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69
ANFIS: AdaptiveNetworkBased Fuzzy Inference System”,
 IEEE Trans. on System, Man and Cybernetics,
, 1993
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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 169 (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.
Integrating design stages of fuzzy systems using genetic algorithms
, 1993
"... Abstract — This paper proposes an automaticfuzzy system design method that uses a Genetic Algorithm and integrates three design stages; our method determines membership functions, the number of fuzzy rules, and the ruleconsequent parameters at the same time. Because these design stages may not be in ..."
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Cited by 110 (1 self)
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Abstract — This paper proposes an automaticfuzzy system design method that uses a Genetic Algorithm and integrates three design stages; our method determines membership functions, the number of fuzzy rules, and the ruleconsequent parameters at the same time. Because these design stages may not be independent, it is important to consider them simultaneously to obtain optimal fuzzy systems. The method includes a genetic algorithm and a penalty strategy that favors systems with fewer rules. The proposed method is applied to the classic inverted pendulum control problem and has been shown to be practical through a comparison with another method. 1 1
Improving the interpretability of TSK fuzzy models by combining global and local learning
 IEEE TRANS. FUZZY SYST
, 1998
"... The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is ..."
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Cited by 47 (1 self)
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The fuzzy inference system proposed by Takagi, Sugeno, and Kang, known as the TSK model in fuzzy system literature, provides a powerful tool for modeling complex nonlinear systems. Unlike conventional modeling where a single model is used to describe the global behavior of a system, TSK modeling is essentially a multimodel approach in which simple submodels (typically linear models) are combined to describe the global behavior of the system. Most existing learning algorithms for identifying the TSK model are based on minimizing the square of the residual between the overall outputs of the real system and the identified model. Although these algorithms can generate a TSK model with good global performance (i.e., the model is capable of approximating the given system with arbitrary accuracy, provided that sufficient rules are used and sufficient training data are available), they cannot guarantee the resulting model to have a good local performance. Often, the submodels in the TSK model may exhibit an erratic local behavior, which is difficult to interpret. Since one of the important motivations of using the TSK model (also other fuzzy models) is to gain insights into the model, it is important to investigate the interpretability issue of the TSK model. In this paper, we propose a new learning algorithm that integrates global learning and local learning in a single algorithmic framework. This algorithm uses the idea of local weighed regression and local approximation in nonparametric statistics, but remains the component of global fitting in the existing learning algorithms. The algorithm is capable of adjusting its parameters based on the user’s preference, generating models with good tradeoff in terms of global fitting and local interpretation. We illustrate the performance of the proposed algorithm using a motorcycle crash modeling example.
Symbolic Interpretation of Artificial Neural Networks
, 1996
"... Hybrid Intelligent Systems that combine knowledge based and artificial neural network systems typically have four phases involving domain knowledge representation, mapping of this knowledge into an initial connectionist architecture, network training and rule extraction respectively. The final phase ..."
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Cited by 46 (1 self)
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Hybrid Intelligent Systems that combine knowledge based and artificial neural network systems typically have four phases involving domain knowledge representation, mapping of this knowledge into an initial connectionist architecture, network training and rule extraction respectively. The final phase is important because it can provide a trained connectionist architecture with explanation power and validate its output decisions. Moreover, it can be used to refine and maintain the initial knowledge acquired from domain experts. In this paper, we present three rule extraction techniques. The first technique extracts a set of binary rules from any type of neural network. The other two techniques are specific to feedforward networks with a single hidden layer of sigmoidal units. Technique 2 extracts partial rules that represent the most important embedded knowledge with an adjustable level of detail, while the third technique provides a more comprehensive and universal approach. A rule eval...
A Fuzzy Neural Network Learning Fuzzy Control Rules and Membership Functions by Fuzzy Error Backpropagation
 In Proc. IEEE Int. Conf. on Neural Networks
, 1993
"... In this paper we present a new kind of neural network architecture designed for control tasks, which we call fuzzy neural network. The structure of the network can be interpreted in terms of a fuzzy controller. It has a threelayered architecture and uses fuzzy sets as its weights. The fuzzy error b ..."
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Cited by 32 (12 self)
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In this paper we present a new kind of neural network architecture designed for control tasks, which we call fuzzy neural network. The structure of the network can be interpreted in terms of a fuzzy controller. It has a threelayered architecture and uses fuzzy sets as its weights. The fuzzy error backpropagation algorithm, a special learning algorithm inspired by the standard BPprocedure for multilayer neural networks, is able to learn the fuzzy sets. The extended version that is presented here is also able to learn fuzzyifthen rules by reducing the number of nodes in the hidden layer of the network. The network does not learn from examples, but by evaluating a special fuzzy error measure. I. Introduction Neural Networks and Fuzzy Controllers are both capable of controlling nonlinear dynamical systems. The disadvantage of neural control is that it is not obvious how the network solves the respective control task. It is not possible in general to retrieve any kind of structural kno...
