Newsgroups: comp.ai.fuzzy
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!howland.reston.ans.net!cs.utexas.edu!utnut!ie.utoronto.ca!bilgic
From: bilgic@fuzzy.ie.utoronto.ca (Taner Bilgic)
Subject: Re: Fuzziness and Fundamental Measurement
Message-ID: <bilgic.787422723@fuzzy>
Sender: readnews@ie.utoronto.ca (News Poster)
Organization: University of Toronto, Department of Industrial Engineering
Date: Wed, 14 Dec 1994 16:32:03 GMT
Lines: 36

Hi all,

It seems that I have not seen how this thread has started.
But for anyone who is interested in measurement-theoretic
axiomatizations of fuzzy set theory, my recent work is
available online

URL:http://analogy.ie.utoronto.ca/~bilgic/tanerpubl.html

There are two related papers: Measurement-theoretic frameworks
for fuzzy set theory (orlpaper.ps.gz) and Measurement-theoretic
justification of connectives in fuzzy set theory
(conectivepaper.ps.Z).

Briefly, I am considering the suitability of t-norms and t-conorms
(of course min and max are in those classes) for fuzzy set theory.
The main conclusion is that fuzzy set theory cannot model the
cardinal aspects of the type of uncertainty (vagueness if you
prefer) it is modelling.

Furthermore, using two distinct measurement problems in which the
primitives are different (but related), I combine these two
problems and show that connectives in fuzzy set theory need not be truth
functional. Truth functionality is a *very* special case.

I'll be happy to hear some comments, criticisms etc.

Cheers, Taner

ps: if you have trouble in retrieving the files please let me know.

--
Taner Bilgic                      bilgic@ie.utoronto.ca
Dept. of Industrial Engineering   Tel:(416) 978-1398 
University of Toronto             Fax:(416) 978-1280
Toronto, Ontario M5S 1A4 Canada   URL:http://analogy.ie.utoronto.ca/~bilgic
