tunefis
Tune fuzzy inference system or tree of fuzzy inference systems
Syntax
Description
fis = tunefis(fis,paramset,custcostfcn)custcostfcn.
fis = tunefis(___,options)options created using tunefisOptions.
Examples
Create the initial fuzzy inference system using genfis.
x = (0:0.1:10)';
y = sin(2*x)./exp(x/5);
options = genfisOptions("GridPartition");
options.NumMembershipFunctions = 5;
fisin = genfis(x,y,options);Obtain the tunable settings of inputs, outputs, and rules of the fuzzy inference system.
[in,out,rule] = getTunableSettings(fisin);
Tune the membership function parameters with "anfis".
fisout = tunefis(fisin,[in;out],x,y,tunefisOptions(Method="anfis"));ANFIS info: Number of nodes: 24 Number of linear parameters: 10 Number of nonlinear parameters: 15 Total number of parameters: 25 Number of training data pairs: 101 Number of checking data pairs: 0 Number of fuzzy rules: 5 Start training ANFIS ... 1 0.0694086 2 0.0680259 3 0.066663 4 0.0653198 Step size increases to 0.011000 after epoch 5. 5 0.0639961 6 0.0626917 7 0.0612787 8 0.0598881 Step size increases to 0.012100 after epoch 9. 9 0.0585193 10 0.0571712 Designated epoch number reached. ANFIS training completed at epoch 10. Minimal training RMSE = 0.0571712
Create the initial fuzzy inference system using genfis.
x = (0:0.1:10)';
y = sin(2*x)./exp(x/5);
options = genfisOptions("GridPartition");
options.NumMembershipFunctions = 5;
fisin = genfis(x,y,options); Obtain the tunable settings of inputs, outputs, and rules of the fuzzy inference system.
[in,out,rule] = getTunableSettings(fisin);
Tune the rule parameter only. In this example, the pattern search method is used.
fisout = tunefis(fisin,rule,x,y,tunefisOptions(Method="patternsearch"));Iter Func-count f(x) MeshSize Method
0 1 0.346649 1
1 15 0.346649 0.5 Refine Mesh
2 33 0.346649 0.25 Refine Mesh
3 51 0.346649 0.125 Refine Mesh
4 69 0.346649 0.0625 Refine Mesh
5 87 0.346649 0.03125 Refine Mesh
6 105 0.346649 0.01562 Refine Mesh
7 123 0.346649 0.007812 Refine Mesh
8 141 0.346649 0.003906 Refine Mesh
9 159 0.346649 0.001953 Refine Mesh
10 177 0.346649 0.0009766 Refine Mesh
11 195 0.346649 0.0004883 Refine Mesh
12 213 0.346649 0.0002441 Refine Mesh
13 231 0.346649 0.0001221 Refine Mesh
14 249 0.346649 6.104e-05 Refine Mesh
15 267 0.346649 3.052e-05 Refine Mesh
16 285 0.346649 1.526e-05 Refine Mesh
17 303 0.346649 7.629e-06 Refine Mesh
18 321 0.346649 3.815e-06 Refine Mesh
19 339 0.346649 1.907e-06 Refine Mesh
20 357 0.346649 9.537e-07 Refine Mesh
patternsearch stopped because the mesh size was less than options.MeshTolerance.
You can configure tunefis to learn the rules of a fuzzy system. For this example, learn rules for a tipping FIS.
Load the original tipping FIS.
fisin = readfis("tipper"); Generate training data using this FIS.
x = 10*rand(100,2); y = evalfis(fisin,x);
Remove the rules from the FIS.
fisin.Rules = [];
To learn rules, set the OptimizationType option of tunefisOptions to "learning".
options = tunefisOptions( ... OptimizationType="learning", ... Display="none");
Set the maximum number of rules in the tuned FIS to 5.
options.NumMaxRules = 5;
Learn the rules without tuning any membership function parameters.
fisout = tunefis(fisin,[],x,y,options);
Create the initial fuzzy inference system using genfis.
x = (0:0.1:10)';
y = sin(2*x)./exp(x/5);
options = genfisOptions("GridPartition");
options.NumMembershipFunctions = 5;
fisin = genfis(x,y,options);Obtain the tunable settings of inputs, outputs, and rules of the fuzzy inference system.
