# Re: similarity problem

Maurice Clerc (maurice.clerc@writeme.com)
Tue, 13 Oct 1998 21:47:19 +0200 (MET DST)

formato ferrante skribis:

> Given two flats, x and y, give a similarity relation based on the
> distance of x and y from the center of a city/town.
> This is not simply a dualisation of a (pseudo)metrics.
> I think that I should first quotient the set of flats w.r.t the
> equivalence relation defined as follows
> xRy if d(x,center)=d(y,center)
> Then, I can proceed as usual,.i.e
> I give a metrics, I normalize it
> w.r.t. the radius (diameter) of a city and then I apply the duality
> function which fits the t-norm. (for example, in the case of the
> minimum, I take 1-d(x,y).
> Is there a better way to solve the problem?

No need to know the diameter of the city. Example:
du=abs(dx-dy)/(dx+dy)
sim(x,y)=sin((Pi/2)*(1-du)
xRy <=>sim(x,y)=1
We have indeed xRx, xRy=yRx and
(xRy and yRz)=> (dx=dy and dy=dz)=>(dy=dz)=>xRz

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