Showing papers on "Fuzzy logic published in 2004"
Posted Content•
TL;DR: In this paper, a new type of identity-based encryption called Fuzzy Identity-Based Encryption (IBE) was introduced, where an identity is viewed as set of descriptive attributes, and a private key for an identity can decrypt a ciphertext encrypted with an identity if and only if the identities are close to each other as measured by the set overlap distance metric.
Abstract: We introduce a new type of Identity-Based Encryption (IBE) scheme that we call Fuzzy Identity-Based Encryption. In Fuzzy IBE we view an identity as set of descriptive attributes. A Fuzzy IBE scheme allows for a private key for an identity, ω, to decrypt a ciphertext encrypted with an identity, ω ′, if and only if the identities ω and ω ′ are close to each other as measured by the “set overlap” distance metric. A Fuzzy IBE scheme can be applied to enable encryption using biometric inputs as identities; the error-tolerance property of a Fuzzy IBE scheme is precisely what allows for the use of biometric identities, which inherently will have some noise each time they are sampled. Additionally, we show that Fuzzy-IBE can be used for a type of application that we term “attribute-based encryption”.
In this paper we present two constructions of Fuzzy IBE schemes. Our constructions can be viewed as an Identity-Based Encryption of a message under several attributes that compose a (fuzzy) identity. Our IBE schemes are both error-tolerant and secure against collusion attacks. Additionally, our basic construction does not use random oracles. We prove the security of our schemes under the Selective-ID security model.
3,128 citations
TL;DR: A review of more than 90 published papers is presented here to analyze the applicability of various methods discussed and it is observed that Analytical Hierarchy Process is the most popular technique followed by outranking techniques PROMETHEE and ELECTRE.
Abstract: Multi-Criteria Decision Making (MCDM) techniques are gaining popularity in sustainable energy management. The techniques provide solutions to the problems involving conflicting and multiple objectives. Several methods based on weighted averages, priority setting, outranking, fuzzy principles and their combinations are employed for energy planning decisions. A review of more than 90 published papers is presented here to analyze the applicability of various methods discussed. A classification on application areas and the year of application is presented to highlight the trends. It is observed that Analytical Hierarchy Process is the most popular technique followed by outranking techniques PROMETHEE and ELECTRE. Validation of results with multiple methods, development of interactive decision support systems and application of fuzzy methods to tackle uncertainties in the data is observed in the published literature.
1,715 citations
01 Apr 2004
TL;DR: An evolutionary recurrent network which automates the design of recurrent neural/fuzzy networks using a new evolutionary learning algorithm based on a hybrid of genetic algorithm (GA) and particle swarm optimization (PSO), and is thus called HGAPSO.
Abstract: An evolutionary recurrent network which automates the design of recurrent neural/fuzzy networks using a new evolutionary learning algorithm is proposed in this paper. This new evolutionary learning algorithm is based on a hybrid of genetic algorithm (GA) and particle swarm optimization (PSO), and is thus called HGAPSO. In HGAPSO, individuals in a new generation are created, not only by crossover and mutation operation as in GA, but also by PSO. The concept of elite strategy is adopted in HGAPSO, where the upper-half of the best-performing individuals in a population are regarded as elites. However, instead of being reproduced directly to the next generation, these elites are first enhanced. The group constituted by the elites is regarded as a swarm, and each elite corresponds to a particle within it. In this regard, the elites are enhanced by PSO, an operation which mimics the maturing phenomenon in nature. These enhanced elites constitute half of the population in the new generation, whereas the other half is generated by performing crossover and mutation operation on these enhanced elites. HGAPSO is applied to recurrent neural/fuzzy network design as follows. For recurrent neural network, a fully connected recurrent neural network is designed and applied to a temporal sequence production problem. For recurrent fuzzy network design, a Takagi-Sugeno-Kang-type recurrent fuzzy network is designed and applied to dynamic plant control. The performance of HGAPSO is compared to both GA and PSO in these recurrent networks design problems, demonstrating its superiority.
961 citations
01 Feb 2004
TL;DR: An approach to the online learning of Takagi-Sugeno (TS) type models is proposed, based on a novel learning algorithm that recursively updates TS model structure and parameters by combining supervised and unsupervised learning.
