# Re: fuzzy relations

JW (shmeebin@hotmail.com)
Fri, 1 May 1998 12:16:06 +0200 (MET DST)

Great example! I really enjoyed it!

> >
> > I mean, you could combine a fuzzy set of lamp-post heights with the
fuzzy
> > set of the weights of african frogs mathematically - but does it have
any
> > real interpretation?
>
> Normally, one wouldn't have a fuzzy set of ``lamp-post heights'', but
> maybe a fuzzy set ``large lamp-post heights'', of which 2 metres would
> probably have a membership zero, and 5 metres and above a mebership of
> 1.0 -- with a smooth transition 0.0--1.0 somewhere in-between, goues
> through 0.5 at 4 metres. In the common fuzzy-rule-based systems -- for
> control, or for function approximation, one would have a fuzzy partition
> of the universe of (all possible)
> ``lamp-post heights'': say small, medium, large. Let us say that the
> average ``lamp-post height'' is 3 metres, then possibly ``medium
> lamp-post height'' would be represented by a triangular membership
> function which rises from 0.0 at 2 metres to 1.0 at 3 metres and falls
> back to zero at 4 metres.
>
> The same can be done for the weights. Let us say that theese are
> partitioned as above, merely swapping kilos for metres.
>
> Now, consider yourself as a seller of odd merchandise. Your best
> customer rings up an asks for immediate delivery of a long lamp-post and
> a medium weight (singing) African frog; you have a 3 kilo frog (A) who
> is so attached to a 4 metre lamp-post that this is the only one he/she
> will sing under; you also have a 3.25 kilo frog (B) who will sing only
> under a 5 metre lamp-post that he/she has grown attached to. You tell
> your custormer that you cannot exactly match his order, he says send the
> best you can. What do you do?
>
> Frog A has medium weight membership 1.0, ond his 4 metre lamp-post has
> large length membership 0.5. Composite membership of ``long lamp-post
> and a medium weight'' = 0.5 (using either product or max. in the
> composition).
>
> Frog B has 0.75 (at 3.25) and 1.0 (at 5), so the composite membership is
> 0.75.
>
> Frog B and the 5 metre lamp-post gets shipped.
>
> >
> > Also, am I correct in presuming that Prof. Mamdani is a bloke? I am
> > preparing a report on the mamdani implication and I don't want to make
any
> > fundamental cock-ups.
>
> He is.
>
> Hope this helps.
>
> Jon Campbell
>
> --
> Jonathan G Campbell Univ. Ulster Magee College Derry BT48 7JL N. Ireland
> +44 1504 375367 JG.Campbell@ulst.ac.uk http://www.infm.ulst.ac.uk/~jgc/
>