IFSA 2007 World Congress
SPECIAL SESSION 5SS
Intuition=
istic
fuzzy sets some related approaches and applications
<= o:p>
ORGANIZERS: E. Sz=
midt
and J. Kacprzyk
Ul. Newelska 6, 01-447 Warsaw, Poland<= /span>
e-mails: szmidt@ibspan.waw.pl , =
kacprzyk@ibspan.waw.pl
SCOPE: =
For se=
veral
centuries (starting from the mid-seventeenth century) uncertainty was
identified and expressed in terms of probability theory only. Uncertainty w=
as a
synonym of randomness. This situation was challenged in the 1960s by other
theories, distinct from probability theory, characterizing different aspect=
s of
uncertain situations. Uncertainty started to be perceived as a multidimensi=
onal
concept manifesting one of its dimensions as randomness. Other dimensions
turned out equally important from the point of view of representing and
processing information. The most visible of the theories, dealing with
different aspects of uncertainty, is Zadeh’s theory
of fuzzy sets.
Many extensions of the conventional theory of fuzzy
sets have appeared over the years. Among those extensions, Atanassov's
theory of intuitionistic fuzzy sets plays an
important role, and has gained popularity in recent years. Basically, it
introduces, for each element of a universe of discourse, a degree of member=
ship
and a degree of non-membership, both from the un=
it
interval, but which do not sum up to 1 as in the conventional fuzzy sets. T=
he
idea of making use of positive and (independently
given) negative information lying in the core of intui=
tionistic
fuzzy sets is natural in real life, and as an obvious consequence, is
well-known in psychology. It also attracted attention of the scientists in =
soft
computing. It would be difficult to deal with machine learning (making use =
of
examples and counter-examples), modeling of preferences or voting without
taking into account positive and (independently given) negative data.
Intuitionistic fuzzy sets making use of both membe=
rship
and non-membership values can represent more adequately the situations when,
for instance, decision makers abstain from expressing their testimonies, so=
me
assessments can not be classified but also can not be discarded, etc.
Therefore, intuitionistic fuzzy sets provide a =
richer
apparatus to grasp imprecision than the conventional fuzzy sets.
CONTACT INFORM=
ATION:
Eulalia Szmidt=
Systems Research Institute
=
Ul. Newelska 6, =
01-447
E-mail: szmidt@ibspan.waw.pl
Janusz=
Kacprzyk
Systems Research Institute
Ul. Newelska 6, 01-447 Warsaw
Poland
E-mail: kacprzyk@ib=
span.waw.pl
URL: http://www.ibspan.waw.pl/~kacprzyk