similarity <-> fuzziness

ferrante formato (formato@bridge.diima.unisa.it)
Wed, 14 Oct 1998 04:10:01 +0200 (MET DST)

The question that was arisen by myself has a likely negative answer.
In fact, if we want to represent a family of fuzzy subsets with a
family prototypes and a UNIQUE similarity, this is impossible, as
Luis Godo has pointed out.
Still, Giangiacomo Gerla made the following remark.
-Given two fuzzy subsets s and s' such that
s(x)=0 for any x in the prototype set Fs' of s'
s'(x)=0 for any x in the prototype set Fs of s
then there exists a similarity (with respect to the minimum) R such
that Sup{ R(x,y) | y is in Fs}=s(x), Sup{ R(x,y) | y is in Fs'}=s'(x)
if and only if s and s' are disjoint.-

At this point, a possible (naive) way out would be the following.
Okay, if there is a domain overlap, just use "syntactic sugar"
and "duplicate" overlapping fuzzy sets!
In this way, two overlapping fuzzy sets will become two different fuzzy
sets on two disjoint domains.
The question is:

- How naive is this suggestion?-

I hope to have been sufficiently clear.
Ferrante Formato

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