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Basic Tools for Fuzzy Modeling
"... ABSTRACT: The lesson will begin with the basics of fuzzy set theory. Fuzzy set theory was first introduced in 1965 by Lotfi A. Zadeh [Zadeh 1965]. It may be regarded both as a generalization of classical set theory and as a generalization of dual logic. In knowledgebased methods, fuzzy sets are emp ..."
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ABSTRACT: The lesson will begin with the basics of fuzzy set theory. Fuzzy set theory was first introduced in 1965 by Lotfi A. Zadeh [Zadeh 1965]. It may be regarded both as a generalization of classical set theory and as a generalization of dual logic. In knowledgebased methods, fuzzy sets are employed primarily to carry out the formal, contentdefined mapping of human knowledge. This makes it possible to process human empirical knowledge with electronic dataprocessing systems. Clustering procedures belong to the algorithmic methods of data analysis. The first aim of clustering is to find structures contained within groups of data. These structures are usually classes to which objects from the data set are assigned. The result of the classification process is usually used as a classifier. Classical clustering assigns each object to exactly one class, whereas in fuzzy clustering the objects are assigned different degrees of membership to the different classes. Traffic data (speed and traffic volume) are measured by inductive loops on the motorway and is forwarded to the Traffic Control Center TCC. The major goal of the TCC is to analyse the traffic situation as basis for control and traffic information services. For that goal the detected trafic data are fuzzified and aggegated by fuzzy knowledgebased methods to classify the traffic situation by linguistic variables like „congested“, „dense “ or „free flow“.