Adaptive neuro-fuzzy inference system

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As Adaptive Neuro Fuzzy Inference System (ANFIS) is in the neuro-computer science an artificial neural network referred to which various illustrating fuzzy - inference - ie mechanisms for logical off Close fuzzy sets - is used. The usual mechanisms are Takagi-Sugeno controllers and Tsukamoto controllers . The name of an ANFIS network is derived from the highest polynomial degree in the THEN part of the control algorithm (e.g. ANFIS first degree ).

ANFIS-based systems combine the principles of neural networks with those of fuzzy logic and thus combine the advantages of both systems:

  • Processing with the inclusion of linguistic (natural language) aspects of the information
  • Decisions based on the level of uncertainty
  • Ability to learn

architecture

In general, an ANFIS can be divided into five stages. If it is known that the Sugeno-Takagi controller has n input quantities ( x 1 , ..., x n ) and m rules, these stages have the following tasks:

  1. At the input of the network, the input variables are determined and each of the premises P ij is calculated. Here i remains in the range {1,…, m } and j in the {1,…, n }. Here is part of P ij to rule i and gets input variable j . It is important to note that not all P ij need exist. It depends on the form of the rules.
  2. These premises are linked by fuzzy operators so that the end premises of the whole IF-parts can be determined. For example, if the first IF part is " P 11 (x 1 ) AND P 12 (x 2 ) ", the result of this whole expression will be an end premise. These end premises are called w 1 , w 2 ,…, w m .
  3. Once all of the end premises are found, they can be normalized by dividing each end premise by the sum of all premises. . This is how you get the new values .
  4. In order to realize the Sugeno-Takagi inference, the normalized end premises have to be multiplied by the corresponding polynomial functions f 1 , ..., f m . These polynomial functions get the input parameters again. All in all, the result of each rule is a product .
  5. Finally, the last determined values ​​are added up and output.

example

A simple Sugeno-Takagi controller with two input quantities and two rules is now observed: 

WENN P11(x1) UND P12(x2) DANN f1(x1, x2)

WENN P21(x1) UND P22(x2) DANN f2(x1, x2)

The ANFIS implementing this controller will look like this:

Sketch of the upper system

Learn

One of the well-known learning algorithms for an ANFIS is the so-called hybrid algorithm that z. For example, during the forward phase of backpropagation, the premise parameters can be assumed to be constant and consistent parameters can be optimized using the least squares method , while in the backward phase the consistent parameters are considered constant and the premise parameters are optimized using the gradient method .

literature