Re: fuzzy + possibility


Subject: Re: fuzzy + possibility
From: Ellen Hisdal (ellen@ifi.uio.no)
Date: Mon Jun 05 2000 - 16:27:29 MET DST


>
> Can anybody recommend me the fundamental papers or books dealing
> with relations between the fuzzy sets theory and the possibility
> theory?
> Thanks for your help.
> Jana
> ----------------------------------------------------------------------
> RNDr.Jana Talasova,CSc.
> katedra matematicke analyzy a numericke matematiky
> Prirodovedecka fakulta Univerzity Palackeho
> Tomkova 40, 77600 Olomouc TALASOVA@matnw.upol.cz
> ----------------------------------------------------------------------

It turns out that that the possibility of u (e.g. u=170 cm)
(for a given label such as `tall') is the same as the grade of membership
of `tall' for u=170 cm. The first paper on possibilities was written
by Lotfi Zadeh,

@article{zposs,
   author = {Zadeh, L.A.},
   title = {Fuzzy Sets as a Basis for a Theory of Possibility},
   journal = {Fuzzy Sets and Systems},
   year = {1978},
   volume = {1},
   pages = {3-28} }

See also section 3 in

@article{inf1p1,
   author = {Hisdal, E.},
   title = {Infinite-Valued Logic Based on Two-Valued Logic and
              Probability, Part~1.1. {D}ifficulties with Present-Day
              Fuzzy Set Theory and their Resolution in the {TEE} Model},
   journal = {Int. J. Man-Machine Studies},
   year = {1986},
   volume = {25},
   pages = {89-111},
   ignored = {page 94 for different words for grade of membership
              page 95 for lack of difference between distr tall|u and u|tall}}

Greetings
             Ellen Hisdal

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