Affiliations: Institute of Mathematics, The University of Warsaw
Banacha 2, 02-097 Warsaw, Poland. E-mail: skowron@mimuw.edu.pl | Department of Computer Science, Białystok
University of Technology Wiejska 45A, 15-351 Białystok, Poland.
E-mail: j.stepaniuk@pb.edu.pl | Department of Computer Science, San Diego State
University 5500 Campanile Drive San Diego, CA 92182, USA and Institute of
Computer Science, Polish Academy of Sciences Ordona 21, 01-237 Warsaw, Poland.
E-mail: rswiniar@sciences.sdsu.edu
Abstract: We discuss some generalizations of the approximation space
definition introduced in 1994 [24, 25]. These generalizations are motivated by
real-life applications. Rough set based strategies for extension of such
generalized approximation spaces from samples of objects onto their extensions
are discussed. This enables us to present the uniform foundations for inducing
approximations of different kinds of granules such as concepts,
classifications, or functions. In particular, we emphasize the fundamental role
of approximation spaces for inducing diverse kinds of classifiers used in
machine learning or data mining.
Keywords: rough sets, granular computing, approximation space, extension of approximation space, concept approximation, function approximation
