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How to determine the width of a Gaussian membership function?

definition

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What does a "Gaussian membership function" look like, if you don't mind saying? –  J. M. Nov 20 '10 at 10:45
    
I uploaded a explanation: imgur.com/mp1D5 –  p0larBoy Nov 20 '10 at 10:55
    
Okay... what else do you have? That's a lot of parameters... –  J. M. Nov 20 '10 at 11:05
    
I just wanna know how do the "s" affects the graph.. –  p0larBoy Nov 20 '10 at 11:16
    
I think the plots you have give a good look at how s affects it. c just shifts x over, and s and m together set the width. –  Ross Millikan Jan 19 '11 at 17:03

4 Answers 4

Since $\mu_A(\lambda x+c,c,\lambda s,m)$ does not depend on $\lambda\ne0$, the graph of the function $x\mapsto\mu_A(x,c,\lambda s,m)$ is the image of the graph of the function $x\mapsto\mu_A(x,c,s,m)$ by the dilation of ratio $1/\lambda$ in the horizontal direction, centered at the vertical line of equation $x=c$.

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You don't say what data you have. If you have (x,y) pairs, you can just use a multidimensional fitting routine like Numerical Recipes or Excel's goal seek function to get all the parameters. If you have random samples it may be hard to distinguish the effects of m and s unless you have a lot of them.

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I just wanna know how do the "s" affects the graph.

Increasing $s$ makes the function "fatter".

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solve for x that are the roots the equation and then take the difference

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