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Mini-track on
INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES
at the
Joint 9th
IFSA World Congress and 20th NAFIPS International Conference
of NAFIPS, the North American Fuzzy Information Processing Society
and IFSA, the International Fuzzy Systems Association IFSA/NAFIPS'01

INTRODUCTION: FUZZY TECHNIQUES

In many application areas, we do not have an exact model of the
situation and of the objects and processes that we want to
objects and processes, knowledge which experts can often only
describe by using imprecise ("fuzzy") words and terms from natural
languages such as "small", "significant", etc. To enable computers to
use this knowledge, it is necessary to reformulate it in
computer-understandable terms, and then be able to process thus
reformulated knowledge. Techniques for reformulating and processing
such "linguistic" (natural-language) knowledge were proposed by Lotfi
Zadeh in early 1960's under the name of "fuzzy techniques".

In the past decades, these techniques have been successfully used in many
application areas, from control to expert systems to medicine.

* The success of these techniques is largely due to the fact that from
the *methodological* viewpoint, these techniques
are based on revolutionary new ideas and approaches, which enabled
researchers and engineers to handle problems which could not be solved
before.

* On the other hand, the practical success of fuzzy techniques
is also due to the fact that from the purely *mathematical* and
*computational* viewpoint, the corresponding techniques are related
to known computational techniques developed and known in non-fuzzy
("crisp") situations. Thus, fuzzy techniques can re-use known
algorithms and programs to solve new problems.

INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES: MAIN RELATION

One of the main examples of crisp techniques which are useful in fuzzy
applications is interval computations.

The reason why interval computations are useful is that the main
object of fuzzy techniques - the fuzzy set -- can be viewed as a
nested family of sets, or, in 1-D case, the nested family of
intervals. These sets (intervals) are called "alpha-cuts" of the
original fuzzy set. Many operations with fuzzy sets can be naturally
reformulated in terms of the corresponding sets (intervals).

Because of this relation, interval methods are widely used in fuzzy
applications. This relation is well recognized: most textbooks and
monographs on fuzzy sets and fuzzy techniques have a chapter on
interval computation (Klir and Yuan have a chapter, Bojadziev's book
is all devoted to this relation, etc.).

INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES: ADDITIONAL RELATIONS

There are many other relations between fuzzy and intervals. For
example, normally, a fuzzy set (e.g., the set of all small objects)
is defined as a function m(x) which assigns,
to every element x from a certain domain, the degree m(x) to which
this element belongs to this fuzzily defined set.

It is difficult to
expect that we can come up with an exact value for this degree. It is
more natural to assume that an expert provides us with an *interval*
of possible values. Thus, we get the idea of "interval-valued"
fuzzy sets, which have been successfully used by I. B. Turksen,
L. Kohout, J. Mendel, and many other researchers. Handling
interval-valued functions requires a lot of interval computations.

INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES: PROBLEMS

Many researchers use interval techniques in fuzzy
applications. However, often, they use outdated (1960s') interval
effective and efficient results. This disconnect is caused by two
reasons:

* On one hand, many researchers in the area of fuzzy methods are not
very familiar with the latest advances in interval computations.

* On the other hand, many interval researchers are not very familiar
with problems and methods of fuzzy techniques.

INTERVAL COMPUTATIONS AND FUZZY TECHNIQUES: UNIQUE OPPORTUNITY

Right now, there is a great opportunity to narrow the gap between
interval and fuzzy communities. In June 25-28, 2001, there will be a
major event: a joint conference of the North American Fuzzy
Information Processing Society (NAFIPS) and the International Fuzzy
Systems Association (IFSA) in Vancouver (see CFP below).

The organizers of this joint conference realized that this disconnect
harms both communities and prevents them from even more successful
applications. Therefore, they suggested that we organize a special
mini-track on interval computations and fuzzy techniques.

The intention is that this mini-track include:

* technical and applied talks on successes and problems
of interval methods in fuzzy techniques;

* survey talks by *interval* researchers on the existing interval
techniques;

* technical talks of *interval* researchers on new algorithms which may
be of use in fuzzy applications;

* talks by *fuzzy* researchers on interval-related fuzzy problems which
may benefit from using improved interval algorithms;

* any related talks on techniques which generalize interval and/or
fuzzy approaches.

THIS IS REALLY URGENT

To provide maximum publicity to this endeavor, the organizers of
NAFIPS'01 want to publicize it during this year's IEEE Conference
FUZZIEEE'2000 which will take place in early May.

To be able to do that, they need to have the preliminary idea of this
mini-track by May 1, 2000. This list does not have to be final, but it
will be used to advertise the conference and its interval mini-track.

Since I am very familiar with both communities, I volunteered to serve
as a preliminary contact point for this mini-track.

talked with several renown researchers who have successfully combined
interval and fuzzy techniques, and many expressed their interest in
presenting their results at this mini-track. But to have an impact, to
provide a breakthrough, we need as many researchers and papers as possible.

If you are interested in presenting a talk at this mini-track, please
send me (by email) your name and the preliminary title of your talk
(abstract is also great, but if it is difficult to produce an abstract
at short notice, abstracts are only due by December 15).

Let us all together make a difference!

Yours