AI - a Guide to Intelligent Systems.pdf - Member of EEPIS

ANFIS: ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM
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Recently, Roger Jang from the Tsing Hua University, Taiwan, proposed a
neural network that is functionally equal to a Sugeno fuzzy inference model
(Jang, 1993). He called it an Adaptive Neuro-Fuzzy Inference System or ANFIS.
8.4 ANFIS: Adaptive Neuro-Fuzzy Inference System
The Sugeno fuzzy model was proposed for a systematic approach to generating
fuzzy rules from a given input-output data set. A typical Sugeno fuzzy rule can be
expressed in the following form:
IF x 1 is A 1
AND x 2 is A 2
.....
AND x m is A m
THEN y ¼ f ðx 1 ; x 2 ; ...; x m Þ
where x 1 ; x 2 ; ...; x m are input variables; A 1 ; A 2 ; ...; A m are fuzzy sets; and y is
either a constant or a linear function of the input variables. When y is a constant,
we obtain a zero-order Sugeno fuzzy model in which the consequent of a rule is
specified by a singleton. When y is a first-order polynomial, i.e.
y ¼ k 0 þ k 1 x 1 þ k 2 x 2 þ ...þ k m x m
we obtain a first-order Sugeno fuzzy model.
Jang’s ANFIS is normally represented by a six-layer feedforward neural
network. Figure 8.10 shows the ANFIS architecture that corresponds to the firstorder
Sugeno fuzzy model. For simplicity, we assume that the ANFIS has two
inputs – x1 and x2 – and one output – y. Each input is represented by two fuzzy
Figure 8.10
Adaptive Neuro-Fuzzy Inference System (ANFIS)