Computational Intelligence, Volume 17, Number 3, 2001 GRANULAR COMPUTING: A ROUGH SET APPROACH Son H. Nguyen and Andrzej Skowron Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland JarosLaw Stepaniuk Institute of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland We discuss information granule calculi as a basis of granular computing. They are defined by con- structs like information granules, basic relations of inclusion and closeness between information granules as well as operations on them. The exact interpretation between granule languages of different infor- mation sources (agents) often does not exist. Hence (rough) inclusion and closeness of granules are considered instead of their equality. Examples of all the basic constructs of information granule calculi are presented. The construction of more complex information granules is described by expressions called terms. We discuss the synthesis problem of robust terms, i.e., descriptions of information granules, satis- fying a given specification in a satisfactory degree. We also present a method for synthesis of information granules represented by robust terms (approximate schemes of reasoning) by means of decomposition of specifications for such granules. The discussed problems of granular computing are of special importance for many applications, in particular related to spatial reasoning as well as to knowledge discovery and data mining. Key words: rough sets, granular computing, knowledge discovery in databases. 1. INTRODUCTION In many application areas there is a need for special tools helping to construct approximate description of complex concepts. Let us consider some examples: • In the area of pattern recognition and computer vision efficient methods of approx- imate reasoning from sensor measurements to conclusion are investigated, e.g., for evaluation of identified situation on the road as safe or not by unmanned aerial vehi- cle receiving sensor measurements from cameras, information geographical systems, etc. (see, e.g., the WITAS project web page). • In the area of multi-agent systems (Huhns and Singh 1998; Stone 2000) researchers are developing methods of approximate reasoning in distributed environment of cooperating and competing agents performing some tasks, like soccer playing (Stone 2000). • Information granulation (Zadeh 1996, 1997; Polkowski and Skowron 1998) is very relevant for data mining and knowledge discovery in spatio-temporal databases (see, e.g., Fayyad 1996; Roddick and Spiliopoulou 1999; B¨ ohlen, Jensen and Scholl 1999; Escrig and Toledo 1998, WWW SPACENET; Renz and Nebel 1998) and for flexible query answering (see, e.g., Zadeh and Kacprzyk 1999). The reasoning used to solve problems in the above mentioned areas should be per- formed on the level allowing to deal with complex objects called information granules used to describe, e.g., concept approximations or complex classifiers. Roughly speak- ing, information granules can be treated as linked collections (clumps) of objects drawn together by the criteria of indiscernibility, similarity or functionality (Zadeh 1996, 1997). Descriptions of some information granules can be induced from sensor measurements. Address correspondence to A. Skowron at the Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland; e-mail: skowron, son@mimuw.edu.pl c  2001 Blackwell Publishers, 350 Main Street, Malden, MA 02148, USA, and 108 Cowley Road, Oxford, OX4 1JF, UK.