[in,out,rule] = getTunableSettings(fisin);
You can tune with custom parameter settings using setTunable or dot notation.
Do not tune input 1.
in(1) = setTunable(in(1),false);
For output 1:
do not tune membership functions 1 and 2,
do not tune membership function 3,
set the minimum parameter range of membership function 4 to -2,
and set the maximum parameter range of membership function 5 to 2.
out(1).MembershipFunctions(1:2) = setTunable(out(1).MembershipFunctions(1:2),false); out(1).MembershipFunctions(3).Parameters.Free = false; out(1).MembershipFunctions(4).Parameters.Minimum = -2; out(1).MembershipFunctions(5).Parameters.Maximum = 2;
For the rule settings,
do not tune rules 1 and 2,
set the antecedent of rule 3 to non-tunable,
allow NOT logic in the antecedent of rule 4,
and do not ignore any outputs in rule 3.
rule(1:2) = setTunable(rule(1:2),false); rule(3).Antecedent.Free = false; rule(4).Antecedent.AllowNot = true; rule(3).Consequent.AllowEmpty = false;
Set the maximum number of iterations to 20 and tune the fuzzy inference system.
opt = tunefisOptions(Method="particleswarm");
opt.MethodOptions.MaxIterations = 20;
fisout = tunefis(fisin,[in;out;rule],x,y,opt); Best Mean Stall
Iteration f-count f(x) f(x) Iterations
0 90 0.3265 1.857 0
1 180 0.3265 4.172 0
2 270 0.3265 3.065 1
3 360 0.3265 3.839 2
4 450 0.3265 3.386 3
5 540 0.3265 3.249 4
6 630 0.3265 3.311 5
7 720 0.3265 2.901 6
8 810 0.3265 2.868 7
9 900 0.3181 2.71 0
10 990 0.3181 2.068 1
11 1080 0.3181 2.692 2
12 1170 0.3165 2.146 0
13 1260 0.3165 1.869 1
14 1350 0.3165 2.364 2
15 1440 0.3165 2.07 0
16 1530 0.3164 1.678 0
17 1620 0.2978 1.592 0
18 1710 0.2977 1.847 0
19 1800 0.2954 1.666 0
20 1890 0.2947 1.608 0
Optimization ended: number of iterations exceeded OPTIONS.MaxIterations.
To prevent the overfitting of your tuned FIS to your training data using k-fold cross validation.
Load training data. This training data set has one input and one output.
load fuzex1trnData.datCreate a fuzzy inference system for the training data.
opt = genfisOptions("GridPartition"); opt.NumMembershipFunctions = 4; opt.InputMembershipFunctionType = "gaussmf"; inputData = fuzex1trnData(:,1); outputData = fuzex1trnData(:,2); fis = genfis(inputData,outputData,opt);
For reproducibility, set the random number generator seed.
rng("default")Configure the options for tuning the FIS. Use the default tuning method with a maximum of 30 iterations.
tuningOpt = tunefisOptions; tuningOpt.MethodOptions.MaxGenerations = 30;
Configure the following options for using k-fold cross validation.
Use a k-fold value of
3.Compute the moving average of the validation cost using a window of length
2.Stop each training-validation iteration when the average cost is 5% greater than the current minimum cost.
tuningOpt.KFoldValue = 3; tuningOpt.ValidationWindowSize = 2; tuningOpt.ValidationTolerance = 0.05;
Obtain the settings for tuning the membership function parameters of the FIS.
[in,out] = getTunableSettings(fis);
Tune the FIS.
