help me in degree of membership function correction in fuzzy logic tool with new membership function creation

function y = nf1(x, params) if nargin ~= 2 error('Two arguments are required by the Normal PDF MF.'); elseif length(params) < 2 error('The Normal PDF MF needs at least four parameters.'); end

sigma1 = params(1); c1 = params(2);

end r1 = exp(-(x-c1).^2 ./ (2 .* sigma1 .^2)) ./ (sigma1 .* (sqrt(2*pi)));

the above code changed using that formula. but, here the curve is not fitting in the 0 to 1 interval. so, please help me fuzzy experts...

Thanking you

Answer 1

[Sam Chak]

That's because the amplitude of your custom function depends on the value of σ. If it is not designed as , then the upper bound of the function is not at .

In your case, the chosen custom function is a Normal Distribution function:

where

the amplitude, .

To make sure that the custom function bounded , then the function has to be carefully designed.

For example, guarantees that .

x      = linspace(-1, 1, 20001);

sigma  = 1/sqrt(2*pi);
center = 0;
mf1    = custmf(x, [sigma center]);

plot(x, mf1), grid on, ylim([-0.1 1.1])
text(-0.05, 1.05, 'mf1')
xlabel('Universe of Discourse, \it{x}')
ylabel('Degree of membership, \mu(\it{x})')

% Custom Membership Function -- Normal distribution

function mf = custmf(x, params)
    sigma = params(1); 
    c     = params(2);
    mf    = exp(-1/2*((x - c)/sigma).^2) / (sigma*(sqrt(2*pi)));
    % mf    = exp(-(x - c).^2./(2*sigma^2));    <-- the same as gaussmf()
end