Successive identification of a fuzzy model and its applications to prediction of a complex system
TL;DR: It is shown from two examples that the successive identification method of a fuzzy model is very useful for modeling complex systems.
About: This article is published in Fuzzy Sets and Systems.The article was published on 1991-08-15. It has received 485 citations till now. The article focuses on the topics: Fuzzy number & Fuzzy set operations.
Citations
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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
TL;DR: The fuzzy block diagrams and the stability analysis are applied to the design problems of a model-based fuzzy controller and a new design technique of a fuzzy controller is proposed.
2,266 citations
Book•
30 Apr 1998
TL;DR: Fuzzy Modeling for Control addresses fuzzy modeling from the systems and control engineering point of view and focuses on the selection of appropriate model structures, on the acquisition of dynamic fuzzy models from process measurements, and on the design of nonlinear controllers based on fuzzy models.
Abstract: From the Publisher:
Fuzzy Modeling for Control addresses fuzzy modeling from the systems and control engineering point of view. It focuses on the selection of appropriate model structures, on the acquisition of dynamic fuzzy models from process measurements (fuzzy identification), and on the design of nonlinear controllers based on fuzzy models. The main features of the presented techniques are illustrated by means of simple examples. In addition, three real-world applications are described. Finally, software tools for building fuzzy models from measurements are available from the author.
1,183 citations
TL;DR: The definition of fuzzy time series is given, some properties of fuzzyTime series are explored, and procedures to develop fuzzy timeseries models are discussed.
1,048 citations
TL;DR: A linear transformation for each input variable can be incorporated into the network so that much fewer rules are needed or higher accuracy can be achieved.
Abstract: A self-constructing neural fuzzy inference network (SONFIN) with online learning ability is proposed in this paper. The SONFIN is inherently a modified Takagi-Sugeno-Kang (TSK)-type fuzzy rule-based model possessing neural network learning ability. There are no rules initially in the SONFIN. They are created and adapted as online learning proceeds via simultaneous structure and parameter identification. In the structure identification of the precondition part, the input space is partitioned in a flexible way according to an aligned clustering-based algorithm. As to the structure identification of the consequent part, only a singleton value selected by a clustering method is assigned to each rule initially. Afterwards, some additional significant terms selected via a projection-based correlation measure for each rule will be added to the consequent part incrementally as learning proceeds. The combined precondition and consequent structure identification scheme can set up an economic and dynamically growing network, a main feature of the SONFIN. In the parameter identification, the consequent parameters are tuned optimally by either least mean squares or recursive least squares algorithms and the precondition parameters are tuned by a backpropagation algorithm. To enhance the knowledge representation ability of the SONFIN, a linear transformation for each input variable can be incorporated into the network so that much fewer rules are needed or higher accuracy can be achieved.
910 citations
Cites methods from "Successive identification of a fuzz..."
...It is reported in [20] that the TSK model can model a sophisticated system using a few rules....
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...It was pointed out by Sugeno and Tanaka [20] that a large number of rules are necessary when representing the behavior of a sophisticated system by the ordinary fuzzy model based on Mamdani’s approach....
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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
01 Jan 1985
TL;DR: A mathematical tool to build a fuzzy model of a system where fuzzy implications and reasoning are used is presented and two applications of the method to industrial processes are discussed: a water cleaning process and a converter in a steel-making process.
Abstract: A mathematical tool to build a fuzzy model of a system where fuzzy implications and reasoning are used is presented. The premise of an implication is the description of fuzzy subspace of inputs and its consequence is a linear input-output relation. The method of identification of a system using its input-output data is then shown. Two applications of the method to industrial processes are also discussed: a water cleaning process and a converter in a steel-making process.
18,803 citations
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
01 Dec 1974
TL;DR: In this article, the authors describe a scheme in which a fuzzy algorithm is used to control plant, in this case, a laboratory-built steam engine, implemented as an interpreter of a set of rules expressed as fuzzy conditional statements.
Abstract: The paper describes a scheme in which a fuzzy algorithm is used to control plant, in this case, a laboratory-built steam engine. The algorithm is implemented as an interpreter of a set of rules expressed as fuzzy conditional statements. This implementation on a digital computer is used online, to control the plant. The merit of such a controller is discussed in the light of the results obtained.
3,916 citations
TL;DR: The problems of structure identification of a fuzzy model are formulated and an algorithm for identifying a structure is suggested and a successive identification algorithm of the parameters is suggested.
2,649 citations