should revolutionize research methods not only in sociology, political science and anthropology but in any field of inquiry dealing with complex patterns of causation.

Interval type-2 fuzzy logic systems: theory and design

Abstract: We present the theory and design of interval type-2 fuzzy logic systems (FLSs). We propose an efficient and simplified method to compute the input and antecedent operations for interval type-2 FLSs: one that is based on a general inference formula for them. We introduce the concept of upper and lower membership functions (MFs) and illustrate our efficient inference method for the case of Gaussian primary MFs. We also propose a method for designing an interval type-2 FLS in which we tune its parameters. Finally, we design type-2 FLSs to perform time-series forecasting when a nonstationary time-series is corrupted by additive noise where SNR is uncertain and demonstrate an improved performance over type-1 FLSs.

Fuzzy-Set Social Science

Abstract: In this innovative approach to the practice of social science, Charles Ragin explores the use of fuzzy sets to bridge the divide between quantitative and qualitative methods. Paradoxically, the fuzzy set is a powerful tool because it replaces an unwieldy, "fuzzy" instrument—the variable, which establishes only the positions of cases relative to each other, with a precise one—degree of membership in a well-defined set. Ragin argues that fuzzy sets allow a far richer dialogue between ideas and evidence in social research than previously possible. They let quantitative researchers abandon "homogenizing assumptions" about cases and causes, they extend diversity-oriented research strategies, and they provide a powerful connection between theory and data analysis. Most important, fuzzy sets can be carefully tailored to fit evolving theoretical concepts, sharpening quantitative tools with in-depth knowledge gained through qualitative, case-oriented inquiry. This book will revolutionize research methods not only in sociology, political science, and anthropology but in any field of inquiry dealing with complex patterns of causation.

New approaches to relaxed quadratic stability condition of fuzzy control systems

Abstract: This paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures. Two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems. The first one employs the S-procedure to utilize information regarding the premise parts of the fuzzy systems. The next one enlarges the class of fuzzy control systems, whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality. The relationships between the suggested stability conditions and the conventional well-known stability conditions reported in the previous literatures are also discussed, and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions. Finally, some examples and simulation results are presented to illustrate the effectiveness of the stability conditions.

Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach

Abstract: Takagi-Sugeno (TS) fuzzy models (1985, 1992) 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 (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller.

Neuro-fuzzy rule generation: survey in soft computing framework

Abstract: The present article is a novel attempt in providing an exhaustive survey of neuro-fuzzy rule generation algorithms. Rule generation from artificial neural networks is gaining in popularity in recent times due to its capability of providing some insight to the user about the symbolic knowledge embedded within the network. Fuzzy sets are an aid in providing this information in a more human comprehensible or natural form, and can handle uncertainties at various levels. The neuro-fuzzy approach, symbiotically combining the merits of connectionist and fuzzy approaches, constitutes a key component of soft computing at this stage. To date, there has been no detailed and integrated categorization of the various neuro-fuzzy models used for rule generation. We propose to bring these together under a unified soft computing framework. Moreover, we include both rule extraction and rule refinement in the broader perspective of rule generation. Rules learned and generated for fuzzy reasoning and fuzzy control are also considered from this wider viewpoint. Models are grouped on the basis of their level of neuro-fuzzy synthesis. Use of other soft computing tools like genetic algorithms and rough sets are emphasized. Rule generation from fuzzy knowledge-based networks, which initially encode some crude domain knowledge, are found to result in more refined rules. Finally, real-life application to medical diagnosis is provided.

Application of fuzzy measures in multi-criteria evaluation in GIS

Abstract: Multi-criteria evaluation (MCE) is perhaps the most fundamental of decision support operations in geographical information systems (GIS). This paper reviews two main MCE approaches employed in GIS, namely Boolean and Weighted Linear Combination (WLC), and discusses issues and problems associated with both. To resolve the conceptual differences between the two approaches, this paper proposes the application of fuzzy measures, a concept that is broader but that includes fuzzy set membership, and argues that the standardized factors of MCE belong to a general class of fuzzy measures and the more specific instance of fuzzy set membership. This perspective provides a strong theoretical basis for the standardization of factors and their subsequent aggregation. In this context, a new aggregation operator that accommodates and extends the Boolean and WLC approaches is discussed: the Ordered Weighted Average. A case study of industrial allocation in Nakuru, Kenya is employed to illustrate the different approaches.

