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# Online Documents (before 1997)

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 Informations Neuro-Fuzzy Papers Neuro-Fuzzy Bibliograpy Fuzzy Cluster Analysis Papers Papers about Uncertainty in Knowledge Based Systems Go to the list of our publications

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## Neuro-Fuzzy Papers

### of the year:

 1992 1993 1994 1995 1996 1997 1998

## Neuro-Fuzzy Papers of 1992

 Eklund/Klawonn/Nauck: Distributing Errors in Neural Fuzzy Control. Paper of IIZUKA 92, Japan, 1992. (iizuka92.ps.gz) ABSTRACT: This paper describes a procedure to integrate techniques for the adaptation of membership functions in a linguistic variable based fuzzy control environment. Nauck/Klawonn/Kruse: Fuzzy Sets, Fuzzy Controllers and Neural Networks. Presented at a workshop in Postsdam/Germany, 1992. (berlin.ps.gz) ABSTRACT: This paper gives a short introduction into Fuzzy Set Theory, presents an overview on fuzzy controllers, and discusses possible combinations between fuzzy controllers and neural networks. Fuzzy Sets suggested by L.A. Zadeh offer a possibility to formally describe linguistic expressions like tall, fast, medium, etc., and to operate on them. Fuzzy controllers use fuzzy sets to represent linguistic values of the input and output variables of a physical system, and describe their relations by fuzzy if-then rules. The idea of fuzzy control is to simulate a human expert who is able to control the system by translation of his or her linguistic inference rules into a control function. Artificial neural networks are highly parallel architectures consisting of simple processing elements which communicate through weighted connections. They are able to approximate functions or to solve certain tasks by learning from examples. Combinations of neural networks and fuzzy controllers can help to overcome problems in the design and tuning processes of fuzzy controllers. Nauck/Kruse: Interpreting changes in the fuzzy sets of a self adapting neural fuzzy controller. Paper of 2nd IFIS workshop, 1992. (ifis92.ps.gz) ABSTRACT: We describe a procedure for the adaptation of membership functions in a fuzzy control environment by using neural network learning principles. The changes in the fuzzy sets can be easily interpreted. By using a fuzzy error that is propagated back through the architecture of our fuzzy controller, we receive an unsupervised learning technique, where each rule tunes the membership functions of its antecedent and its consequence. Nauck/Kruse: A neural fuzzy controller learning by fuzzy error propagation. Paper of NAFIPS '92, Puerto Vallarta, Mexico, 1992. (nafips92.ps.gz) ABSTRACT: In this paper we describe a procedure to integrate techniques for the adaptation of membership functions in a linguistic variable based fuzzy control environment by using neural network learning principles. This is an extension to our work in [ (iizuka92.ps.gz)]. We solve this problem by definining a fuzzy error that is propagated back through the architecture of our fuzzy controller. According to this fuzzy error and the strength of its antecedent each fuzzy rule determines its amount of error. Depending on the current state of the controlled system and the control action derived from the conclusion, each rule tunes the membership functions of its antecedent and its conclusion. By this we get an unsupervised learning technique that enables a fuzzy controller to adapt to a control task by knowing just about the global state and the fuzzy error.

