Which "AND" operator is used for the fuzzy rules created by ANFIS?

Is it the product, boolean, or Zadeh? Does anyone know? Thanks in advance.

Answer 1

[Sam Chak]

Hi @Gary

By default, ANFIS generates a single-output Sugeno fuzzy inference system. The 'AND' operator is specified in one of the FIS properties. Look out for "AndMethod". By default, the product of the fuzzified input values is used.

x1   = (-1:0.01:1)';
x2  = x1;
y   = x1 + x2;
data= [x1, x2, y];
fis = anfis(data);

ANFIS info:
	Number of nodes: 21
	Number of linear parameters: 12
	Number of nonlinear parameters: 12
	Total number of parameters: 24
	Number of training data pairs: 201
	Number of checking data pairs: 0
	Number of fuzzy rules: 4


Start training ANFIS ...

1 	 3.75834e-06
2 	 3.91318e-06
3 	 4.07902e-06
4 	 4.25677e-06
5 	 4.44663e-06
6 	 4.8401e-06
7 	 6.15644e-06
8 	 7.93732e-06
9 	 1.02139e-05
10 	 1.28233e-05

Designated epoch number reached. ANFIS training completed at epoch 10.

Minimal training RMSE = 3.75834e-06

%% View the properties of Sugeno FIS trained by ANFIS
fis

fis = 
  sugfis with properties:

                       Name: "fis"
                  AndMethod: "prod"
                   OrMethod: "max"
          ImplicationMethod: "prod"
          AggregationMethod: "sum"
      DefuzzificationMethod: "wtaver"
    DisableStructuralChecks: 0
                     Inputs: [1x2 fisvar]
                    Outputs: [1x1 fisvar]
                      Rules: [1x4 fisrule]

	See 'getTunableSettings' method for parameter optimization.

showrule(fis)

ans = 4x76 char array
    '1. If (input1 is in1mf1) and (input2 is in2mf1) then (output is out1mf1) (1)'
    '2. If (input1 is in1mf1) and (input2 is in2mf2) then (output is out1mf2) (1)'
    '3. If (input1 is in1mf2) and (input2 is in2mf1) then (output is out1mf3) (1)'
    '4. If (input1 is in1mf2) and (input2 is in2mf2) then (output is out1mf4) (1)'

plotfis(fis)