Mistake in Linear z-shaped membership funciton

https://www.mathworks.com/help/fuzzy/linzmf.html

There is a mistake in the description of Linear z-shaped membership function.

it should be:

(b-x)/(b-a) for a<=x<=b

otherwise you've got for a^- -> 1, for a^+ -> 0

[Sahas]

Hi @Mateusz,

I downloaded the pre-release version of MATLAB R2024b and checked the documentation. It appears that MathWorks has already resolved this issue.

Answer 1

[Sam Chak]

Hi @Mateusz

You can navigate to "Contact Support" and, under "Product Usage," submit a suggestion to correct the information. The document writer was likely considering the mathematical aspects when preparing the documentation, which may have led to confusion with the correct piecewise equation.

x   = linspace(-1, 1, 2001);
a   = x(1);
b   = x(end);
y   = max(-1, min(1, -3*x));    % ideal saturation function with negative slope
mf  = (a - y)./(a - b);         % membership function

tl  = tiledlayout(2, 1, 'TileSpacing', 'Compact');
nexttile
plot(x, y),  grid on, ylabel('y'),   ylim([-1.4, 1.4])
yline(0, 'r-.')
title('ideal saturation function with negative slope')
nexttile
plot(x, mf), grid on, ylabel('\mu'), ylim([-0.2, 1.2])
yline(0, 'r-.')
xlabel(tl, 'x')
title('NEG fuzzy set of ideal saturation function')