## Neuro-Fuzzy Papers of 1993

 Nauck/Klawonn/Kruse: Combining Neural Networks and Fuzzy Controllers. Presented at FLAI'93 in Linz/Austria, 1993. (flai93.ps.gz) ABSTRACT: 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. Nauck: NEFCON-I: Eine Simulationsumgebung fuer Neuronale Fuzzy Regler Paper of the german GI-Workshop "Fuzzy-Systeme'93" in Braunschweig, 21.-22. Oct, 1993 (in German). For the english version see Nauck: Building Neural Fuzzy Controllers with NEFCON-I in: Kruse/Gebhardt/Klawonn: Fuzzy Systems in Computer Sience. Vieweg, Wiesbaden, 1994 (ISBN: 3-528-05456-5), pp.141-151. (bs-fuz93-german.ps.gz) ABSTRACT (the paper is in German): The NEFCON model presented in this paper has the advantage to be both interpretable as a neural network with fuzzy sets as its weights, and as a fuzzy controller. The learning algorithm based on this model does not result in structural changes, and does not affect the semantics of the underlying fuzzy controller. Nauck/Kruse: A fuzzy neural network learning fuzzy control rules and membership functions by fuzzy error backpropagation. Paper of IEEE-ICNN in San Francisco, 1993. (icnn93.ps.gz) ABSTRACT: 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 three-layered architecture and uses fuzzy sets as its weights. The fuzzy error backpropagation algorithm, a special learning algorithm inspired by the standard BP-procedure for multilayer neural networks, is able to learn the fuzzy sets. The extended version that is presented here is also able to learn fuzzy-if-then 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.

## Neuro-Fuzzy Papers of 1994

 Nauck: A Fuzzy Perceptron as a Generic Model for Neuro-Fuzzy Approaches. Paper of the 2nd German GI-Workshop "Fuzzy-Systeme'94 in Munich, Oct. '94" (paper in English). (fuzsys94.ps.gz) ABSTRACT: This paper presents a fuzzy perceptron as a generic model of multilayer fuzzy neural networks, or neural fuzzy systems, respectively. This model is suggested to ease the comparision of different neuro-fuzzy approaches that are known from the literature. A fuzzy perceptron is not a fuzzification of a common neural network architecture, and it is not our intention to enhance neural learning algorithms by fuzzy methods. The idea of the fuzzy perceptron is to provide an architecture that can be initialized with prior knowledge, and that can be trained using neural learning methods. The training is carried out in such a way that the learning result is interpretable in the form of linguistic fuzzy if-then rules. Next to the advantage of having a generic model to compare neuro-fuzzy models, the fuzzy perceptron can be specialized e.g. for data analysis and control tasks. Nauck/Kruse: NEFCON-I: An X-Window Based Simulator for Neural Fuzzy Controllers. Paper of IEEE-ICNN 1994 at WCCI'94 in Orlando. (icnn94.ps.gz) ABSTRACT: In this paper we present NEFCON-I, a graphical simulation environment for building and training neural fuzzy controllers based on the NEFCON model [ (icnn93.ps.gz)]. NEFCON-I is an X-Window based software that allows a user to specify initial fuzzy sets, fuzzy rules and a rule based fuzzy error. The neural fuzzy controller is trained by a reinforcement learning procedure which is derived from the fuzzy error backpropagation algorithm for fuzzy perceptrons /CITE{nauck93d}. NEFCON-I communicates with an external process where a dynamical system is simulated. NEFCON-I is freely available on the internet. Nauck/Kruse: Choosing Appropriate Neuro-Fuzzy Models. Paper of EUFIT'94 1994 in Aachen, Germany. (eufit94.ps.gz) ABSTRACT: To use fuzzy controllers for automization tasks appropriate fuzzy sets and fuzzy rules have to be defined. This can be difficult in some domains, and the resulting controller has to be tuned. Neuro-fuzzy models can help in this tuning process by adapting fuzzy sets and creating fuzzy rules. Combinations of neural networks and fuzzy controllers are suitable if there is only partial knowledge in the form of fuzzy sets and fuzzy rules, but training data is available. To be be able to choose an appropriate model one has to know the different approaches to neural fuzzy control. In this paper we present a classification of generic neural fuzzy controllers and give some hints when to choose a certain type of model.

