anfis
Tune Sugeno-type fuzzy inference system using training data
Syntax
Description
fis = anfis(trainingData)
The training algorithm uses a combination of the least-squares and backpropagation gradient descent methods to model the training data set.
fis = anfis(trainingData,options)
An initial FIS object to tune.
Validation data for preventing overfitting to training data.
Training algorithm options.
Whether to display training progress information.
[ returns the root mean squared training error for each training
epoch.fis,trainError]
= anfis(___)
[ returns the training step size
at each training epoch.fis,trainError,stepSize]
= anfis(___)
[
returns the validation data error for each training epoch,
fis,trainError,stepSize,chkFIS,chkError]
= anfis(trainingData,options)chkError, and the tuned FIS object for which the
validation error is minimum, chkFIS. To use this syntax,
you must specify validation data using
options.ValidationData.
Examples
Load training data. This data has a single input and a single output.
load fuzex1trnData.datGenerate and train a fuzzy inference system. By default, the FIS structure is created using a grid partition of the input variable range with two membership functions.
fis = anfis(fuzex1trnData);
ANFIS info: Number of nodes: 12 Number of linear parameters: 4 Number of nonlinear parameters: 6 Total number of parameters: 10 Number of training data pairs: 25 Number of checking data pairs: 0 Number of fuzzy rules: 2 Start training ANFIS ... 1 0.229709 2 0.22896 3 0.228265 4 0.227624 Step size increases to 0.011000 after epoch 5. 5 0.227036 6 0.2265 7 0.225968 8 0.225488 Step size increases to 0.012100 after epoch 9. 9 0.225052 10 0.22465 Designated epoch number reached. ANFIS training completed at epoch 10. Minimal training RMSE = 0.22465
Plot the ANFIS output and training data.
x = fuzex1trnData(:,1); anfisOutput = evalfis(fis,x); plot(x,fuzex1trnData(:,2),"*r",x,anfisOutput,".b") legend("Training Data","ANFIS Output",Location="NorthWest")
The ANFIS data does not match the training data well. To improve the match:
Increase the number of membership functions in the FIS structure to
4. Doing so adds fuzzy rules and tunable parameters to the system.Increase the number of training epochs.
opt = anfisOptions(InitialFIS=4,EpochNumber=40);
Suppress the error and step size Command Window display.
opt.DisplayErrorValues = 0; opt.DisplayStepSize = 0;
Train the FIS.
fis = anfis(fuzex1trnData,opt);
ANFIS info: Number of nodes: 20 Number of linear parameters: 8 Number of nonlinear parameters: 12 Total number of parameters: 20 Number of training data pairs: 25 Number of checking data pairs: 0 Number of fuzzy rules: 4 Minimal training RMSE = 0.0833853
Plot the ANFIS output and training data.
figure anfisOutput = evalfis(fis,x); plot(x,fuzex1trnData(:,2),"*r",x,anfisOutput,".b") legend("Training Data","ANFIS Output",Location="NorthWest")
The match between the training data and ANFIS output has improved.
Create single-input, single-output training data.
x = (0:0.1:10)'; y = sin(2*x)./exp(x/5);
Define an initial FIS structure with five Gaussian input membership functions.
genOpt = genfisOptions("GridPartition"); genOpt.NumMembershipFunctions = 5; genOpt.InputMembershipFunctionType = "gaussmf"; inFIS = genfis(x,y,genOpt);
Configure the ANFIS training options. Set the initial FIS, and suppress the training progress display.
opt = anfisOptions(InitialFIS=inFIS); opt.DisplayANFISInformation = 0; opt.DisplayErrorValues = 0; opt.DisplayStepSize = 0; opt.DisplayFinalResults = 0;
Train the FIS using the specified options.
outFIS = anfis([x y],opt);
Compare the ANFIS output with the training data.
plot(x,y,x,evalfis(outFIS,x)) legend("Training Data","ANFIS Output")
Load training and validation data. This data has a single input and a single output.
load fuzex2trnData.dat load fuzex2chkData.dat
Specify the training options.
opt = anfisOptions(InitialFIS=4,EpochNumber=40); opt.ValidationData = fuzex2chkData; opt.DisplayANFISInformation = 0; opt.DisplayErrorValues = 0; opt.DisplayStepSize = 0; opt.DisplayFinalResults = 0;
Train the FIS, and return the training error.
