formula for exponential membership function

what is the formula of exponential membership function . How it differs from Gaussian membership function

Answer 1

[Sam Chak]

Technically, it is called the Laplace distribution, or the double exponential distribution. The Gaussian MF has a rounded peak, whereas the Laplacian MF has a pointy peak.

x   = linspace(-1, 1, 2001);

% Gaussian distribution
b1  = 1/4;
c1  = 0;
mu1 = gaussmf(x, [b1, c1]);

% Laplacian distribution
b2  = 1/8;
c2  = c1;
mu2 = exp(- 1/2*abs((x - c2)/b2));

plot(x, [mu1; mu2]), grid on
xlabel('x');
ylabel('Degree of membership');
legend('gaussMF', 'laplaceMF')