Abstract: An approach to the online learning of Takagi-Sugeno (TS) type models is proposed in the paper. It is based on a novel learning algorithm that recursively updates TS model structure and parameters by combining supervised and unsupervised learning. The rule-base and parameters of the TS model continually evolve by adding new rules with more summarization power and by modifying existing rules and parameters. In this way, the rule-base structure is inherited and up-dated when new data become available. By applying this learning concept to the TS model we arrive at a new type adaptive model called the Evolving Takagi-Sugeno model (ETS). The adaptive nature of these evolving TS models in combination with the highly transparent and compact form of fuzzy rules makes them a promising candidate for online modeling and control of complex processes, competitive to neural networks. The approach has been tested on data from an air-conditioning installation serving a real building. The results illustrate the viability and efficiency of the approach. The proposed concept, however, has significantly wider implications in a number of fields, including adaptive nonlinear control, fault detection and diagnostics, performance analysis, forecasting, knowledge extraction, robotics, behavior modeling.
956 citations
TL;DR: A new characterization of the consistency property defined by the additive transitivity property of the fuzzy preference Relations is presented and a method for constructing consistent fuzzy preference relations from a set of n preference data is proposed.
929 citations
TL;DR: The objective of this paper is to provide an account of genetic fuzzy systems, with special attention to genetic fuzzy rule-based systems.
852 citations
TL;DR: The proposed LPR technique consists of two main modules: a license plate locating module and a license number identification module, the former characterized by fuzzy disciplines attempts to extract license plates from an input image, while the latter conceptualized in terms of neural subjects aims to identify the number present in alicense plate.
Abstract: Automatic license plate recognition (LPR) plays an important role in numerous applications and a number of techniques have been proposed. However, most of them worked under restricted conditions, such as fixed illumination, limited vehicle speed, designated routes, and stationary backgrounds. In this study, as few constraints as possible on the working environment are considered. The proposed LPR technique consists of two main modules: a license plate locating module and a license number identification module. The former characterized by fuzzy disciplines attempts to extract license plates from an input image, while the latter conceptualized in terms of neural subjects aims to identify the number present in a license plate. Experiments have been conducted for the respective modules. In the experiment on locating license plates, 1088 images taken from various scenes and under different conditions were employed. Of which, 23 images have been failed to locate the license plates present in the images; the license plate location rate of success is 97.9%. In the experiment on identifying license number, 1065 images, from which license plates have been successfully located, were used. Of which, 47 images have been failed to identify the numbers of the license plates located in the images; the identification rate of success is 95.6%. Combining the above two rates, the overall rate of success for our LPR algorithm is 93.7%.
848 citations
TL;DR: This paper presents the stabilization analysis for a class of nonlinear systems that are represented by a Takagi and Sugeno (TS) discrete fuzzy model using new control laws and new nonquadratic Lyapunov functions.
847 citations
Book•
24 Jun 2004
TL;DR: This chapter discusses trust theory, fuzzy Random Theory, and Birandom Theory, which describes the construction of trust in the context of Fuzzy Rough Theory.
Abstract: Measure and Integral.- Probability Theory.- Credibility Theory.- Nonclassical Credibility Theory.- Trust Theory.- Generalized Trust Theory.- Fuzzy Random Theory.- Random Fuzzy Theory.- Random Rough Theory.- Rough Random Theory.- Fuzzy Rough Theory.- Rough Fuzzy Theory.- Birandom Theory.- Bifuzzy Theory.- Birough Theory.- Multifold Uncertainty.
693 citations
TL;DR: This paper reviews those techniques that preserve the underlying semantics of the data, using crisp and fuzzy rough set-based methodologies, and several approaches to feature selection based on rough set theory are experimentally compared.
Abstract: Semantics-preserving dimensionality reduction refers to the problem of selecting those input features that are most predictive of a given outcome; a problem encountered in many areas such as machine learning, pattern recognition, and signal processing. This has found successful application in tasks that involve data sets containing huge numbers of features (in the order of tens of thousands), which would be impossible to process further. Recent examples include text processing and Web content classification. One of the many successful applications of rough set theory has been to this feature selection area. This paper reviews those techniques that preserve the underlying semantics of the data, using crisp and fuzzy rough set-based methodologies. Several approaches to feature selection based on rough set theory are experimentally compared. Additionally, a new area in feature selection, feature grouping, is highlighted and a rough set-based feature grouping technique is detailed.