Identification and control of dynamic systems using recurrent fuzzy neural networks

Abstract: Proposes a recurrent fuzzy neural network (RFNN) structure for identifying and controlling nonlinear dynamic systems. The RFNN is inherently a recurrent multilayered connectionist network for realizing fuzzy inference using dynamic fuzzy rules. Temporal relations are embedded in the network by adding feedback connections in the second layer of the fuzzy neural network (FNN). The RFNN expands the basic ability of the FNN to cope with temporal problems. In addition, results for the FNN-fuzzy inference engine, universal approximation, and convergence analysis are extended to the RFNN. For the control problem, we present the direct and indirect adaptive control approaches using the RFNN. Based on the Lyapunov stability approach, rigorous proofs are presented to guarantee the convergence of the RFNN by choosing appropriate learning rates. Finally, the RFNN is applied in several simulations (time series prediction, identification, and control of nonlinear systems). The results confirm the effectiveness of the RFNN.

Fuzzy Measures and Integrals: Theory and Applications

Abstract: P. Wakker: Foreword.- M. Grabisch, T. Murofushi, M. Sugeno: Preface.- Theory: T. Murofushi, M. Sugeno: Fuzzy Measures and Fuzzy Integrals.- D. Denneberg: Non-additive Measure and Integral, Basic Concepts and Their Role for Applications.- M. Grabisch: The Interaction and Mobius Representations of Fuzzy Measures on Finite Spaces, k-Additive Measures: A Survey.- K. Fujimoto, T. Murofushi: Hierarchical Decomposition of the Choquet Integral.- I. Kramosil: Towards Generalized Belief Functions.- G. De Cooman: Integration in Possibility Theory.- Z. Wang, K. Xu: On the Autocontinuity of Set Functions.- E. Pap: Pseudo-convolution and Its Applications.- P. Benvenuti, R. Mesiar: Integrals with Respect to a General Fuzzy Measure.- D. Butnariu, E.P. Klement: Measures on Triangular Norm-based Tribes: Properties and Integral Representations.- J.-L. Marichal: On Choquet and Sugeno Integrals as Aggregation Functions.- H. Imaoka: Comparison between Three Fuzzy Integrals.- Applications: A. Chateauneuf, M. Cohen: Choquet Expected Utility Model: A New Approach to Individual Behavior under Uncertainty and to Social Welfare.- D. Dubois, H. Prade, R. Sabbadin: Qualitative Decision Theory with Sugeno Integrals.- T. Murofushi, M. Sugeno: The Choquet Integral in Multicriteria Decision Making.- M. Grabisch, M. Roubens. Application of the Choquet Integral in Multicriteria Decision Making.- S.H. Kwon, M. Sugeno: A Hierarchical Subjective Evaluation Model Using Non-monotonic Fuzzy Measures and the Choquet Integral.- J.F. Peters III, L. Han, S. Ramana: The Choquet Integral in a Rough Software Cost Decision System.- M. Grabisch: Fuzzy Integral for Classification and Feature Extraction.- J.M. Keller, P.D. Gader, A.K. Hocaoglu: Fuzzy Integrals inImage Processing and Recognition.- Z. Wang, G.J. Klir, J. Swan-Stone, K. Xu: An Algorithm for Calculating Natural Extensions with Respect to Lower Probabilities.

Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems

Abstract: FUZZY SET THEORY Classical Set Theory Fuzzy Set Theory Interval Arithmetic Operations on Fuzzy Sets FUZZY LOGIC THEORY Classical Logic Theory The Boolean Algebra Multi-Valued Logic Fuzzy Logic and Approximate Reasoning Fuzzy Relations Fuzzy Logic Rule Base FUZZY SYSTEM MODELING Modeling of the Static Fuzzy Systems Stability Analysis of Discrete-Time Dynamic Fuzzy Systems Modeling of Continuous-Time Dynamic Fuzzy Systems Stability Analysis of Continuous-Time Fuzzy Systems Controllability Analysis of Continuous-Time Dynamic Fuzzy Systems Analysis of Nonlinear Continuous-Time Dynamic Fuzzy Systems FUZZY CONTROL SYSTEMS Classical Programmable Logic Control Fuzzy Logic Control I: A General Model-Free Approach Fuzzy Logic Control II: A General Model-Based Approach FUZZY PID CONTROLLERS Conventional PID Controllers Fuzzy PID Controllers Fuzzy PID Controllers: Stability Analysis ADAPTIVE FUZZY CONTROL Fundamental Adaptive Fuzzy Control Concept Gain Scheduling Fuzzy Self-Tuning Regulator Model Reference Adaptive Fuzzy Systems Dual Control Sub-Optimal Fuzzy Control APPLICATIONS IN FUZZY CONTROL Health Monitoring Fuzzy Diagnostic Systems Fuzzy Control of Image sharpness for Auto-focus Cameras Fuzzy Control for Servo Mechanic Systems Fuzzy PID Controllers for Servo Mechanic Systems Fuzzy Controllers for Robotic Manipulator Note: Each chapter also contains Problems and References

Recent developments of induction motor drives fault diagnosis using AI techniques

Abstract: This paper presents a review of the developments in the field of diagnosis of electrical machines and drives based on artificial intelligence (AI). It covers the application of expert systems, artificial neural networks (ANNs), and fuzzy logic systems that can be integrated into each other and also with more traditional techniques. The application of genetic algorithms is considered as well. In general, a diagnostic procedure starts from a fault tree developed on the basis of the physical behavior of the electrical system under consideration. In this phase, the knowledge of well-tested models able to simulate the electrical machine in different fault conditions is fundamental to obtain the patterns characterizing the faults. The fault tree navigation performed by an expert system inference engine leads to the choice of suitable diagnostic indexes, referred to a particular fault, and relevant to build an input data set for specific AI (NNs, fuzzy logic, or neuro-fuzzy) systems. The discussed methodologies, that play a general role in the diagnostic field, are applied to an induction machine, utilizing as input signals the instantaneous voltages and currents. In addition, the supply converter is also considered to incorporate in the diagnostic procedure the most typical failures of power electronic components. A brief description of the various AI techniques is also given; this highlights the advantages and the limitations of using AI techniques. Some applications examples are also discussed and areas for future research are also indicated.

Fuzzy Classifier Design

Abstract: This book about fuzzy classifier design briefly introduces the fundamentals of supervised pattern recognition and fuzzy set theory. Fuzzy if-then classifiers are defined and some theoretical properties thereof are studied. Popular training algorithms are detailed. Non if-then fuzzy classifiers include relational, k-nearest neighbor, prototype-based designs, etc. A chapter on multiple classifier combination discusses fuzzy and non-fuzzy models for fusion and selection.

GA-fuzzy modeling and classification: complexity and performance

Abstract: The use of genetic algorithms (GAs) and other evolutionary optimization methods to design fuzzy rules for systems modeling and data classification have received much attention in recent literature. Authors have focused on various aspects of these randomized techniques, and a whole scale of algorithms have been proposed. We comment on some recent work and describe a new and efficient two-step approach that leads to good results for function approximation, dynamic systems modeling and data classification problems. First, fuzzy clustering is applied to obtain a compact initial rule-based model. Then this model is optimized by a real-coded GA subjected to constraints that maintain the semantic properties of the rules. We consider four examples from the literature: a synthetic nonlinear dynamic systems model, the iris data classification problem, the wine data classification problem, and the dynamic modeling of a diesel engine turbocharger. The obtained results are compared to other recently proposed methods.

