Prof. Dr. Frank Klawonn 
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Fuzzy Cluster Analysis and Classification 
Cluster analysis is a technique for grouping data and finding structures in data. The most common application of clustering methods is to partition a data set into clusters or classes, where similar data are assigned to the same cluster whereas dissimilar data should belong to different clusters. In real applications there is very often no sharp boundary between clusters so that fuzzy clustering is often better suited for the data. Membership degrees between zero and one are used in fuzzy clustering instead of crisp assigments of the data to clusters. Fuzzy clustering can be applied as an unsupervised learning strategy in order to group data. But fuzzy clustering is also very useful for constructing fuzzy ifthen rules from data. The structure of the rules depends on the considered application. For fault diagnosis and other classification tasks the rules aim at deciding to which class in a finite set of classes (like ok/tolerable/faulty) a given datum should be assigned. In system identification or function approximation the rules describe a usually continuous connection between different variables (like in fuzzy control). Another area of application of fuzzy cluster analysis is image analysis and recognition. Segmentation and the detection of special geometrical shapes like circles and ellipses can be achieved by socalled shell clustering algorithms. Some of the algorithms that we are using or that we have developed in cooperation with the Neural Networks and Fuzzy Systems Research Group at the University of Magdeburg are distributed and sold by companies like MIT GmbH and TransferTech. More details about this work on fuzzy clustering can be found in the list of publications, especially in the German book FuzzyClusteranalyse. For further information please contact Frank Klawonn. 
NeuroFuzzy Systems and Neural Networks 
Artificial neural network models were originally invented in order to simulate the behaviour of single brain cells or small groups of brain cells. Nowadays, a lot of neural networks models have abstracted very far from the original idea of modeling brain cells. To provide an adaptive system that can learn from examples has become the main purpose of neural networks for technical and other applications. Neural networks consist of artificial neurons, that can be interpreted as very simple automata or processors, and weighted connections between these neurons. They perform learning tasks by modifying the weighted connections and sometimes also some other parameters like thresholds in the neurons. In this way, neural networks are able to solve tasks like classification, process control and clustering on the basis of training data. One of their main disadvantage is their black box behaviour. What neural networks actually learn from data is encoded in the connection weights so that knowledge extraction after training them with data as well as incorporating a priori knowledge before training is almost impossible. This is the point were fuzzy systems come into the game. Fuzzy systems were originally designed for representing human knowledge that involves usually some aspects of vaguenes und uncertainty. However, the original fuzzy systems were not designed to learn from examples or to adjust themselves to data. Neurofuzzy systems aim at combining the advantages of neural networks and fuzzy systems in order to have models that are well suited for knowledge representation and extraction and are apable to learn from sample data. More details about this work on neurofuzzy systems and neural networks can be found in the list of publications, especially in the book Foundations of NeuroFuzzy Systems or its German version Neuronale Netze und FuzzySysteme. For further information please contact Frank Klawonn. 
Evolutionary Algorithms 
It is well known that animals and plants are nearly perfectly fitted to their environment. Their bodies and abilities can be seen as results of natural evolution  a process based on principles like survival of the fittest and mutation. Using concepts that are motivated by the process of natural evolution for solving optimization problemd is the underlying idea in evolutionary algorithms. Paradigms like genetic algorithms, mainly for discrete optimization, evolution strategies, for continuous problems, and genetic programming for nonparametric problems are counted as typical examples of evolutionary algorithms. Evolutionary algorithms provide a very general optimization framework that does not require special properties from the objective function. However, as a kind of 'general problem solver' elementary evolutionary algorithms are not always well suited for problems where optimization techniques exist that were designed for the special problem and that exploit problem specific properties. Therefore, it is very important to incorporate problem dependend knowledge in the design of an evolutionary algorithm. For further information please contact Frank Klawonn. 
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