Re: Max-min composition and etc.

Yaochu Jin (jin@neuroinformatik.ruhr-uni-bochum.de)
Sun, 26 Apr 1998 17:30:46 +0200 (MET DST)

On Mon, 20 Apr 1998, Tassanee W. wrote:

> Hi dear friends
> I read the paper "Identification in fuzzy systems" by WITOLD PEDRYCZ IEEE
> tran. on SMC-14 No.2 Mar/Apr1984 page365
> It say y = R * x ( * is max-min composition)
> R = [0.64 0.48 0.30
> 1.00 0.48 0.30
> 0.52 1.00 0.30]
> when x=[0.56 0.91 0.30]
>
> how can we get y=[0.91 0.47 0.30] from max min composition??
> can you show me procedure to getting R for max-min,max-product and
> min-max composition ??
>

I have not read the original paper. However, if R is a 3x3 matrix and x
is an 1x3 vector, then y=x*R=[y1,y2,y3] where

y1=max{min{0.56,0.64},min{0.91,1.00},min{0.30,0.52}}=0.91
y2=max{min{0.56,0.48},min{0.91,0.48},min{0.30,1.00}}=0.48
y3=max{min{0.56,0.30},min{0.91,0.30},min{0.30,0.30}}=0.30

It is similar to matrix multiplication. However, product is replaced by
minimum and sum is replaced by maximum.

Hope this helps.

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