By Nauck D.

Ailing this thesis neuro-fuzzy tools for information research are mentioned. We think of facts research as a strategy that's exploratory to a point. If a fuzzy version is to be created in a knowledge research strategy it is very important have studying algorithms on hand that help this exploratory nature. This thesis systematically offers such studying algorithms, which are used to create fuzzy structures from facts. The algorithms are specially designed for his or her strength to provide interpretable fuzzy platforms. it is vital that in studying the most benefits of a fuzzy procedure - its simplicity and interpretability - don't get misplaced. The algorithms are awarded in one of these approach that they could without problems be used for implementations. as an instance for neuro-fuzzv info analvsis the class svstem NEFCLASS is mentioned.

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Vr } and output layer UO = {z1 , . . , zm }. The number r of hidden units is not larger than the number s of training patterns of a fixed learning problem L˜ which is given for the RBFN. (ii) The weights W (u, v), with u ∈ UI and v ∈ UH , are given by r ≤ s arbitrary ˜ W (uk , vi ) = xj ,k , with but different input patterns of the learning problem L: i k ∈ {1, . . , n}, i ∈ {1, . . , r}, ji ∈ {1, . . , s}. (iii) A assigns an activation function to each unit u ∈ U . For all input units u ∈ UI the activation function Au is used to calculate the activation au : au = Au (exu ) = exu .

INTERPRETABLE FUZZY SYSTEMS FOR DATA ANALYSIS 37 Fuzzy systems have numeric interpolation capabilities and are therefore well-suited for function approximation and prediction. On the other hand they partition variables by fuzzy sets that can be labeled with linguistic terms. Thus they also have a symbolic nature and can be intuitively interpreted. However, there is a trade-off between readability and precision. We can force fuzzy systems to arbitrary precision, but we then we lose interpretability.

However, in many applications expert knowledge is only partially available or not at all. In these cases it must be possible to create a rule base from scratch relying only on the training data. 1. These approaches have drawbacks when the resulting rule base must be interpretable. Readability of the solution can be guaranteed more easily, if the granularity of the data space is defined in advance and the data space is structured by pre-defined fuzzy partitions for all variables. 2 describes supervised rule learning algorithms that are based on a structured data space.

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