Newsgroups: comp.ai.fuzzy
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!fas-news.harvard.edu!newspump.wustl.edu!news.starnet.net!wupost!howland.reston.ans.net!news.sprintlink.net!pipex!sunsite.doc.ic.ac.uk!warwick!bsmail!zeus!entpm
From: entpm@zeus.bris.ac.uk (TP. Martin)
Subject: Re: SEMANTIC UNIFICATION
Message-ID: <D3BInq.5ot@info.bris.ac.uk>
Sender: usenet@info.bris.ac.uk (Usenet news owner)
Nntp-Posting-Host: zeus.bris.ac.uk
Organization: University of Bristol, England
X-Newsreader: TIN [version 1.2 PL2]
References: <3g8fi6$ndo@gina.zfn.uni-bremen.de>
Date: Wed, 1 Feb 1995 11:02:14 GMT
Lines: 31

Mehmet Kus (mehmet@p213.informatik.uni-bremen.de) wrote:
: Hi folks!

: By using the semantic unification (Baldwin) on two distinct
: fuzzy-terms (f|g) you get a support-pair as the result.
: If the fuzzy-terms (e.g. triangle form) are identical (f|f) then
: the result is [0.5;1]. 
: But by using two identical crisp fuzzy-terms the solution is [1;1].
: We have a difference of 0.5
: Is this not a contradiction to the fuzzy concepts?
: Thank you for your help!
:     

I presume that by the phrase "crisp fuzzy-terms" you mean crisp or non-fuzzy
terms. You are then correct to say that if (for example) f = {a, b} then
the support pair for f|f is (1 1).
When f becomes fuzzy, however, there are elements which satisfy f to
some degree, but which also satisfy not-f. e.g. f={a:0.9  b:1}
Now the support pair for f|f is (0.91 1), since there are elements in
f which also satisfy not-f.

In the continuous case with closed sets, you will always get (0.5 1) because 
there is always some element with membership 0.5.
This will happen with the probabilistic formulation of semantic unification,
or with the possibilistic version.

It is not incorrect - it gives bounds on the probability. If you want a
point value, use Baldwin's point-value semantic unification algorithm.
Generally, the point value will be less than 1.