[outputFIS,info] = tunefis(fis,[in;out],inputData,outputData,tuningOpt);
Single objective optimization:
16 Variables
Options:
CreationFcn: @gacreationuniform
CrossoverFcn: @crossoverscattered
SelectionFcn: @selectionstochunif
MutationFcn: @mutationadaptfeasible
Best Mean Stall
Generation Func-count f(x) f(x) Generations
1 400 0.2257 0.534 0
ga stopped by the output or plot function. The reason for stopping:
Validation tolerance exceeded.
Cross validation iteration 1: Minimum validation cost 0.307868 found at training cost 0.262340
Single objective optimization:
16 Variables
Options:
CreationFcn: @gacreationuniform
CrossoverFcn: @crossoverscattered
SelectionFcn: @selectionstochunif
MutationFcn: @mutationadaptfeasible
Best Mean Stall
Generation Func-count f(x) f(x) Generations
1 400 0.26 0.5522 0
2 590 0.222 0.4914 0
ga stopped by the output or plot function. The reason for stopping:
Validation tolerance exceeded.
Cross validation iteration 2: Minimum validation cost 0.253280 found at training cost 0.259991
Single objective optimization:
16 Variables
Options:
CreationFcn: @gacreationuniform
CrossoverFcn: @crossoverscattered
SelectionFcn: @selectionstochunif
MutationFcn: @mutationadaptfeasible
Best Mean Stall
Generation Func-count f(x) f(x) Generations
1 400 0.2588 0.4969 0
2 590 0.2425 0.4366 0
3 780 0.2414 0.4006 0
ga stopped by the output or plot function. The reason for stopping:
Validation tolerance exceeded.
Cross validation iteration 3: Minimum validation cost 0.199193 found at training cost 0.242533
Evaluate the FIS for each of the training input values.
outputTuned = evalfis(outputFIS,inputData);
Plot the output of the tuned FIS along with the expected training output.
plot([outputData,outputTuned]) legend("Expected Output","Tuned Output",Location="southeast") xlabel("Data Index") ylabel("Output value")
Create a FIS tree to model , as shown in the following figure. For more information on creating FIS trees, see FIS Trees.
Create fis1 with two inputs, both with range [0, 10] and three MFs each. Use a smooth, differentiable MF, such as gaussmf, to match the characteristics of the data type you are modeling.
fis1 = sugfis(Name="fis1"); fis1 = addInput(fis1,[0 10], ... NumMFs=3, ... MFType="gaussmf"); fis1 = addInput(fis1,[0 10], ... NumMFs=3, ... MFType="gaussmf");
Add an output with the range [–1.5, 1.5] having nine MFs corresponding to the nine possible input MF combinations. Set the output range according to the possible values of .
fis1 = addOutput(fis1,[-1.5 1.5],"NumMFs",9);Create fis2 with two inputs. Set the range of the first input to [–1.5, 1.5], which matches the range of the output of fis1. The second input is the same as the inputs of fis1. Therefore, use the same input range, [0, 10]. Add three MFs for each of the inputs.
fis2 = sugfis(Name="fis2"); fis2 = addInput(fis2,[-1.5 1.5], ... NumMFs=3, ... MFType="gaussmf"); fis2 = addInput(fis2,[0 10], ... NumMFs=3, ... MFType="gaussmf");
Add an output with range [0, 1] and nine MFs. The output range is set according to the possible values of .
fis2 = addOutput(fis2,[0 1],"NumMFs",9);Connect the inputs and the outputs as shown in the diagram. The first output of fis1 connects to the first input of fis2. The inputs of fis1 connect to each other and the second input of fis1 connects to the second input of fis2.
con1 = ["fis1/output1" "fis2/input1"]; con2 = ["fis1/input1" "fis1/input2"]; con3 = ["fis1/input2" "fis2/input2"];
Create a FIS tree using the specified FISs and connections.