Fuzzy Graphs and Fuzzy Hypergraphs

Abstract: Fuzzy Subsets: Fuzzy Relations.- Fuzzy Equivalence Relations.- Pattern Classification.- Similarity Relations.- References.- Fuzzy Graphs: Paths and Connectedness. Bridges and Cut Vertices. Forests and Trees. Trees and Cycles. A Characterization of Fuzzy Trees. (Fuzzy) Cut Sets. (Fuzzy Chords, (Fuzzy) Cotrees, and (Fuzzy) Twigs. (Fuzzy) 1-Chain with Boundary 0, (Fuzzy) Coboundary, and (Fuzzy) Cocycles. (Fuzzy) Cycle Set and (Fuzzy) Cocycle Set.- Fuzzy Line Graphs.- Fuzzy Interval Graphs. Fuzzy Intersection Graphs. Fuzzy Interval Graphs. The Fulkerson and Gross Characterization. The Gilmore and Hoffman Characterization.- Operations on Fuzzy Graphs: Cartesian Product and Composition. Union and Join.- On Fuzzy Tree Definition.- References.- Applications of Fuzzy Graphs: Clusters.- Cluster Analysis. Cohesiveness. Slicing in Fuzzy Graphs.- Application to Cluster Analysis.- Fuzzy Intersection Equations. Existence of Solutions.- Fuzzy Graphs in Database Theory. Representation of Dependency Structure r(X,Y) by Fuzzy Graphs.- A Description of Strengthening and Weakening Members of a Group. Connectedness Criteria. Inclusive Connectedness Categories. Exclusive Connectedness Categories.- An Application of Fuzzy Graphs to the Problem Concerning Group Structure. Connectedness of a Fuzzy Graph. Weakening and Strenghtening Points of a Fuzzy Directed Graph.- References.- Fuzzy Hypergraphs: Fuzzy Hypergraphs.- Fuzzy Transversals of Fuzzy Hypergraphs. Properties of Tr(H). Construction of H3.- Coloring of Fuzzy Hypergraphs. beta-degree Coloring Procedures. Chromatic Values of Fuzzy Colorings.- Intersecting Fuzzy Hypergraphs. Characterization of Strongly Intersecting Hypergraphs. Simply Ordered Intersecting Hypergraphs. H-dominant Transversals.- Hebbian Structures.- Additional Applications.- References.

Mixed H/sub 2//H/sub /spl infin// fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach

Abstract: This study introduces a mixed H/sub 2//H/sub /spl infin// fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed H/sub 2//H/sub /spl infin// controller is developed to achieve the suboptimal H/sub 2/ control performance with a desired H/sub /spl infin// disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed H/sub 2//H/sub /spl infin// control problem is parametrized in terms of the two eigenvalue problems (EVPs): one for observer and the other for controller. The EVPs can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method.

Dynamic fuzzy neural networks-a novel approach to function approximation

Abstract: In this paper, an architecture of dynamic fuzzy neural networks (D-FNN) implementing Takagi-Sugeno-Kang (TSK) fuzzy systems based on extended radial basis function (RBF) neural networks is proposed. A novel learning algorithm based on D-FNN is also presented. The salient characteristics of the algorithm are: 1) hierarchical on-line self-organizing learning is used; 2) neurons can be recruited or deleted dynamically according to their significance to the system's performance; and 3) fast learning speed can be achieved. Simulation studies and comprehensive comparisons with some other learning algorithms demonstrate that a more compact structure with higher performance can be achieved by the proposed approach.

Foundations for an Empirically Determined Scale of Trust in Automated Systems

Abstract: Hazard communications often contain adverbial or adjectival phrases that qualify the meaning of verbs or nouns. For example, a warning label might contain the phrase prolonged exposure. Fuzzy set theory provides a method of quantitatively describing the meaning of such phrases, using membership functions. For example, a membership function might map how strongly workers feel exposure times between 0 and 24 hr belong to the fuzzy set prolonged exposure. The focus of this study was on documenting worker understanding of adverbial or adjectival phrases used in hazard communications using fuzzy sets. Emphasis was placed on documenting how membership functions changed between contexts. To do this, 353 workers at 9 locations were asked to interpret the meaning of hazard communication phrases containing fuzzy qualifiers, such as "safe," "weak," "strong," "prolonged," "extremely," "slightly," "poorly," or "adequate." Workers interpreted the phrases in meaningful ways, confirming that fuzzy qualifiers can play a u...

