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709
ANFIS: adaptivenetworkbased fuzzy inference system,” in
 IEEE Transactions on Systems, Man and Cybernetics
, 1993
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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 231 (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.
Selecting fuzzy ifthen rules for classification problems using genetic algorithms
 IEEE TRANS. FUZZY SYST
, 1995
"... This paper proposes a geneticalgorithmbased method for selecting a small number of significant fuzzy ifthen rules to construct a compact fuzzy classification system with high classification power. The rule selection problem is formulated as a combinatorial optimization problem with two objectives ..."
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Cited by 132 (21 self)
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This paper proposes a geneticalgorithmbased method for selecting a small number of significant fuzzy ifthen rules to construct a compact fuzzy classification system with high classification power. The rule selection problem is formulated as a combinatorial optimization problem with two objectives: to maximize the number of correctly classified patterns and to minimize the number of fuzzy ifthen rules. Genetic algorithms are applied to this problem. A set of fuzzy ifthen rules is coded into a string and treated as an individual in genetic algorithms. The fitness of each individual is specified by the two objectives in the combinatorial optimization problem. The performance of the proposed method for training data and test data is examined by computer simulations on the iris data of Fisher.
Fuzzy logic controllers are universal approximators
 IEEE Trans. on SMC
, 1995
"... AbstractIn this paper, we consider a fundamental theoretical question, Why does fuzzy control have such good performance for a wide variety of practical problems?. We try to answer this fundamental question by proving that for each fixed fuzzy logic belonging to a wide class of fuzzy logics, and fo ..."
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Cited by 114 (7 self)
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AbstractIn this paper, we consider a fundamental theoretical question, Why does fuzzy control have such good performance for a wide variety of practical problems?. We try to answer this fundamental question by proving that for each fixed fuzzy logic belonging to a wide class of fuzzy logics, and for each fixed type of membership function belonging to a wide class of membership functions, the fuzzy logic control systems using these two and any method of defdcation are capable of approximating any real continuous function on a compact set to arbitrary accuracy. On the other hand, this result can be viewed as an existence theorem of an optimal fuzzy logic control system for a wide variety of problems. 1 I.
A ThreeStage Evolutionary Process for Learning Descriptive and Approximate FuzzyLogicController Knowledge Bases From Examples
, 1997
"... Nowadays fuzzy logic controllers have been successfully applied to a wide range of engineering control processes. Several tasks have to be performed in order to design an intelligent control system of this kind for a concrete application. One of the most important and difficult ones is the extractio ..."
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Cited by 103 (61 self)
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Nowadays fuzzy logic controllers have been successfully applied to a wide range of engineering control processes. Several tasks have to be performed in order to design an intelligent control system of this kind for a concrete application. One of the most important and difficult ones is the extraction of the expert known knowledge of the controlled system. The aim of this paper is to present an evolutionary process based on genetic algorithms and evolution strategies for learning the fuzzylogiccontroller knowledge base from examples in three different stages. The process allows us to generate two different kinds of knowledge bases, descriptive and approximate ones, depending on the scope of the fuzzy sets giving meaning to the fuzzycontrolrule linguistic terms, taking preliminary linguisticvariable fuzzy partitions as a base. The performance of the method proposed is shown by measuring the accuracy of the fuzzy logic controllers designed in the fuzzy modeling of three threedimensional surfaces presenting different
Performance evaluation of fuzzy classifier systems for multidimensional pattern classification problems
 IEEE TRANS. SYSTEMS, MAN CYBERNETICS—PART B: CYBERNET
, 1999
"... We examine the performance of a fuzzy geneticsbased machine learning method for multidimensional pattern classification problems with continuous attributes. In our method, each fuzzy if–then rule is handled as an individual, and a fitness value is assigned to each rule. Thus, our method can be vi ..."
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Cited by 94 (11 self)
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We examine the performance of a fuzzy geneticsbased machine learning method for multidimensional pattern classification problems with continuous attributes. In our method, each fuzzy if–then rule is handled as an individual, and a fitness value is assigned to each rule. Thus, our method can be viewed as a classifier system. In this paper, we first describe fuzzy if–then rules and fuzzy reasoning for pattern classification problems. Then we explain a geneticsbased machine learning method that automatically generates fuzzy if–then rules for pattern classification problems from numerical data. Because our method uses linguistic values with fixed membership functions as antecedent fuzzy sets, a linguistic interpretation of each fuzzy if–then rule is easily obtained. The fixed membership functions also lead to a simple implementation of our method as a computer program. The simplicity of implementation and the linguistic interpretation of the generated fuzzy if–then rules are the main characteristic features of our method. The performance of our method is evaluated by computer simulations on some wellknown test problems. While our method involves no tuning mechanism of membership functions, it works very well in comparison with other classification methods such as nonfuzzy machine learning techniques and neural networks.
