Interval-Related Talks at the
2007 IEEE Symposium Series on
Honolulu, Hawaii, April 1–5, 2007
Symposium Series. On April 1–5, 2007, IEEE Computational Intelligence Society
organized the ﬁrst Symposium Series on Computational Intelligence in Honolulu,
Hawaii. The main objective of this series is to bring together researchers and
practitioners from different areas related to computational intelligence, so that
they can learn new techniques and hopefully start fruitful combination of different
techniques and approaches.
In particular, one of the corresponding symposia—Symposium on Foundations
of Computational Intelligence FOCI’07—had a special session on interval method-
ologies. Several other interval-related talks were presented at other session and
other symposia. The interest in interval computations was emphasized by Jerry
Mendel from the University of Southern California, one of the leaders in using
interval techniques in computational intelligence, and a co-Chair of FOCI’07.
Interval computations and computational intelligence. Interval computations
are naturally related to computational intelligence, especially to fuzzy techniques.
In the fuzzy techniques, to formalize a common-sense term like “small,” we do
not simply divide all the values (of, say, height) into small and non-small ones.
Instead, we assign to each possible value a degree to which this value is small—
or, equivalently, we describe, for each real value alpha from the interval [0
) of values which are small with degree at least alpha. The resulting
nested family of intervals is usually called a fuzzy number. How do we process
these fuzzy numbers? In other words, if we know fuzzy numbers describing inputs
, and we have an algorithm y =
) which transforms these inputs
into the desired value, how do we compute the fuzzy number corresponding to
y? It turns out that a natural way to process them is to deﬁne, for every alpha,
) as the range of
) when each x
is in the corresponding interval
). In other words, fuzzy computations can be viewed as layer-by-layer interval
computations—and this is exactly how they are usually performed.
In some cases, we do not need the whole scale of [0
1], it is sufﬁcient to dis-
tinguish between three possible degrees: true, false, and unknown. This restriction
Reliable Computing (2007) 13:435–440
DOI: 10.1007/s11155-007-9040-y © Springer 2007