Are Fuzzy Systems Universal Approximators?

Klement, Erich Peter; Kóczy, László T.; Moser, Bernhard

doi:10.1080/03081079908935238

Cited by 62 publications

(23 citation statements)

References 26 publications

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“…Clearly, expression (15) is equivalent to Eq. (14) in case one deals with standard Gaussian functions.…”

Section: Neuro-fuzzy Architecturementioning

confidence: 99%

“…In many engineering applications it is a very important property, since it allows the transformation of data (information) into (human) knowledge. This problem has recently been faced for classiÿcation problems by Shanahan [25], Fuessel and Isermann [9], Binaghi [2], Sanchez [23], Ishibuchi [12]; in the prediction of process behavior by Maier [18]; in decision making and data mining by Gorzalczany and Piasta [10,15]; in theoretical developments on fuzzy systems by Klement [14]; in intelligent control and robotics by Stoica [26]; in function approximation, by Nauck and Kruse [19]. Jin [13] addresses interpretability by using similarity measures to check the similarity of each rule; the structure and parameters of the fuzzy rules are optimized and interpretability is improved by ÿne-tuning the fuzzy rules with regularization.…”

Section: Introductionmentioning

confidence: 99%

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Interpretability and learning in neuro-fuzzy systems

Paiva

Dourado

2004

Fuzzy Sets and Systems

107

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A methodology for the development of linguistically interpretable fuzzy models from data is presented. The implementation of the model is conducted through the training of a neuro-fuzzy network, i.e., a neural net architecture capable of representing a fuzzy system. In the ÿrst phase, the structure of the model is obtained by means of subtractive clustering, which allows the extraction of a set of relevant rules based on a set of representative input-output data samples. In the second phase, the parameters of the model are tuned via the training of a neural network through backpropagation. In order to attain interpretability goals, the method proposed imposes some constraints on the tuning of the parameters and performs membership function merging. In this way, it will be easy to assign linguistic labels to each of the membership functions obtained, after training. Therefore, the model obtained for the system under analysis will be described by a set of linguistic rules, easily interpretable.

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“…Clearly, expression (15) is equivalent to Eq. (14) in case one deals with standard Gaussian functions.…”

Section: Neuro-fuzzy Architecturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interpretability and learning in neuro-fuzzy systems

Paiva

Dourado

2004

Fuzzy Sets and Systems

107

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“…Since 1993, the FLLL has been involved in a number of projects, most of which resulted in software packages for quality control (see, e.g., [1]- [10]). …”

Section: Flll Experiencementioning

confidence: 99%

Applications of soft computing - some personal reflections

Klement

1998

Soft Computing - A Fusion of Foundations, Methodologies and App

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“…Fuzzy algorithm is used just for realisation of specific, non-linear controller here. It has been proved that fuzzy system can approximate, realise any function as exacdy as needed (Kosko, 1992), (Klement, 1995), (Bauer, 1994). So any control law, any control function, including that one, which realise optimal control can be made by fuzzy controller as weIl.…”

Section: Initial Ideamentioning

confidence: 99%