Newsgroups: sci.stat.math,comp.ai.fuzzy
Path: cantaloupe.srv.cs.cmu.edu!das-news.harvard.edu!news2.near.net!MathWorks.Com!europa.eng.gtefsd.com!howland.reston.ans.net!cs.utexas.edu!utnut!ie.utoronto.ca!bilgic
From: bilgic@fuzzy.ie.utoronto.ca (Taner Bilgic)
Subject: Re: Discussion on Fuzzy logic ??
Message-ID: <bilgic.780444168@fuzzy.ie.utoronto.ca>
Sender: readnews@ie.utoronto.ca (News Poster)
Organization: University of Toronto, Department of Industrial Engineering
References: <haukland.30.779704047@linnea.gih.no> <Cw8Lt8.1E1@unx.sas.com> <mscarton.184.00099948@mudshark.sunquest.com>
Date: Sat, 24 Sep 1994 22:02:48 GMT
Lines: 47
Xref: glinda.oz.cs.cmu.edu sci.stat.math:2733 comp.ai.fuzzy:2976

mscarton@mudshark.sunquest.com (Mark A. Scarton) writes:

>Posted in sci.stat.math:
>>> Is this newsgroup the right one for discussion about issues in fuzzy
>>> logic ??
>>Probably not, since fuzziness and probability are more or less
>>orthogonal concepts.

>I disagree with the point of their being orthogonal.  Fuzziness is a
>generalization of probability theory, loosening the constraints by not
>requiring DeMorgan's law and additivity.  Articles abound discussing 
>this; my favorite is the write-up of Dr. George Klir's debate at Oxford 
>"Is there more to probability theory ...".

Probably one should make the distiction between fuzzy set theory (or fuzzy
logic) and fuzzy measure theory. Fuzzy measure theory is a generalization 
of measure theory (and hence probability theory) whereas the concepts of
fuzzy sets and probability are orthogonal.

Among their other publications Dubois and Prade emphasize such differences
and similarities in:

@article{Dubo&Prad89,
    author  = {D. Dubois and H. Prade},
    title   = {Fuzzy Sets, Probability and Measurement},
    journal = {European Journal of Operational Research},
    year    = {1989},
    volume  = {40},
    pages   = {135--154},
}

@inproceedings{Dubo&Prad93,
    author  = {D. Dubois and H. Prade},
    title   = {Fuzzy sets and probability: Misunderstandings, bridges and gaps},
    booktitle = {Second IEEE International Conference on Fuzzy Systems},
    organization = {IEEE},
    year    = {1993},
    pages   = {1059--1068},
    note    = {San Fransisco, California March 28--April 1, 1993},
}


--
Taner Bilgic                      bilgic@ie.utoronto.ca
Dept. of Industrial Engineering   
University of Toronto             Tel:(416) 978-0880
Toronto, Ontario M5S 1A4 Canada   Fax:(416) 978-1280