Fuzzy EMG classification for prosthesis control

Abstract: 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.

Temperature prediction using fuzzy time series

Abstract: A drawback of traditional forecasting methods is that they can not deal with forecasting problems in which the historical data are represented by linguistic values. Using fuzzy time series to deal with forecasting problems can overcome this drawback. In this paper, we propose a new fuzzy time series model called the two-factors time-variant fuzzy time series model to deal with forecasting problems. Based on the proposed model, we develop two algorithms for temperature prediction. Both algorithms have the advantage of obtaining good forecasting results.

Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters

Abstract: Presents a kind of adaptive filter: type-2 fuzzy adaptive filter (FAF); one that is realized using an unnormalized type-2 Takagi-Sugeno-Kang (TSK) fuzzy logic system (FLS). We apply this filter to equalization of a nonlinear time-varying channel and demonstrate that it can implement the Bayesian equalizer for such a channel, has a simple structure, and provides fast inference. A clustering method is used to adaptively design the parameters of the FAF. Two structures are used for the equalizer: transversal equalizer (TE) and decision feedback equalizer (DFE). A decision tree structure is used to implement the decision feedback equalizer, in which each leaf of the tree is a type-2 FAF. This DFE vastly reduces computational complexity as compared to a TE. Simulation results show that equalizers based on type-2 FAFs perform much better than nearest neighbor classifiers (NNC) or equalizers based on type-1 FAFs.

Fuzzy descriptor systems and nonlinear model following control

Abstract: This paper defines a fuzzy descriptor system by extending the ordinary Takagi-Sugeno (T-S) fuzzy model. Several kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities (LMIs). We illustrate an example of defining the fuzzy descriptor system instead of the ordinary T-S fuzzy model. An LMI design approach is employed to find stable feedback gains and a common Lyapunov function. In addition, this paper presents a nonlinear model following control for the fuzzy descriptor system. A new parallel distributed compensation, the so-called "twin parallel distributed compensations" (TPDC) to realize the nonlinear model following control, is proposed. We present a design technique based on the TPDC. The proposed method is a unified approach to nonlinear model following control. It contains the regulation and servo control problems as special cases.

Classification of Hydrometeors Based on Polarimetric Radar Measurements: Development of Fuzzy Logic and Neuro-Fuzzy Systems, and In Situ Verification

Abstract: A fuzzy logic and neuro-fuzzy system for classification of hydrometeor type based on polarimetric radar measurements is described in this paper. The hydrometeor classification system is implemented by using fuzzy logic and a neural network, where the fuzzy logic is used to infer hydrometeor type, and the neural network learning algorithm is used for automatic adjustment of the parameters of the fuzzy sets in the fuzzy logic system according to prior knowledge. Five radar measurements, namely, horizontal reflectivity ( ZH), differential reflectivity (ZDR), differential propagation phase shift ( KDP), correlation coefficient [rHV(0)], and linear depolarization ratio (LDR), and corresponding altitude, have been used as input variables to the neuro-fuzzy network. The output of the neuro-fuzzy system is one of the many possible hydrometeor types: 1) drizzle, 2) rain, 3) dry and low density snow, 4) dry and high-density crystals, 5) wet and melting snow, 6) dry graupel, 7) wet graupel, 8) small hail, 9) large hail, and 10) a mixture of rain and hail. The neuro-fuzzy classifier is more advantageous than a simple neural network or a fuzzy logic classifier because it is more transparent (instead of a ‘‘black box’’) and can learn the parameter of the system from the past data (unlike a fuzzy logic system). The hydrometeor classifier has been applied to several case studies and the results are compared against in situ observations.

On the interpretation and identification of dynamic Takagi-Sugeno fuzzy models

Abstract: Dynamic Takagi-Sugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. It is shown that there exists a close relationship between dynamic Takagi-Sugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parametrization when applied in transient operating regimes. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples.