Rough Sets and Infomorphisms: Towards Approximation of Relations in Distributed Environments

We discuss the relationships between information systems and classifications as well as between infomorphisms and definability of relations (between whole objects and their parts) in information systems. Infomorphisms between information systems (classifications) and make it possible to define some formulas over by means of formulas over The remaining formulas over can be approximatively defined by means of formulas over The approximation operations are defined using the rough set approach. We present definitions and examples of such approximations. The research has been supported by the State Committee for Scientific Research of the Republic of Poland (KBN) research grant 8 T11C 025 19 and partially by the Wallenberg Foundation grant. The paper has been prepared within the framework of COST Action 274 “Theory and Application of Relational Structures as Knowledge Instruments”. Address for correspondence: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland The research has been supported by the State Committee for Scientific Research of the Republic of Poland (KBN) research grant 8 T11C 025 19. The research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) research grant 185986. 264 A. Skowron et al. / Rough Sets and Infomorphisms