[trainFIS,trainFISError,~,validationFIS,validationFISError] = ...
anfis(fuzex2trnData,opt);trainFISError contains the root mean squared error for the training data at each training epoch. The training error for trainFIS is the minimum value in trainFISError.
trainFISRMSE = min(trainFISError)
trainFISRMSE = 0.2572
validationFISError contains the root mean squared error for the validation data at each training epoch. The validation error for validationFIS is the minimum value in validationFISError.
validationFISRMSE = min(validationFISError)
validationFISRMSE = 0.6300
Create single-input, single-output training data.
x = (0:0.1:10)'; y = sin(2*x)./exp(x/5);
Configure the ANFIS training options. Set the initial FIS, and suppress the training progress display.
opt = anfisOptions(InitialFIS=4,EpochNumber=60); opt.DisplayANFISInformation = 0; opt.DisplayErrorValues = 0; opt.DisplayStepSize = 0; opt.DisplayFinalResults = 0;
A larger step size increase rate can make the training converge faster. However, increasing the step size increase rate too much can lead to poor convergence. For this example, try doubling the step size increase rate.
opt.StepSizeIncreaseRate = 2*opt.StepSizeIncreaseRate;
Train the FIS, and return the step size array.
[fis,~,stepSize] = anfis([x y],opt);
Plot the step size profile. An optimal step size profile should increase initially, reach a maximum, and then decrease for the rest of the training.
figure plot(stepSize)
Load training data.
load fuzex1trnData.datLoad validation data.
load fuzex1chkData.datSpecify the following training options:
4input membership functions30training epochsSuppress training progress display
opt = anfisOptions(InitialFIS=4,EpochNumber=30); opt.DisplayANFISInformation = 0; opt.DisplayErrorValues = 0; opt.DisplayStepSize = 0; opt.DisplayFinalResults = 0;
Add the validation data to the training options.
opt.ValidationData = fuzex1chkData;
Train the FIS, and return the validation results.
[fis,trainError,stepSize,chkFIS,chkError] = anfis(fuzex1trnData,opt);
The training error, trainError, and validation error, chkError, arrays each contain one error value per training epoch. Plot the training error and the validation error.
x = [1:30]; plot(x,trainError,".b",x,chkError,"*r")
The minimum validation error occurs at epoch 17. The increase in validation error after this point indicates overfitting of the model parameters to the training data. Therefore, the tuned FIS at epoch 17, chkFIS, exhibits the best generalization performance.
Input Arguments
Output Arguments
Alternative Functionality
tunefis Function
Starting in R2019a, you can tune a fuzzy system using tunefis. This function provides
several other options for tuning algorithms, specified by the tunefisOptions
object.
To use ANFIS, specify the tuning algorithm as "anfis" in
tunefisOptions. Then, use
the options object as an input argument for tunefis. For example:
Create the initial fuzzy inference system, and define the tunable parameter settings.
x = (0:0.1:10)';
y = sin(2*x)./exp(x/5);
options = genfisOptions('GridPartition');
options.NumMembershipFunctions = 5;
fisin = genfis(x,y,options);
[in,out,rule] = getTunableSettings(fisin);Tune the membership function parameters with "anfis".
opt = tunefisOptions("Method","anfis"); fisout = tunefis(fisin,[in;out],x,y,opt);
Fuzzy Logic Designer App
Starting in R2023a, you can interactively tune an ANFIS system using the Fuzzy Logic Designer app. For an example, see Train Adaptive Neuro-Fuzzy Inference Systems.
References
[1] Jang, J.-S. R. "Fuzzy Modeling Using Generalized Neural Networks and Kalman Filter Algorithm." Proceedings of the Ninth National Conference on Artificial Intelligence (AAAI-91). (July 1991): 762–767.
[2] Jang, J.-S. R. "ANFIS: Adaptive-Network-based Fuzzy Inference Systems." IEEE Transactions on Systems, Man, and Cybernetics 23, no. 3 (May 1993): 665–685.
