# Zdzislaw Pawlak Wins Lofti A. Zadeh Best Paper Award

## The Award

Zdzislaw Pawlak, a professor and research scientist at the
Institute of Theoretical and Applied Informatics in the Polish
Academy of Sciences, has won the 1996 Lotfi A. Zadeh Best Paper Award
in the scientific field of soft computing for a paper entitled
"On Rough Set Theory".
The award, which includes a cash prize of $2,500, will be presented
during the Third Joint Conference on Information Sciences to be
held March 2-5, 1997, at the Sheraton Imperial Hotel and
Convention Center in Research Triangle Park, N.C.

## Rough Set Theory

Pawlak is credited with creating "rough set theory", a
mathematical tool for dealing with vagueness or uncertainty.

Rough set theory is a natural generalization of "twin" theory
(well known in
interval mathematics). In both theories, we are
interested in a set *S*;

- it can be the set of possible values of some quantity, or
- it can be a set of pixels that form an image.

In many real-life situations, we have only partial information about
the set *S*:
- for some points
*s*,
we know for sure that *s* belongs to the set
*S*;
- for some other points
*s*,
we know for sure that *s* does not
belong to this set *S*;
- for other points
*s*,
we do not know whether this point *s*
belongs to the (unknown) set *S* or not.

In this case, the only information that we have about the set
*S* is
that the set *S* is "in between"
the set __L__ of all points
that *definitely* belong to
*S* and the set
*U* of all points
that *may* belong to
*S* (i.e., about which we
do not know for sure that
they do not belong to *S*):
*L* is a subset of
*S*, and
*S* is a subset of
*U*.
In other words, the available information about the (unknown)
set *s*
can be represented by a pair of sets
*(L,U)* such that
*L* is a subset of
*U*.
When both lower and upper approximation sets
*L* and
*U* are intervals, we get
a *twin*. In knowledge
representation, it is natural to consider more
general sets defined by *properties*. Namely, if the only
information that we have about the elements
*s* consist of the values
of *n* basic properties
*P1(s),...,Pn(s)*,
then we have to define the
approximation sets in terms of these properties, i.e., as the set of
all points that satisfy a given propositional combination of the
formulas *Pi(s)*
(e.g., *(P1(s) & P2(s)) V (not P1(s)
& P3(s))*).
In mathematical terms, we consider the
*set algebra*
generated by the sets
*Si={s|Pi(s)}* (i.e., the smallest class
that contains all these sets and that is closed under union,
intersection, and complement), and we take pairs
*(L,U)* of elements from this algebra.
Such a pair is called a *rough set*.

Rough set theory has attracted the attention of researchers and
theoreticians worldwide and has been successfully applied in fields ranging
from medicine to finance.

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