634 citations
TL;DR: In this article, a fuzzy multi-criteria analysis approach for selecting of planning and design (P&D) alternatives in public office building is presented, where fuzzy numbers for linguistic terms are used to deal with subjectivity and vagueness in the alternatives selection process.
TL;DR: Results showed that the ANFIS forecasted flow series preserves the statistical properties of the original flow series, and a comparative analysis suggests that the proposed modeling approach outperforms ANNs and other traditional time series models in terms of computational speed, forecast errors, efficiency, peak flow estimation etc.
TL;DR: A novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data is presented using a kernel-induced distance metric and a spatial penalty on the membership functions to compensate for the intensity inhomogeneities of MR image.
TL;DR: A guaranteed cost control method for nonlinear systems with time-delays which can be represented by Takagi-Sugeno (T-S) fuzzy model which guarantees that the controller without any delay information can stabilize time-delay T-S fuzzy systems is introduced.
Abstract: This study introduces a guaranteed cost control method for nonlinear systems with time-delays which can be represented by Takagi-Sugeno (T-S) fuzzy models with time-delays. The state feedback and generalized dynamic output feedback approaches are considered. The generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base. It considers both the dynamic part and the output part of T-S fuzzy model which guarantees that the controller without any delay information can stabilize time-delay T-S fuzzy systems. Based on delay-dependent Lyapunov functional approach, some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation (PDC) first. Second, the corresponding conditions are extended into the generalized dynamic output feedback closed-loop system via so-called generalized PDC technique. The upper bound of time-delay can be obtained using convex optimization such that the system can be stabilized for all time-delays whose sizes are not larger than the bound. The minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function. The effectiveness of the proposed method can be shown by the simulation examples.
TL;DR: The proposed approach has the capability to handle realistic situations in a fuzzy environment and provides a better decision tool for the vendor selection decision in a supply chain.
TL;DR: Experimental results show that fuzzy–rough reduction is more powerful than the conventional rough set-based approach, and classifiers that use a lower dimensional set of attributes which are retained by fuzzy-rough reduction outperform those that employ more attributes returned by the existing crisp rough reduction method.
TL;DR: Sgurev et al. as discussed by the authors defined the notion of intuitionistic fuzzy metric spaces and proved Baire's theorem and the Uniform limit theorem for intuitionistic metric spaces using fuzzy sets.
Abstract: Using the idea of intuitionistic fuzzy set due to Atanassov [Intuitionistic fuzzy sets. in: V. Sgurev (Ed.), VII ITKR's Session, Sofia June, 1983; Fuzzy Sets Syst. 20 (1986) 87], we define the notion of intuitionistic fuzzy metric spaces as a natural generalization of fuzzy metric spaces due to George and Veeramani [Fuzzy Sets Syst. 64 (1994) 395] and prove some known results of metric spaces including Baire's theorem and the Uniform limit theorem for intuitionistic fuzzy metric spaces.
Book•
01 Jan 2004
TL;DR: This chapter discusses how to construct a Fuzzy Expert System using the Dempster-Shafer Method, a simple, scalable, and scalable approach that automates the very labor-intensive and therefore time-heavy process of designing and implementing an Expert System.
