By Nauck D.

Ailing this thesis neuro-fuzzy equipment for info research are mentioned. We ponder facts research as a strategy that's exploratory to some degree. If a fuzzy version is to be created in an information research strategy you will need to have studying algorithms on hand that aid this exploratory nature. This thesis systematically provides such studying algorithms, that are used to create fuzzy platforms from facts. The algorithms are specially designed for his or her strength to provide interpretable fuzzy platforms. it will be important that in studying the most benefits of a fuzzy method - its simplicity and interpretability - don't get misplaced. The algorithms are awarded in any such means that they could effortlessly be used for implementations. for example for neuro-fuzzv information analvsis the class svstem NEFCLASS is mentioned.

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**Extra info for Data Analysis with Neuro-Fuzzy Methods**

**Sample text**

This approach can be viewed as a cluster anlysis, where the clusters are hyperboxes which are aligned on a grid. It can therefore also be interpreted as hyperbox-oriented. 2. The clusters are given by membership functions and not vice versa. 1. STRUCTURE LEARNING 47 clustering can be well interpreted, because the fuzzy rules do not use individual fuzzy sets. It is also possible to use neural networks to create fuzzy rule bases. 10) can be used to obtain a (Sugeno-type) fuzzy rule base. An RBF network uses multi-dimensional radial basis functions in the nodes of its hidden layer.

Each domain is partitioned by fuzzy sets. Then an unsupervised learning algorithm modiﬁes the fuzzy sets to improve the partitioning of the data space. It is required that for each pattern the degrees of membership add up to 1. This approach can be viewed as a cluster anlysis, where the clusters are hyperboxes which are aligned on a grid. It can therefore also be interpreted as hyperbox-oriented. 2. The clusters are given by membership functions and not vice versa. 1. STRUCTURE LEARNING 47 clustering can be well interpreted, because the fuzzy rules do not use individual fuzzy sets.

However, there is a trade-oﬀ between readability and precision. We can force fuzzy systems to arbitrary precision, but we then we lose interpretability. To be very precise, a fuzzy system needs a ﬁne granularity and many fuzzy rules. It is obvious that the larger the rule base of a fuzzy system becomes the less interpretable it gets. If we are interested in a very precise prediction, then we are usually not so much interested in the interpretability of the solution. In this case we want to use another feature of fuzzy systems: the convenient combination of local models to an overall solution.