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89
ANFIS: AdaptiveNetworkBased Fuzzy Inference System
, 1993
"... This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping bas ..."
Abstract

Cited by 432 (5 self)
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This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping based on both human knowledge (in the form of fuzzy ifthen rules) and stipulated inputoutput data pairs. In our simulation, we employ the ANFIS architecture to model nonlinear functions, identify nonlinear components onlinely in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificail neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. 1 Introduction System modeling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with illdefine...
Neurofuzzy modeling and control
 IEEE Proceedings
, 1995
"... Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framew ..."
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Cited by 147 (1 self)
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Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (AdaptiveNetworkbased Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neurofuzzy approaches are also addressed. KeywordsFuzzy logic, neural networks, fuzzy modeling, neurofuzzy modeling, neurofuzzy control, ANFIS. I.
Functional Equivalence between Radial Basis Function Networks and Fuzzy Inference Systems
, 1993
"... This short article shows that under some minor restrictions, the functional behavior of radial basis function networks and fuzzy inference systems are actually equivalent. This functional equivalence implies that advances in each literature, such as new learning rules or analysis on representational ..."
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Cited by 126 (4 self)
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This short article shows that under some minor restrictions, the functional behavior of radial basis function networks and fuzzy inference systems are actually equivalent. This functional equivalence implies that advances in each literature, such as new learning rules or analysis on representational power, etc., can be applied to both models directly. It is of interest to observe that twomodels stemming from different origins turn out to be functional equivalent.
New Neural Transfer Functions
 Neural Computing Surveys
, 1997
"... In this article advantages of various neural transfer functions are discussed. ..."
Abstract

Cited by 35 (28 self)
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In this article advantages of various neural transfer functions are discussed.
Generating Fuzzy Rules from Examples using Genetic Algorithms
 Fuzzy Logic and Soft Computing
, 1995
"... The problem of generation desirable fuzzy rules is very important in the development of fuzzy systems. The purpose of this paper is to present a generation method of fuzzy control rules by learning from examples using genetic algorithms. We propose a real coded genetic algorithm for learning fuzzy r ..."
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Cited by 29 (8 self)
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The problem of generation desirable fuzzy rules is very important in the development of fuzzy systems. The purpose of this paper is to present a generation method of fuzzy control rules by learning from examples using genetic algorithms. We propose a real coded genetic algorithm for learning fuzzy rules, and an iterative process for obtaining a set of rules which covers the examples set with a covering value previously defined. Keywords: Fuzzy rules, learning, genetic algorithms. 1. Introduction Fuzzy rules based systems have been shown to be an important tool for modeling complex systems, where due to the complexity or the imprecision, classical tools are unsuccessful. In [19, 5] it was proved that fuzzy systems are universal approximators in the sense that for any continuous systems is possible to find a set of fuzzy rules able of approximating it with arbitrary accuracy. The problem is how to find the rules. There are different modes to derive them:  Based on Expert Experience ...
Nonlinear Predictive Control Using Local Models  Applied To A Batch Fermentation Process
 PRACTICE
, 1994
"... The problem of controlling processes that operate within a wide range of operating conditions is addressed. The operation of the process is decomposed into a set of operating regimes, and simple local statespace model structures are developed for each regime. These are combined into a global model ..."
Abstract