Abstract: Preface. 1 Introduction. 1.1 Characteristics of Expert Systems. 1.2 Neural Nets. 1.3 Symbolic Reasoning. 1.4 Developing a Rule-Based Expert System. 1.5 Fuzzy Rule-Based Systems. 1.6 Problems in Learning How to Construct Fuzzy Expert Systems. 1.7 Tools for Learning How to Construct Fuzzy Expert Systems. 1.8 Auxiliary Reading. 1.9 Summary. 1.10 Questions. 2 Rule-Based Systems: Overview. 2.1 Expert Knowledge: Rules and Data. 2.2 Rule Antecedent and Consequent. 2.3 Data-Driven Systems. 2.4 Run and Command Modes. 2.5 Forward and Backward Chaining. 2.6 Program Modularization and Blackboard Systems. 2.7 Handling Uncertainties in an Expert System. 2.8 Summary. 2.9 Questions. 3 Fuzzy Logic, Fuzzy Sets, and Fuzzy Numbers: I. 3.1 Classical Logic. 3.2 Elementary Fuzzy Logic and Fuzzy Propositions. 3.3 Fuzzy Sets. 3.4 Fuzzy Relations. 3.5 Truth Value of Fuzzy Propositions. 3.6 Fuzzification and Defuzzification. 3.7 Questions. 4 Fuzzy Logic, Fuzzy Sets, and Fuzzy Numbers: II. 4.1 Introduction. 4.2 Algebra of Fuzzy Sets. 4.3 Approximate Reasoning. 4.4 Hedges. 4.5 Fuzzy Arithmetic. 4.6 Comparisons between Fuzzy Numbers. 4.7 Fuzzy Propositions. 4.8 Questions. 5 Combining Uncertainties. 5.1 Generalizing AND and OR Operators. 5.2 Combining Single Truth Values. 5.3 Combining Fuzzy Numbers and Membership Functions. 5.4 Bayesian Methods. 5.5 The Dempster-Shafer Method. 5.6 Summary. 5.7 Questions. 6 Inference in an Expert System I. 6.1 Overview. 6.2 Types of Fuzzy Inference. 6.3 Nature of Inference in a Fuzzy Expert System. 6.4 Modification and Assignment of Truth Values. 6.5 Approximate Reasoning. 6.6 Tests of Procedures to Obtain the Truth Value of a Consequent from the Truth Value of Its Antecedent. 6.7 Summary. 6.8 Questions. 7 Inference in a Fuzzy Expert System II: Modification of Data and Truth Values. 7.1 Modification of Existing Data by Rule Consequent Instructions. 7.2 Modification of Numeric Discrete Fuzzy Sets: Linguistic Variables and Linguistic Terms. 7.3 Selection of Reasoning Type and Grade-of-Membership Initialization. 7.4 Fuzzification and Defuzzification. 7.5 Non-numeric Discrete Fuzzy Sets. 7.6 Discrete Fuzzy Sets: Fuzziness, Ambiguity, and Contradiction. 7.7 Invalidation of Data: Non-monotonic Reasoning. 7.8 Modification of Values of Data. 7.9 Modeling the Entire Rule Space. 7.10 Reducing the Number of Classification Rules Required in the Conventional Intersection Rule Configuration. 7.11 Summary. 7.12 Questions. 8 Resolving Contradictions: Possibility and Necessity. 8.1 Definition of Possibility and Necessity. 8.2 Possibility and Necessity Suitable for MultiStep Rule-Based Fuzzy Reasoning. 8.3 Modification of Truth Values During a Fuzzy Reasoning Process. 8.4 Formulation of Rules for Possibility and Necessity. 8.5 Resolving Contradictions Using Possibility in a Necessity-Based System. 8.6 Summary. 8.7 Questions. 9 Expert System Shells and the Integrated Development Environment (IDE). 9.1 Overview. 9.2 Help Files. 9.3 Program Editing. 9.4 Running the Program. 9.5 Features of General-Purpose Fuzzy Expert Systems. 9.6 Program Debugging. 9.7 Summary. 9.8 Questions. 10 Simple Example Programs. 10.1 Simple FLOPS Programs. 10.2 Numbers.fps. 10.3 Sum.fps. 10.4 Sum.par. 10.5 Comparison of Serial and Parallel FLOPS. 10.6 Membership Functions, Fuzzification and Defuzzification. 10.7 Summary. 10.8 Questions. 11 Running and Debugging Fuzzy Expert Systems I: Parallel Programs. 11.1 Overview. 11.2 Debugging Tools. 11.3 Debugging Short Simple Programs. 11.4 Isolating the Bug: System Modularization. 11.5 The Debug Run. 11.6 Interrupting the Program for Debug Checks. 11.7 Locating Program Defects with Debug Commands. 11.8 Summary. 11.9 Questions. 12 Running and Debugging Expert Systems II: Sequential Rule-Firing. 12.1 Data Acquisition: From a User Versus Automatically Acquired. 12.2 Ways of Solving a Tree-Search Problem. 12.3 Expert Knowledge in Rules auto1.fps. 12.4 Expert Knowledge in a Database: auto2.fps. 12.5 Other Applications of Sequential Rule Firing. 12.5.1 Missionaries and Cannibals. 12.6 Rules that Make Themselves Refireable: Runaway Programs and Recursion. 12.7 Summary. 12.8 Questions. 13 Solving "What?" Problems when the Answer is Expressed in Words. 13.1 General Methods. 13.2 Iris.par: What Species Is It? 13.3 Echocardiogram Pattern Recognition. 13.4 Schizo.par. 13.5 Discussion. 13.6 Questions. 14 Programs that Can Learn from Experience. 14.1 General Methods. 14.2 Pavlov1.par: Learning by Adding Rules. 14.3 Pavlov2.par: Learning by Adding Facts to Long-Term Memory. 14.4 Defining New Data Elements and New: RULEGEN.FPS. 14.5 Most General Way of Creating New Rules and Data Descriptors. 14.6 Discussion. 14.7 Questions. 15 Running On-Line in Real-Time. 15.1 Overview of On-Line Real-Time Work. 15.2 Input/Output On-Line in Real-Time. 15.3 On-Line Real-Time Processing. 15.4 Types of Rules Useful in Real-Time On-Line Work. 15.5 Memory Management. 15.6 Development of On-Line Real-Time Programs. 15.7 Speeding Up a Program. 15.8 Debugging Real-Time Online Programs. 15.9 Discussion. 15.10 Questions. Appendix. Answers. References. Index.