## Neuro-Fuzzy Papers of 1995

 Nauck/Kruse: NEFCLASS - A Neuro-Fuzzy Approach for the Classification of Data. Paper of Symposium on Applied Computing 1995 (SAC'95) in Nashville. (acm95.ps.gz) ABSTRACT: In this paper we present NEFCLASS, a neuro-fuzzy system for the classification of data. This approach is based on our generic model of a fuzzy perceptron which can be used to derive fuzzy neural networks or neural fuzzy systems for specific domains. The presented model derives fuzzy rules from data to classify patterns into a number of (crisp) classes. NEFCLASS uses a supervised learning algorithm based on fuzzy error backpropagation that is used in other derivations of the fuzzy perceptron. Nauck: Beyond Neuro-Fuzzy: Perspectives and Directions. Paper of Third European Congress on Intelligent Techniques and Soft Computing (EUFIT'95) in Aachen. (eufit95.ps.gz) ABSTRACT: The interest in neuro-fuzzy systems has grown tremendously over the last few years. First approaches concentrated mainly on neuro-fuzzy controllers, whereas newer approaches can also be found in the domain of data analysis. After successful applications in Japan neuro-fuzzy concepts also find their way into the European industries, though mainly simple models, like FAMs, still prevail. This paper shortly reviews some modern neuro-fuzzy concepts. After this a generic neuro-fuzzy model is presented, that serves a foundation for specific derived neuro-fuzzy applications, this is shown with a model for neuro-fuzzy data analysis, which we see as an important perspective for the neuro-fuzzy domain. The paper concludes with some thoughts on further research directions that go beyond simple neuro-fuzzy control applications. Nauck/Kruse/Stellmach: New Learning Algorithms for the Neuro-Fuzzy Environment NEFCON-I. Paper for the Third German GI-Workshop "Fuzzy-Neuro-Systeme'95", Darmstadt, Germany, November 15 - 17, 1995. (fuz95a.ps.gz) ABSTRACT: NEFCON-I is an X-Window based graphical simulation environment for neuro-fuzzy controllers, and it is freely available on the Internet. The NEFCON model is based on a generic fuzzy perceptron, and it is able to learn fuzzy sets and fuzzy rules by a reinforcement learning algorithm that uses a fuzzy error measure. The former version of NEFCON had some restrictions on the form of the membership functions of the conclusions, and an expensive rule learning procedure. The new version of the NEFCON model incorporates new learning algorithms for both the fuzzy sets, and the fuzzy rules, and it removes the restrictions on the conclusion fuzzy sets. Klawonn/Nauck/Kruse: Generating Rules from Data by Fuzzy and Neuro-Fuzzy Methods. Paper for the Third German GI-Workshop "Fuzzy-Neuro-Systeme'95", Darmstadt, Germany, November 15 - 17, 1995. (fuz95b.ps.gz) ABSTRACT: In this paper we present an approach to neuro-fuzzy classification that is able to learn fuzzy sets and fuzzy rules from data. The fuzzy rules that are created by this approach can be very well interpreted, however, they do not classify as good as the rules derived by sophisticated fuzzy clustering algorithms. They on the other hand supply usually unsatisfying fuzzy sets what makes it hard to interpret the rules. Combining both approaches can eliminate these disadvantages. Kruse/Nauck: Learning Methods for Fuzzy Systems. Paper for the Third German GI-Workshop "Fuzzy-Neuro-Systeme'95", Darmstadt, Germany, November 15 - 17, 1995. (fuz95c.ps.gz) ABSTRACT: In this paper we discuss one aspect on learning methods for fuzzy systems: the semantics of neuro-fuzzy systems. We show how a neuro-fuzzy system should be structured, so it can be easily interpreted, and how learning algorithms for these models can be constructed. Learning in neuro-fuzzy systems should always lead to interpretable fuzzy rules. As an example, we compare the fuzzy rules resulting from a fuzzy clustering procedure to the the learning results of a neuro-fuzzy system in the context of pattern classification.

