Plot fuzzy membership function for specified parameters (x, u(x))

Since I'm new to Fuzzy Logic and Matlab too, I have two fuzzy subsets and it's membership functions in a picture, and I need to plot the graphs from the membership functions with Matlab. I've already found the waty to plot the graphs, in this doc from Matlab official site: https://www.mathworks.com/help/fuzzy/plotmf.html

But I don't know how to create the .fis file (Fuzzy inference system), containing the fuzzy subsets, just so I can read it in a new code and plot the graph, like in:

fis = readfis('tipper'); #I need to create this.
plot(xOut(:,2),yOut(:,2))
xlabel('food')
ylabel('delicious membership')

Here are the fuzzy subsets I need to transform in a fis file:

And the original set is U = {0, 1, 2, 3, 4, 5, 6, 7, 9}, as seen in the picture.

Please don't send me to a similar question beacause I really need help with this case. What should I do?

Answer 1

[Sam Chak]

One proper way to plot the membership functions (MFs) is to create custom MFs based on the given fuzzy sets.

https://www.mathworks.com/help/fuzzy/building-fuzzy-inference-systems-using-custom-functions.html

Since this is not possible to save customMF.m online, the Logistic function (aka Sigmoidal MF) from the toolbox can be used to approximate the fuzzy sets.

% Data Sets
u = (0:9)';
A = [0.0 0.0 0.1 0.2 0.3 0.8 0.9 1.0 1.0 1.0]';
B = [1.0 1.0 0.9 0.8 0.7 0.5 0.4 0.2 0.2 0.0]';

% Curve-fitting
fo = fitoptions('Method','NonlinearLeastSquares',...
               'Lower',[-10, -10],...
               'Upper',[ 10,  10],...
               'StartPoint', [1 1]);
ft = fittype('1/(1 + exp(-a*(x - c)))', 'options', fo);
[sigmA, gof] = fit(u, A, ft)

sigmA = 
     General model:
     sigmA(x) = 1/(1 + exp(-a*(x - c)))
     Coefficients (with 95% confidence bounds):
       a =       1.436  (0.9784, 1.893)
       c =       4.302  (4.05, 4.554)

gof = struct with fields:
           sse: 0.0229
       rsquare: 0.9872
           dfe: 8
    adjrsquare: 0.9855
          rmse: 0.0535

[sigmB, gof] = fit(u, B, ft)

sigmB = 
     General model:
     sigmB(x) = 1/(1 + exp(-a*(x - c)))
     Coefficients (with 95% confidence bounds):
       a =     -0.6925  (-0.8296, -0.5554)
       c =       5.201  (4.888, 5.513)

gof = struct with fields:
           sse: 0.0168
       rsquare: 0.9858
           dfe: 8
    adjrsquare: 0.9840
          rmse: 0.0459

figure(1)
plot(u,  A, '.'), hold on
plot(sigmA, 'r'), hold off
grid on, xlabel('u'), ylabel('A(u)')
legend('Set A', 'Fitted Sigmoid', 'location', 'best')

figure(2)
plot(u,  B, '.'), hold on
plot(sigmB, 'r'), hold off
grid on, xlabel('u'), ylabel('B(u)')
legend('Set B', 'Fitted Sigmoid', 'location', 'best')

% Creating FIS and putting the input MFs into FIS
fis = mamfis('Name', "user_FIS");

% Fuzzy Input
fis = addInput(fis, [0 9], 'Name', 'U');
fis = addMF(fis, 'U', 'sigmf', [sigmB.a sigmB.c], 'Name', 'LO');
fis = addMF(fis, 'U', 'sigmf', [sigmA.a sigmA.c], 'Name', 'HI');

% Plot membership functions
figure(3)
plotmf(fis, 'input', 1), grid on, title('U')