TL;DR: A theorem is presented characterizing the hierarchical structure of formal fuzzy concepts arising in a given formal fuzzy context, Dedekind–MacNeille completion of a partial fuzzy order and results provide foundations for formal concept analysis of vague data.
Book•
07 Oct 2004
TL;DR: Fuzzy Sets, Fusion of Fuzzy System and Neural Networks, and Fusion of fuzzy Systems and Genetic Algorithms are presented.
Abstract: Fuzzy Sets.- The Operation of Fuzzy Set.- Fuzzy Relation and Composition.- Fuzzy Graph and Relation.- Fuzzy Number.- Fuzzy Function.- Probabilisy and Uncertainty.- Fuzzy Logic.- Fuzzy Inference.- Fuzzy Control and Fuzzy Expert Systems.- Fusion of Fuzzy System and Neural Networks.- Fusion of Fuzzy Systems and Genetic Algorithms.
TL;DR: This paper shows how a small number of simple fuzzy if-then rules can be selected for pattern classification problems with many continuous attributes and proposes an idea of utilizing the two rule evaluation measures as prescreening criteria of candidate rules for fuzzy rule selection.
Book•
19 Feb 2004
TL;DR: This paper presents a meta-modelling procedure called “fuzzy modeling” that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of estimating uncertainty in Structural Parameters.
Abstract: 1 Introduction.- 2 Mathematical Basics for the Formal Description of Uncertainty.- 3 Description of Uncertain Structural Parameters as Fuzzy Variables.- 4 Description of Uncertain Structural Parameters as Fuzzy Random Variables.- 5 Fuzzy and Fuzzy Stochastic Structural Analysis.- 6 Fuzzy Probabilistic Safety Assessment.- 7 Structural Design Based on Clustering.- References.
21 Mar 2004
TL;DR: A new handover criteria is introduced along with a new hand over decision strategy for fuzzy multiple attribute decision making (MADM) problem, and fuzzy logic is applied to deal with the imprecise information of some criteria and user preference.
Abstract: In the next generation heterogeneous wireless networks, a user with a multi-interface terminal may have a network access from different service providers using various technologies. It is believed that handover decision is based on multiple criteria as well as user preference. Various approaches have been proposed to solve the handover decision problem, but the choice of decision method appears to be arbitrary and some of the methods even give disputable results. In this paper, a new handover criteria is introduced along with a new handover decision strategy. In addition, handover decision is identified us a fuzzy multiple attribute decision making (MADM) problem, and fuzzy logic is applied to deal with the imprecise information of some criteria and user preference. After a systematic analysis of various fuzzy MADM methods, a feasible approach is presented. In the end, examples are provided illustrating the proposed methods and the sensitivity of the methods is also analysed.
Book•
19 Nov 2004
TL;DR: The authors describes how soft computing techniques like fuzzy logic, evolutionary computation and neural networks can be used for extracting interpretable knowledge in the form of linguistic if-then rules from numerical data for classification and modeling.
Abstract: This book clearly describes how soft computing techniques like fuzzy logic, evolutionary computation and neural networks can be used for extracting interpretable knowledge in the form of linguistic if-then rules from numerical data for classification and modeling. While emphasis is placed on the interpretability of linguistic knowledge, this book covers almost all soft computing techniques for linguistic data mining.
