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185
ANFIS: AdaptiveNetworkbased Fuzzy Inference Systems
 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.
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 168 (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.
Improving the interpretability of TSK fuzzy models by combining global and local learning
 IEEE Trans. Fuzzy Syst
, 1998
"... Abstract — 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 ..."
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Cited by 47 (1 self)
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Abstract — 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. Index Terms—Fuzzy modeling, fuzzy systems, learning algorithms, TSK model. I.
New Neural Transfer Functions
 Neural Computing Surveys
, 1997
"... In this article advantages of various neural transfer functions are discussed. ..."
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Cited by 38 (29 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 33 (9 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 ...
Rulebase structure identification in an adaptivenetworkbased fuzzy inference system
 IEEE Trans. Fuzzy Syst
, 1994
"... AbstructFuzzy rulebase modeling is the task of identifying the structure and the parameters of a fuzzy IFTHEN rule base so that a desired input/output mapping is achieved. Recently, using adaptive networks to finetune membership functions in a fuzzy rule base has received more and more attention ..."
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Cited by 32 (0 self)
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AbstructFuzzy rulebase modeling is the task of identifying the structure and the parameters of a fuzzy IFTHEN rule base so that a desired input/output mapping is achieved. Recently, using adaptive networks to finetune membership functions in a fuzzy rule base has received more and more attention. In this paper we summarize Jang’s architecture of employing an adaptive network and the Kalman filtering algorithm to identify the system parameters. Given a surface structure, the adaptively adjusted inference system performs well on a number of interpolation problems. We generalize Jang’s basic model so that it can be used to solve classification problems by employing parameterized tnorms. We also enhance the model to include weights of importance so that feature selection becomes a component of the modeling scheme. Next, we discuss two ways of identifying system structures based on Jang’s architecture. For the topdown approach, we summarize several ways of partitioning the feature space and propose a method of using clustering objective functions to evaluate possible partitions. We analyze the overall learning and operation complexity. In particular, we pinpoint the dilemma between two desired properties: modeling accuracy and pattern matching efficiency. Based on the analysis, we suggest a bottomup approach of using rule organization to meet the conflicting requirements. We introduce a data structure, called a fuzzy binary boxtree, to organize rules so that the rule base can be matched against input signals with logarithmic efficiency. To preserve the advantage of parallel processing assumed in fuzzy rulebased inference systems, we give a parallel algorithm for pattern matching with a linear speedup. Moreover, as we consider the communication and storage cost of an interpolation model, it is important to extract the essential components of the modeled system and use the rest as a backup. We propose a rule combination mechanism to build a simplified version of the original rule base according to a given focus set. This scheme can be used in various situations of pattern representation or data compression, such as in image coding or in hierarchical pattern recognition.
Selecting input variables for fuzzy models
 Journal of Intelligent and Fuzzy Systems
, 1996
"... We present an efficient method for selecting important input variables when building a fuzzy model from data. Past methods for input variable selection require generating different models while searching for the optimal combination of variables; our method requires generating only one model that emp ..."
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Cited by 32 (1 self)
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We present an efficient method for selecting important input variables when building a fuzzy model from data. Past methods for input variable selection require generating different models while searching for the optimal combination of variables; our method requires generating only one model that employs all possible input variables. To determine the important variables, premises in the fuzzy rules of this initial model are systematically removed to search for the best simplified model without actually generating any new models. We also present an efficient method for generating the initial model that typically must incorporate a large number of input variables. These methods are illustrated through application to the benchmark Box and Jenkins gas furnace data; the results are compared with those of other fuzzy models found in literature. 1.
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 ..."
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Cited by 31 (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.
Support Vector Learning for Fuzzy RuleBased Classification Systems
, 2003
"... To design a fuzzy rulebased classi cation system (fuzzy classi er) with good generalization abilityina high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, support vector machine (SVM) is known to ..."
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Cited by 28 (1 self)
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To design a fuzzy rulebased classi cation system (fuzzy classi er) with good generalization abilityina high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, support vector machine (SVM) is known to have good generalization ability. More importantly, an SVM can work very well on a high (or even in nite) dimensional feature space. This paper investigates the connection between fuzzy classi ers and kernel machines, establishes a link between fuzzy rules and kernels, and proposes a learning algorithm for fuzzy classi ers. We rst show that a fuzzy classi er implicitly de nes a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function. Fuzzy inference on the IFpart of a fuzzy rule can be viewed as evaluating the kernel function. The kernel function is then proven to be a Mercer kernel if the reference functions meet certain spectral requirement. The corresponding fuzzy classi er is named positive de  nite fuzzy classi er (PDFC). A PDFC can be built from the given training samples based on a support vector learning approach with the IFpart fuzzy rules given by the support vectors. Since the learning process minimizes an upper bound on the expected risk (expected prediction error) instead of the empirical risk (training error), the resulting PDFC usually has good generalization. Moreover, because of the sparsity properties of the SVMs, the number of fuzzy rules is irrelevant to the dimension of input space. In this sense, we avoid the "curse of dimensionality." Finally, PDFCs with dierent reference functions are constructed using the su...