The value of membership functions for x

hi

how to define the output fuzzy set as fuzzy values - which mean's that the outputs membership functions multi-valued as in picture below .

So in Matlab for example I want to ses the MF value for the input X.

Which code or function should use to have the values of MF as outputs if x is a vector e.g. x= [2 5.5 23 14 6.5 7 9 20]?

Thanks in advance

Answer 1

[Sam Chak]

@Gadelhag M Omar Mohmed

To obtain the fuzzy set values, the evalmf() function can be used. In this example, the fuzzy sets are constructed using the Gaussian Membership functions:

x   = 0:0.1:25;
mf1 = fismf("gaussmf", [2, 0]);
mf2 = fismf("gaussmf", [2, 5]);
mf3 = fismf("gaussmf", [2, 10]);
mf4 = fismf("gaussmf", [2, 15]);
mf5 = fismf("gaussmf", [2, 20]);
y1  = evalmf(mf1, x);
y2  = evalmf(mf2, x);
y3  = evalmf(mf3, x);
y4  = evalmf(mf4, x);
y5  = evalmf(mf5, x);
plot(x, [y1; y2; y3; y4; y5]'), grid on, ylim([-0.2 1.2]), xlabel('\it{x}'), ylabel('\mu(\it{x})')

If we want to find the MF values over specific input values in x, then the following syntax is used:

X   = [2 5.5 23 14 6.5 7 9 20];
Y1  = evalmf(mf1, X)

Y1 = 1×8

0.6065 0.0228 0.0000 0.0000 0.0051 0.0022 0.0000 0.0000

Y2  = evalmf(mf2, X)

Y2 = 1×8

0.3247 0.9692 0.0000 0.0000 0.7548 0.6065 0.1353 0.0000

Y3  = evalmf(mf3, X)

Y3 = 1×8

0.0003 0.0796 0.0000 0.1353 0.2163 0.3247 0.8825 0.0000

Y4  = evalmf(mf4, X)

Y4 = 1×8

0.0000 0.0000 0.0003 0.8825 0.0001 0.0003 0.0111 0.0439

Y5  = evalmf(mf5, X)

Y5 = 1×8

0.0000 0.0000 0.3247 0.0111 0.0000 0.0000 0.0000 1.0000