Showing papers on "Fuzzy logic published in 1992"

Fuzzy basis functions, universal approximation, and orthogonal least-squares learning

Abstract: Fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions. Using the Stone-Weierstrass theorem, it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy. Based on the fuzzy basis function representations, an orthogonal least-squares (OLS) learning algorithm is developed for designing fuzzy systems based on given input-output pairs; then, the OLS algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system. The fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system, and the simulation results show that the control performance is improved by incorporating some common-sense fuzzy control rules. >

Fuzzy ARTMAP: A neural network architecture for incremental supervised learning of analog multidimensional maps

Abstract: A neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors, which may represent fuzzy or crisp sets of features. The architecture, called fuzzy ARTMAP, achieves a synthesis of fuzzy logic and adaptive resonance theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Four classes of simulation illustrated fuzzy ARTMAP performance in relation to benchmark backpropagation and generic algorithm systems. These simulations include finding points inside versus outside a circle, learning to tell two spirals apart, incremental approximation of a piecewise-continuous function, and a letter recognition database. The fuzzy ARTMAP system is also compared with Salzberg's NGE systems and with Simpson's FMMC system. >

Fuzzy systems are universal approximators

Abstract: The author proves that fuzzy systems are universal approximators. The Stone-Weierstrass theorem is used to prove that fuzzy systems with product inference, centroid defuzzification, and a Gaussian membership function are capable of approximating any real continuous function on a compact set to arbitrary accuracy. This result can be viewed as an existence theorem of an optimal fuzzy system for a wide variety of problems. >

Multilayer perceptron, fuzzy sets, and classification

Abstract: A fuzzy neural network model based on the multilayer perceptron, using the backpropagation algorithm, and capable of fuzzy classification of patterns is described. The input vector consists of membership values to linguistic properties while the output vector is defined in terms of fuzzy class membership values. This allows efficient modeling of fuzzy uncertain patterns with appropriate weights being assigned to the backpropagated errors depending upon the membership values at the corresponding outputs. During training, the learning rate is gradually decreased in discrete steps until the network converges to a minimum error solution. The effectiveness of the algorithm is demonstrated on a speech recognition problem. The results are compared with those of the conventional MLP, the Bayes classifier, and other related models. >

Learning and tuning fuzzy logic controllers through reinforcements

Abstract: A method for learning and tuning a fuzzy logic controller based on reinforcements from a dynamic system is presented. It is shown that: the generalized approximate-reasoning-based intelligent control (GARIC) architecture learns and tunes a fuzzy logic controller even when only weak reinforcement, such as a binary failure signal, is available; introduces a new conjunction operator in computing the rule strengths of fuzzy control rules; introduces a new localized mean of maximum (LMOM) method in combining the conclusions of several firing control rules; and learns to produce real-valued control actions. Learning is achieved by integrating fuzzy inference into a feedforward network, which can then adaptively improve performance by using gradient descent methods. The GARIC architecture is applied to a cart-pole balancing system and demonstrates significant improvements in terms of the speed of learning and robustness to changes in the dynamic system's parameters over previous schemes for cart-pole balancing. >

Self-learning fuzzy controllers based on temporal backpropagation

Abstract: A generalized control strategy that enhances fuzzy controllers with self-learning capability for achieving prescribed control objectives in a near-optimal manner is presented. This methodology, termed temporal backpropagation, is model-sensitive in the sense that it can deal with plants that can be represented in a piecewise-differentiable format, such as difference equations, neural networks, GMDH structures, and fuzzy models. Regardless of the numbers of inputs and outputs of the plants under consideration, the proposed approach can either refine the fuzzy if-then rules of human experts or automatically derive the fuzzy if-then rules if human experts are not available. The inverted pendulum system is employed as a testbed to demonstrate the effectiveness of the proposed control scheme and the robustness of the acquired fuzzy controller. >

On fuzzy modeling using fuzzy neural networks with the back-propagation algorithm

Abstract: A fuzzy modeling method using fuzzy neural networks with the backpropagation algorithm is presented. The method can identify the fuzzy model of a nonlinear system automatically. The feasibility of the method is examined using simple numerical data. >

