the neuro fuzzy sistem modify the membership function in input or in output?

Hello, I wanted to understand what happens to the membership function (in input/output) or rules when I insert in the anfis editor: Sugeno file and a training set.

Answer 1

[Sam Chak]

Hi @astrubale ponzio

In the following simple example, the ANFIS is trained to fit a trapezoidal set-based fuzzy system to the input/output data of an ideal saturation function. We can clearly observe that both the initial trapezoidal input membership function (MF) and the constant output MF are slightly different from the final trapezoidal input MF and constant output MF. ANFIS will update the parameters of both the input and output membership functions.

%% data
x   = (-1:0.01:1)';
y   = min(max(-5*x, -1), 1);        % <-- ideal saturation function

genOpt                              = genfisOptions('GridPartition');
genOpt.NumMembershipFunctions       = 2;
genOpt.InputMembershipFunctionType  = 'trapmf';
genOpt.OutputMembershipFunctionType = 'constant';
inFIS = genfis(x,y,genOpt);
showrule(inFIS)

ans = 2x53 char array
    '1. If (input1 is in1mf1) then (output is out1mf1) (1)'
    '2. If (input1 is in1mf2) then (output is out1mf2) (1)'

opt                         = anfisOptions('InitialFIS', inFIS, 'EpochNumber', 50);
opt.DisplayANFISInformation = 0;
opt.DisplayErrorValues      = 0;
opt.DisplayStepSize         = 0;
opt.DisplayFinalResults     = 0;
outFIS = anfis([x y],opt);

%% plot result
figure
subplot(211)
plotmf(inFIS, 'input', 1), grid on
title('inFIS Input Fuzzy Sets')
subplot(212)
plot(x, [y, evalfis(inFIS,  x)]), grid on, ylim([-1.2, 1.2])
title('Compare Data with Untrained ANFIS Output')
legend('Data', 'Untrained ANFIS Output')

inFIS.inputs(1).MembershipFunctions(1).Name

ans = "in1mf1"

inFIS.inputs(1).MembershipFunctions(1).Type

ans = "trapmf"

inFIS.inputs(1).MembershipFunctions(1).Parameters

ans = 1×4

-2.4000 -1.6000 -0.4000 0.4000

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inFIS.Outputs(1).MembershipFunctions(1).Name

ans = "out1mf1"

inFIS.Outputs(1).MembershipFunctions(1).Type

ans = "constant"

inFIS.Outputs(1).MembershipFunctions(1).Parameters

ans = 0

figure
subplot(211)
plotmf(outFIS, 'input', 1), grid on
title('outFIS Input Fuzzy Sets')
subplot(212)
plot(x, [y, evalfis(outFIS, x)]), grid on, ylim([-1.2, 1.2])
title('Compare Data with Trained ANFIS Output')
legend('Data', 'Trained ANFIS Output')

outFIS.inputs(1).MembershipFunctions(1).Name

ans = "in1mf1"

outFIS.inputs(1).MembershipFunctions(1).Type

ans = "trapmf"

outFIS.inputs(1).MembershipFunctions(1).Parameters

ans = 1×4

-2.4000 -1.6000 -0.4000 0.1997

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outFIS.Outputs(1).MembershipFunctions(1).Name

ans = "out1mf1"

outFIS.Outputs(1).MembershipFunctions(1).Type

ans = "constant"

outFIS.Outputs(1).MembershipFunctions(1).Parameters

ans = 0.9999