Vectorial use of membership functions

Hello I have a family of membership functions, that is n s-shaped mf with different parameters. Then I have n points and each of them must be tested on a singular MF. I tried:

res = smf([x_1;x_2;..;x_n],[a_1 b_1;a_2 b_2;...; a_n b_n])

of course is not working. Is it possible to implement this problem with a singular instruction or shall I implement a cycle ?

Answer 1

[Sam Chak]

Here is a demo in which six different S-shaped membership functions are generated and evaluated at a target input using a for-loop approach. The results are then tabulated using the array2table() command.

%% settings
x   = linspace(-1, 1, 201);
a   = -0.5:0.1:0.0;         % 1st parameter of smf
b   =  0.0:0.1:0.5;         % 2nd parameter of smf
y   = zeros(numel(a), 2);   % initialization
tgt = 0;                    % target

%% generate plots
hold on
for i = 1:numel(a)
    mf = @(x) smf(x, [a(i), b(i)]);
    y(i,:) = [mf(tgt), i];
    plot(x, mf(x))
    plot(tgt, mf(tgt), 'k.')
end
hold off

%% labels
grid on, ylim([-0.5, 1.5])
xlabel('x'), ylabel('Degree of membership')
title('A family of S-shaped membership functions')

T = array2table(y, 'VariableNames', {'mu', 'i'}); 
fprintf('The degree of membership evaluated at x = %.4f.\n', tgt); disp(T)

The degree of membership evaluated at x = 0.0000.
     mu     i
    ____    _

       1    1
    0.92    2
    0.68    3
    0.32    4
    0.08    5
       0    6