An online selfconstructing neural fuzzy inference network and its applications
 IEEE. Trans. Fuzzy. Sys
, 1998
"... Abstract—A selfconstructing 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 rulebased model possessing neural network’s learning ability. There are no rules initially in the SO ..."
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Cited by 92 (21 self)
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Abstract—A selfconstructing 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 rulebased model possessing neural network’s 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 a aligned clusteringbased 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 (input variables) selected via a projectionbased correlation measure for each rule will be added to the consequent part (forming a linear equation of input variables) 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 (LMS) or recursive least squares (RLS) algorithms and the precondition parameters are tuned by backpropagation algorithm. Both the structure and parameter identification are done simultaneously to form a fast learning scheme, which is another feature of the SONFIN. Furthermore, 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. Proper linear transformations are also learned dynamically in the parameter identification phase of the SONFIN. To demonstrate the capability of the proposed SONFIN, simulations in different areas including control, communication, and signal processing are done. Effectiveness of the SONFIN is verified from these simulations. Index Terms—Equalizer, noisy speech recognition, projectionbased correlation measure, similarity measure, TSK fuzzy rule.
A BehaviorBased System For OffRoad Navigation
 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION
, 1994
"... In this paper, we describe a core system for autonomous navigation in outdoor natural terrain. The system consists of three parts: a perception module which processes range images to identify untraversable regions of the terrain, a local map management module which maintains a representation of the ..."
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Cited by 79 (8 self)
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In this paper, we describe a core system for autonomous navigation in outdoor natural terrain. The system consists of three parts: a perception module which processes range images to identify untraversable regions of the terrain, a local map management module which maintains a representation of the environment in the vicinity of the vehicle, and a planning module which issues commands to the vehicle controller. Our approach is to use the concept of "early traversability evaluation," in which the perception module decides which parts of the terrain are traversable as soon as a new image is taken, and on the use of a behaviorbased architecture for generating commands to drive the vehicle. We argue that our approach leads to a robust and efficient navigation system. We illustrate our approach by an experiment in which a vehicle travelled autonomously for one kilometer through unmapped crosscountry terrain. The system used in this experiment can be viewed as a core navigation system in t...
Effect of rule weights in fuzzy rulebased classification systems
 IEEE Transactions on Fuzzy Systems
, 2001
"... Abstract—This paper examines the effect of rule weights in fuzzy rulebased classification systems. Each fuzzy IF–THEN rule in our classification system has antecedent linguistic values and a single consequent class. We use a fuzzy reasoning method based on a single winner rule in the classification ..."
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Cited by 78 (14 self)
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Abstract—This paper examines the effect of rule weights in fuzzy rulebased classification systems. Each fuzzy IF–THEN rule in our classification system has antecedent linguistic values and a single consequent class. We use a fuzzy reasoning method based on a single winner rule in the classification phase. The winner rule for a new pattern is the fuzzy IF–THEN rule that has the maximum compatibility grade with the new pattern. When we use fuzzy IF–THEN rules with certainty grades (i.e., rule weights), the winner is determined as the rule with the maximum product of the compatibility grade and the certainty grade. In this paper, the effect of rule weights is illustrated by drawing classification boundaries using fuzzy IF–THEN rules with/without certainty grades. It is also shown that certainty grades play an important role when a fuzzy rulebased classification system is a mixture of general rules and specific rules. Through computer simulations, we show that comprehensible fuzzy rulebased systems with high classification performance can be designed without modifying the membership functions of antecedent linguistic values when we use fuzzy IF–THEN rules with certainty grades. Index Terms—Fuzzy reasoning, fuzzy rulebased systems, pattern classification, rule extraction. I.
Soft Computing: the Convergence of Emerging Reasoning Technologies
 Soft Computing
, 1997
"... The term Soft Computing (SC) represents the combination of emerging problemsolving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to so ..."
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Cited by 68 (11 self)
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The term Soft Computing (SC) represents the combination of emerging problemsolving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to solve complex, realworld problems. After a brief description of each of these technologies, we will analyze some of their most useful combinations, such as the use of FL to control GAs and NNs parameters; the application of GAs to evolve NNs (topologies or weights) or to tune FL controllers; and the implementation of FL controllers as NNs tuned by backpropagationtype algorithms.