01 Jan 2004
TL;DR: A mathematical description ofFCM is presented and a new methodology based on fuzzy logic techniques for developing the FCM is examined, and the applicability of FCM to model the supervisor of complex systems is discussed.
Abstract: This research deals with the soft computing methodology of fuzzy cognitive map (FCM). Here a mathematical description of FCM is presented and a new methodology based on fuzzy logic techniques for developing the FCM is examined. The capability and usefulness of FCM in modeling complex systems and the application of FCM to modeling and describing the behavior of a heat exchanger system is presented. The applicability of FCM to model the supervisor of complex systems is discussed and the FCM-supervisor for evaluating the performance of a system is constructed; simulation results are presented and discussed.
01 Dec 2004
TL;DR: The proposed fuzzy prioritisation method uses fuzzy pairwise comparison judgements rather than exact numerical values of the comparison ratios and transforms the initial fuzzy prioritisations problem into a non-linear program, which eliminates the need of additional aggregation and ranking procedures.
Abstract: This paper proposes a new approach for tackling the uncertainty and imprecision of the service evaluation process. Identifying suitable service offers, evaluating the offers and choosing the best alternatives are activities that set the scene for the consequent stages in negotiations and influence in a unique manner the following deliberations. The pre-negotiation problem in negotiations over services is regarded as decision-making under uncertainty, based on multiple criteria of quantitative and qualitative nature, where the imprecise decision-maker’s judgements are represented as fuzzy numbers. A new fuzzy modification of the analytic hierarchy process is applied as an evaluation technique. The proposed fuzzy prioritisation method uses fuzzy pairwise comparison judgements rather than exact numerical values of the comparison ratios and transforms the initial fuzzy prioritisation problem into a non-linear program. Unlike the known fuzzy prioritisation techniques, the proposed method derives crisp weights from consistent and inconsistent fuzzy comparison matrices, which eliminates the need of additional aggregation and ranking procedures. A detailed numerical example, illustrating the application of our approach to service evaluation is given.
25 Oct 2004
TL;DR: This work describes the conditions that fuzzy extractors need to satisfy to be secure, and presents generic constructions from ordinary building blocks, and demonstrates how to use a biometric secret in a remote fuzzy authentication protocol that does not require any storage on the client's side.
Abstract: We show that a number of recent definitions and constructions of fuzzy extractors are not adequate for multiple uses of the same fuzzy secret---a major shortcoming in the case of biometric applications. We propose two particularly stringent security models that specifically address the case of fuzzy secret reuse, respectively from an outsider and an insider perspective, in what we call a chosen perturbation attack. We characterize the conditions that fuzzy extractors need to satisfy to be secure, and present generic constructions from ordinary building blocks. As an illustration, we demonstrate how to use a biometric secret in a remote fuzzy authentication protocol that does not require any storage on the client's side.
TL;DR: This paper describes a fuzzy AHP (fuzzy analytic hierarchy process) to determine the weighting of subjective judgments and combines the grey relation model based on the concepts of TOPSIS to evaluate and select the best alternative.
01 May 2004
TL;DR: A unified and systematic procedure is employed to derive two kinds of novel robust adaptive tracking controllers by use of the input-to-state stability (ISS) and by combining the backstepping technique and generalized small gain approach.
Abstract: In this paper, a robust adaptive tracking control problem is discussed for a general class of strict-feedback uncertain nonlinear systems. The systems may possess a wide class of uncertainties referred to as unstructured uncertainties, which are not linearly parameterized and do not have any prior knowledge of the bounding functions. The Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertainties. A unified and systematic procedure is employed to derive two kinds of novel robust adaptive tracking controllers by use of the input-to-state stability (ISS) and by combining the backstepping technique and generalized small gain approach. One is the robust adaptive fuzzy tracking controller (RAFTC) for the system without input gain uncertainty. The other is the robust adaptive fuzzy sliding tracking controller (RAFSTC) for the system with input gain uncertainty. Both algorithms have two advantages, those are, semi-global uniform ultimate boundedness of adaptive control system in the presence of unstructured uncertainties and the adaptive mechanism with minimal learning parameterizations. Four application examples, including a pendulum system with motor, a one-link robot, a ship roll stabilization with actuator and a single-link manipulator with flexible joint, are used to demonstrate the effectiveness and performance of proposed schemes.