Cited by 24 (3 self)
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The problem of controlling processes that operate within a wide range of operating conditions is addressed. The operation of the process is decomposed into a set of operating regimes, and simple local statespace model structures are developed for each regime. These are combined into a global model structure using an interpolation method. Unknown local model parameters are identified using empirical data. The control problem is solved using a model predictive controller based on this model representation. As an example, a simulated batch fermentation reactor is studied. The modelbased controller's performance is compared to the performance with an exact process model, and a linear model. It is experienced that a nonlinear model with good prediction capabilities can be constructed using elementary and qualitative process knowledge combined with a sufficiently large amount of process data.
Fuzzy RuleBased Networks for Control
 IEEE Transactions on Fuzzy Systems
, 1994
"... We present a method for the learning of fuzzy logic membership functions and rules to approximate a numerical function from a set of examples of the function's independent variables and the resulting function value. This method uses a threestep approach to building a complete function approximation ..."
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Cited by 16 (0 self)
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We present a method for the learning of fuzzy logic membership functions and rules to approximate a numerical function from a set of examples of the function's independent variables and the resulting function value. This method uses a threestep approach to building a complete function approximation system: first, learning the membership functions and creating a cellbased rule representation; second, simplifying the cellbased rules using an informationtheoretic approach for induction of rules from discretevalued data; and finally, constructing a computational (neural) network to compute the function value given its independent variables. This function approximation system is demonstrated with a simple control example: learning the truck and trailer backerupper control system. I. Introduction The problem of approximating a function from a set of examples can be solved in a multitude of ways, including mathematicalmethods using an explicit model for the function to be learned and mo...
A systematic approach to a selfgenerating fuzzy ruletable for function approximation
 IEEE Trans Syst., Man, Cybern
, 2000
"... Abstract—In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the iden ..."
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Cited by 16 (10 self)
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Abstract—In this paper, a systematic design is proposed to determine fuzzy system structure and learning its parameters, from a set of given training examples. In particular, two fundamental problems concerning fuzzy system modeling are addressed: 1) fuzzy rule parameter optimization and 2) the identification of system structure (i.e., the number of membership functions and fuzzy rules). A fourstep approach to build a fuzzy system automatically is presented: Step 1 directly obtains the optimum fuzzy rules for a given membership function configuration. Step 2 optimizes the allocation of the membership functions and the conclusion of the rules, in order to achieve a better approximation. Step 3 determines a new and more suitable topology with the information derived from the approximation error distribution; it decides which variables should increase the number of membership functions. Finally, Step 4 determines which structure should be selected to approximate the function, from the possible configurations provided by the algorithm in the three previous steps. The results of applying this method to the problem of function approximation are presented and then compared with other methodologies proposed in the bibliography. Index Terms—Function approximation, fuzzy system construction, fuzzy system design, knowledge acquisition. I.
Structure Determination in Fuzzy Modeling: A Fuzzy CART Approach
, 1994
"... This paper presents an innovative approach to the structure determination problem in fuzzy modeling. By using the wellknown CART (classification and regression tree) algorithm as a quick preprocess, the proposed method can roughly estimate the structure (numbers of membership functions and number o ..."
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Cited by 15 (2 self)
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This paper presents an innovative approach to the structure determination problem in fuzzy modeling. By using the wellknown CART (classification and regression tree) algorithm as a quick preprocess, the proposed method can roughly estimate the structure (numbers of membership functions and number of fuzzy rules, etc.) of a fuzzy inference system; then the parameter identification is carried out by the hybrid learning scheme developed in our previous work [3, 2, 5]. Morevoer, the identified fuzzy inference system has the property that the total of firing strengths is always equal to one; this speeds up learning processes and reduces roundoff errors. 1 Introduction Fuzzy modeling [11, 10] is a new branch of system identification which concerns with the construction of a fuzzy inference system (or fuzzy model) that can predict and hopefully explain the behavior of an unknown system described by a set of sample data. Two primary tasks of fuzzy modeling are structure determination...
Input Selection for ANFIS Learning
 IN PROCEEDINGS OF THE IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS
, 1996
"... We present a quick and straightfoward way of input selection for neurofuzzy modeling using ANFIS. The method is tested on two realworld problems: the nonlinear regression problem of automobile MPG (miles per gallon) prediction, and the nonlinear system identification using the Box and Jenkins gas ..."
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Cited by 14 (0 self)
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We present a quick and straightfoward way of input selection for neurofuzzy modeling using ANFIS. The method is tested on two realworld problems: the nonlinear regression problem of automobile MPG (miles per gallon) prediction, and the nonlinear system identification using the Box and Jenkins gas furnace data [1].