# 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. Back to the Honors Received by Interval Researchers page