Fuzzy Logic for the Management of Uncertainty

Abstract: Partial table of contents: ISSUES IN THE MANAGEMENT OF UNCERTAINTY A Survey of Uncertain and Approximate Inference (R. Neapolitan) Rough Sets: A New Approach to Vagueness (Z. Pawlak) ASPECTS OF FUZZY LOGIC: THEORY AND IMPLEMENTATIONS LT-Fuzzy Logics (H. Rasiowa & N. Cat Ho) On Fuzzy Intuitionistic Logic (E. Turunen) On Modifier Logic (J. Mattila) FUZZY LOGIC FOR APPROXIMATE REASONING Presumption, Prejudice, and Regularity in Fuzzy Material Implication (T. Whalen & B. Schott) Inference for Information Systems Containing Probabilistic and Fuzzy Uncertainties (J. Baldwin) FUZZY LOGIC FOR KNOWLEDGE REPRESENTATION AND ELICITATION Approximate Reasoning in Diagnosis, Therapy, and Prognosis (A. Rocha, et al.) Elementary Learning in a Fuzzy Expert System (J. Buckley) KNOWLEDGE-BASED SYSTEMS USING FUZZY LOGIC Structured Local Fuzzy Logics in MILORD (J. Agustm, et al.) The Validation of Fuzzy Knowledge-Based Systems (A. Chang & L. Hall) FUZZY LOGIC FOR INTELLIGENT DATABASE MANAGEMENT SYSTEMS Fuzzy Querying in Conventional Databases (P. Bosc & O. Pivert) Index.

An Introduction to Fuzzy Logic Applications in Intelligent Systems

Abstract: Knowledge Representation in Fuzzy Logic LA Zadeh Expert Systems Using Fuzzy Logic RR Yager Fuzzy Rules in Knowledge-Based Systems D Dubois, H Prade Fuzzy Logic Controllers H Berenji Methods and Applications of Fuzzy Mathematical Programming HJ Zimmermann Fuzzy Set Methods in Computer Vision JM Keller, R Krishnapuram Fuzziness, Image Information and Scene Analysis SK Pal Fuzzy Sets in Natural Language Processing V Novak Fuzzy-Set-Theoretic Applications in Modeling of Man-Machine Interactions W Karwowski, G Salvendy Questionnaires and Fuzziness B Bouchon-Meunier Fuzzy Logic Knowledge Systems and Artificial Neural Networks in Medicine and Biology E Sanchez The Representation and Use of Uncertainty and Metaknowledge in Milord R Lopez de Montaras, C Sierra, J Augusti Fuzzy Logic with Linguistic Quantifiers in Group Decision Making J Kacprzyk, M Fedrizzi, H Nurmi Learning in Uncertain Environments M Botta, A Giordana, L Saitta Evidential Reasoning Under Probabilistic and Fuzzy Uncertainties JF Baldwin Probabilistic Sets-Probabilistic Extension of Fuzzy Sets K Hirota Index

A decision theoretic framework for approximating concepts

Abstract: This paper explores the implications of approximating a concept based on the Bayesian decision procedure, which provides a plausible unification of the fuzzy set and rough set approaches for approximating a concept. We show that if a given concept is approximated by one set, the same result given by the α-cut in the fuzzy set theory is obtained. On the other hand, if a given concept is approximated by two sets, we can derive both the algebraic and probabilistic rough set approximations. Moreover, based on the well known principle of maximum (minimum) entropy, we give a useful interpretation of fuzzy intersection and union. Our results enhance the understanding and broaden the applications of both fuzzy and rough sets.

Stable adaptive fuzzy control of nonlinear systems

Abstract: The author develops a direct adaptive fuzzy controller which does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy control rules directly into the controllers, and guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. The specific formula of the bounds is provided so that controller designers can determine the bounds based on their requirements. The direct adaptive fuzzy controller is used to regulate an unstable system to the origin. Simulation results show that the direct adaptive fuzzy controller can perform successful control without using any fuzzy control rules. After incorporating some fuzzy control rules into the controllers the adaptation speed became much faster. The author also showed explicitly how the supervisory control forced the state to be within the constraint set and how the adaptive fuzzy controller learned to regain control. >

