Advantages of ANF systems: Although there are many ways to implement a Neuro-fuzzy system, the advan- tages described for these systems are remarkably uni- form across the literature. The advantages attributed to Neuro-fuzzy systems as compared to ANNs are usually related to the following aspects:
• Faster to train: This is due to the massive num- ber of connections present in the ANN, and the non-trivial number of calculations associated with each. As well, most neural fuzzy systems can be trained by going through the data once, whereas a neural network may need to be exposed to the same training data many times before it converges. • Less computational resources: Neural fuzzy sys-
tem is smaller in size and contains fewer internal connections than a comparable ANN, hence it is
faster and use significantly less resources.
• Offer the possibility to extract the rules: This is a major advantage over ANNs in that the rules governing a system can be communicated to the human users in an easily understandable form.
Limitation of ANF systems: The greatest limitation
in creating adaptive systems is known as the “Curse of
Dimensionality”, which is named after the exponen- tial growth in the number of features that the model has to keep track of as the number of input attributes increases. Each attribute in the model is a variable in the system, which corresponds to an axis in a multidi- mensional graph that the function is mapped into. The connections between different attributes correspond to the number of potential rules in the system as given by the formula:
Nrules = (Llingustic_terms)variables (Gorrostieta et al., 2006)
This formula becomes more complicated if there are different numbers of linguistic variables (fuzzy sets) covering each attribute dimension. Fortunately there are ways around this problem. As the neural fuzzy system is only approximating the function being modeled, the system may not need all the attributes to achieve the desired results.
Another area of criticism in the Neuro-fuzzy field is
related to aspects that can’t be learned or approximated. One of the most known aspects here is the caveat at- tached to the universal approximation. In fact, the function being approximated has to be continuous; a continuous function is a function that does not have
a singularity, a point where it goes to infinity. Other
functions that Adaptive Neuro-fuzzy systems may have problems learning are things like encryption algorithms, which are purposely designed to be resistant to this type of analysis.
Future developments: Predicting the future has always been hard; however for ANF technology the future expansion has been made easy because of the widespread use of its basis technology (neural networks and fuzzy logic). Mixing of these technologies creates synergies as they remediate to each other weaknesses. ANF technology allows complex system to be grown instead of someone having to build them.
One of the most promising areas for ANF systems is System Mining. There exist many cases where we wish to automate a system that cannot be systematically described in a mathematical manner. This means there is no way of creating a system using classical development methodologies (i.e. Programming a simulation.). If we have an adequately large set of examples of inputs and their corresponding outputs, ANF can be used to get a model of the system. The rules and their associated
Adaptive Neuro-Fuzzy Systems
fuzzy sets can then be extracted from this system and examined for details about how the system works. This knowledge can be used to build the system directly. One interesting application of this technology is to audit existing complex systems. The extracted rules could be used to determine if the rules match the exceptions of what the system is supposed to do, and even detect fraud actions. Alternatively, the extracted model may
show an alternative, and or more efficient manner of
implementing the system.
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Adaptive Neuro-Fuzzy Systems