## Neuro-Fuzzy Papers of 1996

 Nauck/Nauck/Kruse:Generating Classification Rules with the Neuro--Fuzzy System NEFCLASS. Paper of NAFIPS'96 in Berkeley. (nafips96.ps.gz) ABSTRACT: Neuro-fuzzy systems have recently gained a lot of interest in research and application. In this paper we discuss NEFCLASS, a neuro-fuzzy approach for data analysis. We present new learning strategies to derive fuzzy classification rules from data, and show some results. Klawonn/Nauck:Neuro-Fuzzy Classification Initialized by Fuzzy Clustering. Paper of EUFIT'96 in Aachen. (eufit96.ps.gz) ABSTRACT: In this paper we discuss how a neuro-fuzzy classifier can be initialized by rules generated by fuzzy clustering. The neuro-fuzzy classifier NEFCLASS can learn fuzzy classification rules completely from data. The learning algorithm for fuzzy sets can be constrained in order to obtain interpretable classifiers. However, fuzzy clustering provides more sophisticated rule learning procedures. We show that the learning process of NEFCLASS produces better results, if it is initialized by fuzzy clustering. Kruse/Nauck:Neuronale Fuzzy-Systeme. Beitrag zur Herbstschule Konnektionismus und Neuronale Netze 1996 (HeKoNN'96). (hekonn96.ps.gz)(paper in German) ABSTRACT: Dieser Beitrag gibt eine kurze Einführung in Fuzzy-Systeme und Neuro-Fuzzy-Systeme (12 Seiten).