Back-propagation fuzzy system as nonlinear dynamic system identifiers

Abstract: The authors develop a training algorithm, similar to the backpropagation algorithm for neural networks, to train fuzzy systems to match desired input-output pairs. The key ideas in developing this training algorithm are to view a fuzzy system as a three-layer feedforward network, and to use the chain rule to determine gradients of the output errors of the fuzzy system with respect to its design parameters. It is shown that this training algorithm performs an error backpropagation procedure: hence, the fuzzy system equipped with the backpropagation training algorithm is called the backpropagation fuzzy system (BP FS). An online initial parameter choosing method is proposed for the BP FS, and it is shown that it is straightforward to incorporate linguistic if-then rules into the BP FS. Two examples are presented which demonstrate (1) how the fuzzy system learns to match an unknown nonlinear mapping as training progresses and (2) that performance is improved by incorporating linguistic rules. >

Fuzzy fundamentals

Abstract: An orderly design procedure that can save time and help prevent problems in the development of fuzzy logic systems is presented. The nature of fuzzy logic is examined, and the design of fuzzy control systems is discussed. The architecture of a simple fuzzy controller for a steam turbine is used as an example, to show how fuzzy control models work. A four-step methodology for fuzzy system design is described. >

Sliding mode fuzzy control

Abstract: Fuzzy controllers work like modified sliding mode controllers (SMCs). Compared to ordinary SMCs, fuzzy controllers (FCs) have the advantage of higher robustness. The structure of a FC is derived from a nonlinear state equation representing a large class of physical systems. The following aspects are discussed: stability conditions, scaling of the state vector, choice of the switching line, and determination of the break frequencies of the controller. By the choice of an additional boundary layer in the phase plane the FC is modified so that drastic changes of the manipulated variable can be avoided, especially at the boundary of the normalized phase plane. In this context, the higher robustness of the modified FC over the modified SMC is discussed. An FC for a higher-order system is proposed. >

A fuzzy systems approach in data envelopment analysis

Abstract: The use of fuzzy set-theoretic measures is explored here in the context of data envelopment analysis, which utilizes a nonparametric approach to measure efficiency. Three types of fuzzy statics are employed here e.g., fuzzy mathematical programme, fuzzy regression and fuzzy entropy, to illustrate the types of decisions and solutions that are achievable, when the data are vague and prior information is inexact and imprecise.

Fuzzy classification methods for determining land suitability from soil profile observations and topography

Abstract: SUMMARY Because conventional Boolean retrieval of soil survey data and logical models for assessing land suitability treat both spatial units and attribute value ranges as exactly specifiable quantities, they ignore the continuous nature of soil and landscape variation and uncertainties in measurement which can result in the misclassification of sites that just fail to match strictly defined requirements. This paper uses fuzzy classification to determine land suitability from (i) multivariate point observations of soil attributes, (ii) topographically controlled site drainage conditions, and (iii) minimum contiguous areas, and compares the results obtained with conventional Boolean methods. The methods are illustrated using data from the Alberta Agricultural Department experimental farm at Lacombe in Alberta, Canada. Data on site elevation and soil chemical and physical properties measured at 154 soil profiles were interpolated by ordinary block kriging to 15 m × 15 m cells on a 50 × 50 grid. The soil property data for each cell were classified by Boolean and fuzzy methods. The digital elevation model created by interpolating the elevation data was used to determine the surface drainage network and map it in terms of the numbers of cells draining through each cell on the grid. This map was reclassified to yield Boolean and fuzzy maps of surface wetness which were then intersected with the soil profile classes. The resulting classification maps were examined for contiguity to locate areas where a block of minimum size (45m × 45m) could be located successfully. In this study Boolean methods reject larger numbers of cells than fuzzy classification, and select cells that are insufficiently contiguous to meet the aims of the land classification. Fuzzy methods produce contiguous areas and reject less information at all stages of the analyses than Boolean methods. They are much better than Boolean methods for classification of continuous variation, such as the results of the drainage analysis.

