How to decide center and standard deviation of gaussian membership function if we have divided our metric ,say, distance into 3 fuzzy sets?
close 0-30
medium 30-120
Far 120-200
Plz help.
According to Ross (2010), there are various ways to decide the type and parameters of fuzzy membership functions: 1.Intuition, 2.Inference, 3.Rank ordering, 4.Neural networks, 5.Genetic algorithms and 6.Inductive reasoning.
If you have data, you can partition your data into training and test sets and choose the parameters of gaussian membership functions so that the error is minimized. You can do it either by trial and error or by using optimization algorithms (such as GA, as discussed in ROSS(2010)) in a more systematic approach.
Ross, T. J. (2009). Fuzzy logic with engineering applications. John Wiley & Sons
According to Ross (2010), there are various ways to decide the type and parameters of fuzzy membership functions: 1.Intuition, 2.Inference, 3.Rank ordering, 4.Neural networks, 5.Genetic algorithms and 6.Inductive reasoning.
If you have data, you can partition your data into training and test sets and choose the parameters of gaussian membership functions so that the error is minimized. You can do it either by trial and error or by using optimization algorithms (such as GA, as discussed in ROSS(2010)) in a more systematic approach.
Ross, T. J. (2009). Fuzzy logic with engineering applications. John Wiley & Sons
Thanks all for kind reply. Can anyone find center and standard deviation for each of the fuzzy sets i have given in my problem and plot the Gaussian MF for me.
Well, as you know the symmetric Gaussian function depends on two parameters σ and c, where c is the center. For an interpretable distribution of membership functions I suggest the following code (matlab):
y1 = gaussmf(x, [21 15]);
y2 = gaussmf(x, [30 75]);
y3 = gaussmf(x, [42 160]);
plot(x, [y1 y2 y3]);
grid
Remember gaussmf functions in matlab:
gaussmf(X, PARAMS);
where PARAMS= [SIGMA, C]
I would like to know how standard deviation is evaluated in y1 = gaussmf(x, [21 15]); y2 = gaussmf(x, [30 75]) and y3 = gaussmf(x, [42 160]).
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