explanation needed.

Wen-Feng Hsiao (d8442803@student.nsysu.edu.tw)
Fri, 17 Sep 1999 10:16:40 +0200 (MET DST)

Dear experts,

In one fuzzy sets theory textbook, I found the following description.

"... They define a membership function in a similar way to the
possibilistic method of inducing a possibility function from a histogram:

Ms(x) = kp(x) if kp(x)<1, and
= 1 if kp(x)>=1.

where p(x) is the probability density function for x on S and k is a
constant to be solved for by solving

kF(p(x))-c = 0,

where F(p(x)) is the integral of (p(x))^2 dx over the region for which
kp(x)<1 plus the integral of p(x)dx over the region where kp(x)>=1, and c
is the desired confidence level."

My question is how to obtain the F(p(x)) and why it has relation to
confidence level c? I have no cue.

Thanks a lot!

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