|Neuro-Fuzzy Systems||Neuro-Fuzzy Software|
This is the abstract of our view on neuro-fuzzy systems which we explain in more detail below.
Modern neuro-fuzzy systems are usually represented as special multilayer feedforward neural networks (see for example models like ANFIS , FuNe , Fuzzy RuleNet , GARIC , or NEFCLASS and NEFCON ). However, fuzzifications of other neural network architectures are also considered, for example self--organizing feature maps [2, 10]. In those neuro--fuzzy networks, connection weights and propagation and activation functions differ from common neural networks. Although there are a lot of different approaches [3, 4, 7, 8], we usually use the term neuro--fuzzy system for approaches which display the following properties:
|A neuro-fuzzy system is based on a fuzzy system which is trained by a learning algorithm derived from neural network theory. The (heuristical) learning procedure operates on local information, and causes only local modifications in the underlying fuzzy system.|
A neuro-fuzzy system can be viewed as a 3-layer feedforward
The first layer represents input variables, the middle (hidden) layer
represents fuzzy rules and the third layer represents output variables.
Fuzzy sets are encoded as (fuzzy) connection weights. It is not necessary to represent a fuzzy system like this to apply a learning algorithm to it. However, it can be convenient, because it represents the data flow of input processing and learning within the model.
Remark: Sometimes a 5-layer architecture is used, where the fuzzy sets are represented in the units of the second and fourth layer.
A neuro-fuzzy system can be always (i.e.\ before, during and
interpreted as a system of fuzzy rules. It is also possible to create
the system out of training data from scratch, as it is possible to
initialize it by prior knowledge in form of fuzzy rules.
Remark: Not all neuro-fuzzy models specifiy learning procedures for fuzzy rule creation.
The learning procedure of a neuro-fuzzy system takes the
of the underlying fuzzy system into account. This results in
constraints on the possible modifications applicable to the system
Remark: Not all neuro-fuzzy approaches have this property.
|A neuro-fuzzy system approximates an $n$-dimensional (unknown) function that is partially defined by the training data. The fuzzy rules encoded within the system represent vague samples, and can be viewed as prototypes of the training data. A neuro-fuzzy system should not be seen as a kind of (fuzzy) expert system, and it has nothing to do with fuzzy logic in the narrow sense.|
See also our list of online papers, and our list of publications.
Detlef Nauck (email@example.com), Feb. 7, 1997 18:35