Should the number of fuzzy rules in ANFIS be equal to the number of input MFs?

After the training and trial process is executed, Is the number of rules to be equal to the number of MFs? For information, input number is 5 while after training the number of MF is 3. Prior to training, the trial method was used with different types and numbers of MF.

Answer 1

[Sam Chak]

Yes, if the Subtractive Clustering method is used to generate the initial fuzzy system in ANFIS.

%% The McDonald's Logo
x   = linspace(-6.5, 6.5, 261)';
y   = 6*abs(x) - x.^2 + 3.25;

genOpt = genfisOptions('SubtractiveClustering');
inFIS  = genfis(x,y,genOpt);
figure
plotrule(inFIS)

opt                         = anfisOptions('InitialFIS', inFIS, 'EpochNumber', 500);
opt.DisplayANFISInformation = 0;
opt.DisplayErrorValues      = 0;
opt.DisplayStepSize         = 0;
opt.DisplayFinalResults     = 0;
outFIS = anfis([x y],opt);
figure
plotrule(outFIS)

%% plot results
figure
subplot(211)
plotmf(inFIS, 'input', 1), grid on
title('Input MFs in Untrained ANFIS')

subplot(212)
plotmf(outFIS, 'input', 1), grid on
title('Input MFs in Trained ANFIS')

figure
x1  = linspace(-6.5, 6.5, 27*3)';
y1  = 6*abs(x1) - x1.^2 + 3.25;
plot(x1, y1, 'o'), hold on
plot(x, evalfis(outFIS, x), 'linewidth', 1.5), hold off
grid on, ylim([-1 13])
legend('Training Data', 'ANFIS Output', 'location', 'south')
axis equal
xlabel('x'), ylabel('y')
title('Compare Data with Trained ANFIS Output')