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Journal ArticleDOI

Generating fuzzy rules by learning from examples

01 Jan 1992-Vol. 22, Iss: 6, pp 1414-1427
TL;DR: The mapping is proved to be capable of approximating any real continuous function on a compact set to arbitrary accuracy and applications to truck backer-upper control and time series prediction problems are presented.
Abstract: A general method is developed to generate fuzzy rules from numerical data. The method consists of five steps: divide the input and output spaces of the given numerical data into fuzzy regions; generate fuzzy rules from the given data; assign a degree of each of the generated rules for the purpose of resolving conflicts among the generated rules; create a combined fuzzy rule base based on both the generated rules and linguistic rules of human experts; and determine a mapping from input space to output space based on the combined fuzzy rule base using a defuzzifying procedure. The mapping is proved to be capable of approximating any real continuous function on a compact set to arbitrary accuracy. Applications to truck backer-upper control and time series prediction problems are presented. >
Citations
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Journal ArticleDOI
TL;DR: An efficient method for estimating cluster centers of numerical data that can be used to determine the number of clusters and their initial values for initializing iterative optimization-based clustering algorithms such as fuzzy C-means is presented.
Abstract: We present an efficient method for estimating cluster centers of numerical data. This method can be used to determine the number of clusters and their initial values for initializing iterative optimization-based clustering algorithms such as fuzzy C-means. Here we use the cluster estimation method as the basis of a fast and robust algorithm for identifying fuzzy models. A benchmark problem involving the prediction of a chaotic time series shows this model identification method compares favorably with other, more computationally intensive methods. We also illustrate an application of this method in modeling the relationship between automobile trips and demographic factors.

2,815 citations

Journal ArticleDOI
TL;DR: 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.
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. >

2,575 citations

Journal ArticleDOI
01 Mar 1995
TL;DR: After synthesizing a FLS, it is demonstrated that it can be expressed mathematically as a linear combination of fuzzy basis functions, and is a nonlinear universal function approximator, a property that it shares with feedforward neural networks.
Abstract: A fuzzy logic system (FLS) is unique in that it is able to simultaneously handle numerical data and linguistic knowledge. It is a nonlinear mapping of an input data (feature) vector into a scalar output, i.e., it maps numbers into numbers. Fuzzy set theory and fuzzy logic establish the specifics of the nonlinear mapping. This tutorial paper provides a guided tour through those aspects of fuzzy sets and fuzzy logic that are necessary to synthesize an FLS. It does this by starting with crisp set theory and dual logic and demonstrating how both can be extended to their fuzzy counterparts. Because engineering systems are, for the most part, causal, we impose causality as a constraint on the development of the FLS. After synthesizing a FLS, we demonstrate that it can be expressed mathematically as a linear combination of fuzzy basis functions, and is a nonlinear universal function approximator, a property that it shares with feedforward neural networks. The fuzzy basis function expansion is very powerful because its basis functions can be derived from either numerical data or linguistic knowledge, both of which can be cast into the forms of IF-THEN rules. >

2,024 citations

Journal ArticleDOI
TL;DR: A direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy if-then 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 is developed.
Abstract: A direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control, is capable of incorporating fuzzy if-then 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 is developed. The specific formula for 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 and to control the Duffing chaotic system to track a trajectory. The simulation results show that the controller worked without using any fuzzy control rules, and that after fuzzy control rules were incorporated the adaptation speed became much faster. It is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control. >

1,488 citations

Journal ArticleDOI
15 Oct 2008
TL;DR: KEEL as discussed by the authors is a software tool to assess evolutionary algorithms for data mining problems of various kinds including regression, classification, unsupervised learning, etc., which includes evolutionary learning algorithms based on different approaches: Pittsburgh, Michigan and IRL.
Abstract: This paper introduces a software tool named KEEL which is a software tool to assess evolutionary algorithms for Data Mining problems of various kinds including as regression, classification, unsupervised learning, etc. It includes evolutionary learning algorithms based on different approaches: Pittsburgh, Michigan and IRL, as well as the integration of evolutionary learning techniques with different pre-processing techniques, allowing it to perform a complete analysis of any learning model in comparison to existing software tools. Moreover, KEEL has been designed with a double goal: research and educational.

1,297 citations


Cites methods from "Generating fuzzy rules by learning ..."

  • ...Our purpose is to observe the learning process of a regression algorithm using fuzzy rule learning (Wang and Mendel 1992) over an electrical energy distribution problem (Cordón et al. 1999) by using five labels per variable....

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  • ...In this example, they can prove for themselves that Wand and Mendel’s ad-hoc method (Wang and Mendel 1992) is very fast but its results far from accurate....

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References
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Book
01 Jan 1970
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
Abstract: From the Publisher: This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application —forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.

19,748 citations

Journal ArticleDOI
TL;DR: It is rigorously established that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available.

18,794 citations

Journal ArticleDOI
TL;DR: This revision of a classic, seminal, and authoritative book explores the building of stochastic models for time series and their use in important areas of application —forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control.
Abstract: From the Publisher: This is a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970. It focuses on practical techniques throughout, rather than a rigorous mathematical treatment of the subject. It explores the building of stochastic (statistical) models for time series and their use in important areas of application —forecasting, model specification, estimation, and checking, transfer function modeling of dynamic relationships, modeling the effects of intervention events, and process control. Features sections on: recently developed methods for model specification, such as canonical correlation analysis and the use of model selection criteria; results on testing for unit root nonstationarity in ARIMA processes; the state space representation of ARMA models and its use for likelihood estimation and forecasting; score test for model checking; and deterministic components and structural components in time series models and their estimation based on regression-time series model methods.

12,650 citations


"Generating fuzzy rules by learning ..." refers background in this paper

  • ...Time-series prediction is a very important practical problem [ 2 ]....

    [...]

Journal ArticleDOI
TL;DR: It is demonstrated that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube.
Abstract: In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single hidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks.

12,286 citations