fisT = fistree([fis1 fis2],[con1;con2;con3]);
Add an additional output to the FIS tree to access the output of fis1.
fisT.Outputs = ["fis1/output1";fisT.Outputs];For this example, generate input and output training data using the known mathematical operations. Generate data for both the intermediate and final output of the FIS tree.
x = (0:0.1:10)'; y1 = sin(x)+cos(x); y2 = y1./exp(x); y = [y1 y2];
Learn the rules of the FIS tree using particle swarm optimization, which is a global optimization method.
options = tunefisOptions( ... Method="particleswarm", ... OptimizationType="learning");
This tuning step uses a small number of iterations to learn a rule base without overfitting the training data.
options.MethodOptions.MaxIterations = 5; rng("default") % for reproducibility fisTout1 = tunefis(fisT,[],x,y,options);
Best Mean Stall
Iteration f-count f(x) f(x) Iterations
0 100 0.6682 0.9395 0
1 200 0.6682 1.023 0
2 300 0.6652 0.9308 0
3 400 0.6259 0.958 0
4 500 0.6259 0.918 1
5 600 0.5969 0.9179 0
Optimization ended: number of iterations exceeded OPTIONS.MaxIterations.
Tune all the FIS tree parameters at once using pattern search, which is a local optimization method.
options.Method = "patternsearch";
options.MethodOptions.MaxIterations = 25;Use getTunableSettings to obtain input, output, and rule parameter settings from the FIS tree.
[in,out,rule] = getTunableSettings(fisTout1);
Tune the FIS tree parameters.
fisTout2 = tunefis(fisTout1,[in;out;rule],x,y,options);
Iter Func-count f(x) MeshSize Method
0 1 0.596926 1
1 8 0.594989 2 Successful Poll
2 14 0.580893 4 Successful Poll
3 14 0.580893 2 Refine Mesh
4 36 0.580893 1 Refine Mesh
5 43 0.577757 2 Successful Poll
6 65 0.577757 1 Refine Mesh
7 79 0.52794 2 Successful Poll
8 102 0.52794 1 Refine Mesh
9 120 0.524443 2 Successful Poll
10 143 0.524443 1 Refine Mesh
11 170 0.52425 2 Successful Poll
12 193 0.52425 1 Refine Mesh
13 221 0.524205 2 Successful Poll
14 244 0.524205 1 Refine Mesh
15 329 0.508752 2 Successful Poll
16 352 0.508752 1 Refine Mesh
17 434 0.508233 2 Successful Poll
18 457 0.508233 1 Refine Mesh
19 546 0.506136 2 Successful Poll
20 569 0.506136 1 Refine Mesh
21 659 0.505982 2 Successful Poll
22 682 0.505982 1 Refine Mesh
23 795 0.505811 2 Successful Poll
24 818 0.505811 1 Refine Mesh
25 936 0.505811 0.5 Refine Mesh
26 950 0.504362 1 Successful Poll
patternsearch stopped because it exceeded options.MaxIterations.
The optimization cost is lower after the second tuning process.
Evaluate the FIS tree using the input training data.
yOut = evalfis(fisTout2,x);
Plot the final output along with the corresponding output training data.
plot(x,y(:,2),"-",x,yOut(:,2),"-") legend("Training Data","FIS Tree Output")
The results do not perform well at the beginning and end of the input range. To improve performance, you could try:
Increasing the number of training iterations in each stage of the tuning process.
Increasing the number of membership functions for the input and output variables.
Using a custom cost function to model the known mathematical operations. For an example, see Tune FIS Using Custom Cost Function.
Input Arguments
Output Arguments
Alternative Functionality
Fuzzy Logic Designer App
Starting in R2023a, you can interactively tune fuzzy inference systems using the Fuzzy Logic Designer app. For an example, see Tune Fuzzy Inference System Using Fuzzy Logic Designer.