## Neuro-Fuzzy Papers of 1997

 Nauck/Kruse:Ein Neuro-Fuzzy System zur Funktionsapproximation. Beitrag zum 2. Internationalen Workshop Neuronale Netze in Ingenieuranwendungen 1997 in Stuttgart. (nniia97.ps.gz) (paper in German) ABSTRACT: In diesem Beitrag wird eine Neuro-Fuzzy-Architektur zur Funktionsapproximation vorgestellt. Der Lernalgorithmus ist in der Lage, sowohl die Struktur als auch die Parameter eines Fuzzy-Systems zu bestimmen. Der Ansatz entspricht einer Erweiterung der bereits vorgestellten Modelle NEFCON und NEFCLASS, die für regelungstechnische Anwendungen bzw. Klassifikationsaufgaben eingesetzt werden. Das vorgestellte Modell NEFPROX ist allgemeiner und kann für beliebige auf Funktionsapproximation basierenden Anwendungen eingesetzt werden. Nürnberger/Nauck/Kruse: Neuro-Fuzzy-Regelung mit NEFCON unter MATLAB/SIMULINK, In Proc. of Neuronale Netze in Ingenieuranwendungen 1997 (NNIIA’97), Stuttgart, Germany. (nniia97nnk.ps.gz) (paper in German) ABSTRACT: Zur Erstellung und Optimierung von Fuzzy-Reglern werden häufig Verfahren eingesetzt, die aus der Kombination Neuronaler Netze mit Fuzzy-Reglern entstanden sind. Im folgenden wird die Implementierung eines hybriden Neuro-Fuzzy-Modells beschrieben, das ist in der Lage ist, die Regelbasis eines konventionellen Fuzzy-Reglers zu erlernen und zu optimieren. Durch die Implementierung unter dem Simulationssystem MATLAB/SIMULINK, kann das Modell sehr einfach zur Entwicklung und Optimierung von Fuzzy-Reglern für verschiedenste dynamische Systeme eingesetzt werden. Nauck/Kruse: Neuro-Fuzzy Systems for Function Approximation. Paper of the 4. International Workshop Fuzzy-Neuro Systems 1997 in Soest. (fns97.ps.gz) ABSTRACT: We propose a neuro-fuzzy architecture for function approximation based on supervised learning. The learning algorithm is able to determine the structure and the parameters of a fuzzy system. The approach is an extension to our already published NEFCON and NEFCLASS models which are used for control or classification purposes. The proposed extended model, which we call NEFPROX, is more general and can be used for any application based on function approximation Nürnberger/Nauck/Kruse: Neuro-Fuzzy Control Based on the NEFCON-Model Under MATLAB/SIMULINK. Presented at the 2nd On-line World Conference on Soft Computing in Engineering Design and Manufacturing (WSC2) On the Internet (World-Wide Web). (wsc297.ps.gz) or (wsc2.html) ABSTRACT: A first prototype of a fuzzy controller can be designed rapidly in most cases. The optimization process is usually more time consuming since the system must be tuned by 'trial-and-error' methods. To simplify the design and optimization process learning techniques derived from neural networks (so called neuro-fuzzy approaches) can be used. In this paper we describe an updated version of the neuro-fuzzy model NEFCON. This model is able to learn and to optimize the rulebase of a Mamdani-like fuzzy controller online by a reinforcement learning algorithm that uses a fuzzy error measure. Therefore we also describe some methods to determine a fuzzy error measure of a dynamic system. Besides we present an implementation of the model and an application example under the MATLAB/SIMULINK development environment. The optimized fuzzy controller can be detached from the development environment and can be used in realtime environments. The tool is available via the Internet. Nauck/Kruse: What are Neuro-Fuzzy Classifiers?">NEFCLASS Paper appears in Proc. Seventh International Fuzzy Systems Association World Congress IFSA'97, Vol. IV, pp. 228-233, Academia Prague, 1997. (ifsa97_1.ps.gz) ABSTRACT: Neuro-fuzzy combination are considered for several years already. However, the term neuro-fuzzy still lacks of proper definition, and it has the flavor of a buzz word. In this paper we try to give it a meaning in the context of fuzzy classification systems. From our point of view neuro-fuzzy means the employment of heuristic learning strategies derived from the domain of neural network theory to support the development of a fuzzy system. We illustrate our ideas using our NEFCLASS model which is used to create a fuzzy classification system from data. Nauck/Kruse: New Learning Strategies for NEFCLASS Paper appears in Proc. Seventh International Fuzzy Systems Association World Congress IFSA'97, Vol. IV, pp. 50-55, Academia Prague, 1997. (ifsa97_2.ps.gz) ABSTRACT: Neuro-fuzzy classification systems offer means to obtain fuzzy classification rules by a learning algorithm. It is usually no problem to find a suitable fuzzy classifier by learning from data, however, it can be hard to obtain a classifier that can be interpreted conveniently. In this paper we discuss extensions to the learning algorithms of NEFCLASS, a neuro-fuzzy approach for data analysis that we have presented before. We show how interactive strategies for pruning rules and variables from a trained classifier can enhance its interpretability. Nauck: Neuro-Fuzzy Systems: Review and Prospects Paper appears in Proc. Fifth European Congress on Intelligent Techniques and Soft Computing (EUFIT'97), Aachen, Sep. 8-11, 1997, pp. 1044-1053. (eufit97b.ps.gz) ABSTRACT: This paper reviews neuro-fuzzy systems, which combine methods from neural network theory with fuzzy systems. Such combinations have been considered for several years already. However, the term neuro-fuzzy still lacks proper definition, and still has the flavour of a buzzword to it. Surprisingly few neuro-fuzzy approaches do actually employ neural networks, even though they are very often depicted in form of some kind of neural network structure. However, all approaches display some kind of learning capability, as it is known from neural networks. This means, they use algorithms which enable them to determine their parameters from training data in an iterative process. In this paper we review some of our neuro-fuzzy approaches to illustrate our view of neuro-fuzzy techniques and our understanding on how these approaches should be used. From our point of view neuro-fuzzy means using heuristic learning strategies derived from the domain of neural network theory to support the development of a fuzzy system.