Measurement Of Membership Functions: Theoretical And Empirical Work
, 1995
"... This chapter presents a review of various interpretations of the fuzzy membership function together with ways of obtaining a membership function. We emphasize that different interpretations of the membership function call for different elicitation methods. We try to make this distinction clear u ..."
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Cited by 31 (1 self)
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This chapter presents a review of various interpretations of the fuzzy membership function together with ways of obtaining a membership function. We emphasize that different interpretations of the membership function call for different elicitation methods. We try to make this distinction clear using techniques from measurement theory.
A twostage evolutionary process for designing TSK fuzzy rulebased systems
 IEEE Trans. Syst., Man, Cybern. B
, 1999
"... Abstract—Nowadays, fuzzy rulebased systems are successfully applied to many different realworld problems. Unfortunately, relatively few wellstructured methodologies exist for designing them and, in many cases, human experts are not able to express the knowledge needed to solve the problem in the ..."
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Cited by 28 (11 self)
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Abstract—Nowadays, fuzzy rulebased systems are successfully applied to many different realworld problems. Unfortunately, relatively few wellstructured methodologies exist for designing them and, in many cases, human experts are not able to express the knowledge needed to solve the problem in the form of fuzzy rules. Takagi–Sugeno –Kang (TSK) fuzzy rulebased systems were enunciated in order to solve this design problem because they are usually identified using numerical data. In this paper we present a twostage evolutionary process for designing TSK fuzzy rulebased systems from examples combining a generation stage based on a ( ;)evolution strategy, in which the fuzzy rules with different consequents compete among themselves to form part of a preliminary knowledge base, and a refinement stage, in which both the antecedent and consequent parts of the fuzzy rules in this previous knowledge base are adapted by a hybrid evolutionary process composed of a genetic algorithm and an evolution strategy to obtain the final Knowledge Base whose rules cooperate in the best possible way. Some aspects make this process different from others proposed until now: the design problem is addressed in two different stages, the use of an angular coding of the consequent parameters that allows us to search across the whole space of possible solutions, and the use of the available knowledge about the system under identification to generate the initial populations of the Evolutionary Algorithms that causes the search process to obtain good solutions more quickly. The performance of the method proposed is shown by solving two different problems: the fuzzy modeling of some threedimensional surfaces and the computing of the maintenance costs of electrical medium line in Spanish towns. Results obtained are compared with other kind of techniques, evolutionary learning processes to design TSK and Mamdanitype fuzzy rulebased systems in the first case, and classical regression and neural modeling in the second. Index Terms — Evolution strategies, evolutionary algorithms, genetic algorithms, learning, Takagi–Sugeno –Kang (TSK) fuzzy
Modifications of Genetic Algorithms for Designing and Optimizing Fuzzy Controllers
 In Proc. First IEEE Conf. on Evolutionary Computing (ICEC'94
, 1994
"... This paper investigates the possibilities for applications of genetic algorithms to tuning and optimizing fuzzy controllers, or even to generate fuzzy controllers automatically. There are various adhoc approaches to use genetic algorithms for the design of fuzzy controllers, which already indicate ..."
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Cited by 27 (2 self)
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This paper investigates the possibilities for applications of genetic algorithms to tuning and optimizing fuzzy controllers, or even to generate fuzzy controllers automatically. There are various adhoc approaches to use genetic algorithms for the design of fuzzy controllers, which already indicated good results. However, there is a need for systematic techniques that take the properties of fuzzy controllers and genetic algorithm into account in order to obtain fast convergence and to be able to tackle more complex control problems. I. Introduction Fuzzy control (for an overview see for example [11, 12]) is a control strategy that is not based on a mathematical description of the process to be controlled, but intends to model the behaviour of a human operator who would (theoretically) be able to control the process. The expert's knowledge is specified in terms of linguistic control rules in which expressions like negative big, positive small, etc. appear. These linguistic expressions...
Combining Neural Networks and Fuzzy Controllers
 Fuzzy Logic in Artificial Intelligence (FLAI93
, 1993
"... . Fuzzy controllers are designed to work with knowledge in the form of linguistic control rules. But the translation of these linguistic rules into the framework of fuzzy set theory depends on the choice of certain parameters, for which no formal method is known. The optimization of these parameters ..."
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Cited by 20 (5 self)
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. Fuzzy controllers are designed to work with knowledge in the form of linguistic control rules. But the translation of these linguistic rules into the framework of fuzzy set theory depends on the choice of certain parameters, for which no formal method is known. The optimization of these parameters can be carried out by neural networks, which are designed to learn from training data, but which are in general not able to profit from structural knowledge. In this paper we discuss approaches which combine fuzzy controllers and neural networks, and present our own hybrid architecture where principles from fuzzy control theory and from neural networks are integrated into one system. 1 Introduction Classical control theory is based on mathematical models that describe the behavior of the plant under consideration. The main idea of fuzzy control [11, 14], which has proved to be a very successful method [7], is to build a model of a human control expert who is capable of controlling the plan...