Adaptive fuzzy systems for backing up a truck-and-trailer

Abstract: Fuzzy control systems and neural-network control systems for backing up a simulated truck, and truck-and-trailer, to a loading dock in a parking lot are presented. The supervised backpropagation learning algorithm trained the neural network systems. The robustness of the neural systems was tested by removing random subsets of training data in learning sequences. The neural systems performed well but required extensive computation for training. The fuzzy systems performed well until over 50% of their fuzzy-associative-memory (FAM) rules were removed. They also performed well when the key FAM equilibration rule was replaced with destructive, or 'sabotage', rules. Unsupervised differential competitive learning (DCL) and product-space clustering adaptively generated FAM rules from training data. The original fuzzy control systems and neural control systems generated trajectory data. The DCL system rapidly recovered the underlying FAM rules. Product-space clustering converted the neural truck systems into structured sets of FAM rules that approximated the neural system's behavior. >

A continuum approach to soil classification by modified fuzzy k‐means with extragrades

Abstract: SUMMARY The need for a more continuous approach to soil classification is discussed, and methods based on the mathematical constructs known as fuzzy sets are considered most appropriate for this. A centroidal grouping method, fuzzy k-means with extragrades, which quantifies the intragrading and extragrading of soil individuals is described. An example of the application of this technique to an area of 4800 ha at Wesepe in The Netherlands is presented. The results show that the technique could create a classification that reflects the main pedological features of the area in a continuous way. Although there may be problems in selecting the optimal number of groups and degree of fuzziness, we conclude that the method is most promising and worthy of consideration when any type of quantitative soil classification is required.

Fuzzy Logic Controllers

Abstract: Fuzzy Set Theory, introduced by Zadeh in 1965 [77], has been the subject of much controversy and debate. In recent years, it has found many applications in a variety of fields. Among the most successful applications of this theory has been the area of Fuzzy Logic Control (FLC) initiated by the work of Mamdani and Assilian [36]. FLC has had considerable success in Japan, where many commercial products using this technology, have been built.

Optimal apportionment of reliability and redundancy in series systems under multiple objectives

Abstract: A multiobjective reliability apportionment problem for a series system with time-dependent reliability is presented. The resulting mathematical programming formulation determines the optimal level of component reliability and the number of redundant components at each stage. The problem is a multiobjective, nonlinear, mixed-integer mathematical programming problem, subject to several design constraints. Sequential unconstrained minimization techniques in conjunction with heuristic algorithms are used to find an optimum solution. A generalization of the problem in view of inherent vagueness in the objective and the constraint functions results in an ill-structured reliability apportionment problem. This multiobjective fuzzy optimization problem is solved using nonlinear programming. The computational procedure is illustrated through a numerical example. The fuzzy optimization techniques can be useful during initial stages of the conceptual design of engineering systems where the design goals and design constraints have not been clearly identified or stated, and for decision making problems in ill-structured situations. >

Fuzzy Kohonen clustering networks

Abstract: The authors propose a fuzzy Kohonen clustering network which integrates the fuzzy c-means (FCM) model into the learning rate and updating strategies of the Kohonen network. This yields an optimization problem related to FCM, and the numerical results show improved convergence as well as reduced labeling errors. It is proved that the proposed scheme is equivalent to the c-means algorithms. The new method can be viewed as a Kohonen type of FCM, but it is self-organizing, since the size of the update neighborhood and the learning rate in the competitive layer are automatically adjusted during learning. Anderson's IRIS data were used to illustrate this method. The results are compared with the standard Kohonen approach. >

Adaptive fuzzy c-shells clustering and detection of ellipses

Abstract: Several generalizations of the fuzzy c-shells (FCS) algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells. An earlier generalization, the adaptive fuzzy c-shells (AFCS) algorithm, is examined in detail and is found to have global convergence problems when the shapes to be detected are partial. New formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the AFCS algorithm. The resulting algorithm, called the AFCS-U algorithm, performs better for partial shapes. Another formulation based on the second-order quadrics equation is considered. These algorithms can detect ellipses and circles in 2D data. They are compared with the Hough transform (HT)-based methods for ellipse detection. Existing HT-based methods for ellipse detection are evaluated, and a multistage method incorporating the good features of all the methods is used for comparison. Numerical examples of real image data show that the AFCS algorithm requires less memory than the HT-based methods, and it is at least an order of magnitude faster than the HT approach. >