## Neuro-Fuzzy Papers of 1998

 Nauck/Kruse: How the Learning of Rule Weights Affects the Interpretability of Fuzzy Systems Paper appears in Proc. IEEE International Conference on Fuzzy Systems 1998 (FUZZ-IEEE'98), Anchorage, AK, May 4-9, 1998, pp. 1235-1240. (wcci98_1.ps.gz) ABSTRACT: Neuro-fuzzy systems have recently gained a lot of interest in research and application. These are approaches that learn fuzzy systems from data. Many of them use rule weights for this task. In this paper we discuss the influence of rule weights on the interpretability of fuzzy systems. We show how rule weights can be equivalently replaced by modifications in the membership functions of a fuzzy system. By this we elucidate the effects rule weights have on a fuzzy rule base. Using our neuro-fuzzy model NEFCLASS we demonstrate at a simple example the problems of using rule weights, and we show, that learning in fuzzy systems can be done without them. Nauck/Kruse: A Neuro-Fuzzy Approach to Obtain Interpretable Fuzzy Systems for Function Approximation Paper appears in Proc. IEEE International Conference on Fuzzy Systems 1998 (FUZZ-IEEE'98), Anchorage, AK, May 4-9, 1998, pp. 1106-1111. (wcci98_2.ps.gz) ABSTRACT: Fuzzy systems can be used for function approximation based on a set of linguistic rules. We present a method to obtain the necessary parameters for such a fuzzy system by a neuro-fuzzy training method. The learning algorithm is able to determine the structure and the parameters of a fuzzy system from sample data. The approach is an extension to our already published NEFCON and NEFCLASS models which are used for control or classification purposes. The NEFPROX model, which is discussed in this paper is more general, and it can be used for any problem based on function approximation. We especially consider the problem to obtain interpretable fuzzy systems by learning.

## Neuro-Fuzzy bibliography

A bibliography of articles, books, etc. of neuro-fuzzy combinations. Will be updated from time to time. Format is BibTeX, ASCII. (fuzzy-nn.bib)

### If you don't know what BibTeX is:

The file is a BibTeX database ready to use in LaTeX documents. You can refer to it via the \cite{} command. Then you have to use the bibtex command after you completed the first latex run. You will then receive a file that can be used by LaTeX in the next two runs to fill your citations in your text with the correct references. For more information see e.g. the LaTeX book by Leslie Lamport.

If you want to print the whole file, you can use the following latex document:

\documentstyle{article} \begin{document} \nocite{*} \bibliography{fuzzy-nn} \bibliographystyle{alpha} \end{document} Put this in a file, say foo.tex and then use the commands: latex foo bibtex foo latex foo latex foo You will receive a dvi-file containing all references in alphabetical order. If you don't have latex, you can get the bibliography in printable form. Choose between dvi format fuzzy-nn.dvi.gz or PostScript format fuzzy-nn.ps.gz.

## Papers about Fuzzy Cluster Analysis

 F.Klawonn and R. Kruse: Derivation of Fuzzy Classification Rules from Multidimensional Data. fuzz_class_rule.ps.gz ABSTRACT: This paper describes techniques for deriving fuzzy classification rules based on special modified fuzzy clustering algorithms. The basic idea is that each fuzzy cluster induces a fuzzy clssification rule. The fuzzy sets appearing in a rule associated with a fuzzy cluster are obtained by projecting the cluster to the one-dimensional coordinate spaces. In order to allow clusters of varying shape and size we derive special fuzzy clustering algorithms which are searching for clusters in the form of axes-parallel hyper-ellipsoids. Our method can be applied to classification tasks where the classification of the sample data is known as well as when it is not known.

## Papers about Uncertainty in Knowledge Based Systems

 Jörg Gebhardt, Rudolf Kruse: Learning Possibilistic Networks from Data. learn_poss_net.ps.gz ABSTRACT: We introduce a method for inducing the structure of (causal) possibilistic networks from databases of sample cases. In comparison to the construction of Bayesian belief networks, the proposed framework has some advantages , namely the explicit consideration of imprecise (set valued) data, and the realization of a controlled form of information compression in order to increase the efficiency of the learning strategy as well as approximate reasoning using local propagation techniques. Our learning method has been applied to reconstruct a non-singly connected network of 22 nodes and 24 arcs without the need of any priori supplied node ordering.