IOS Press A Comparative Study of Some Generalized Rough Approximations.pdfVIP

Fundamenta Informaticae 51 (2002) 103–119 103 IOS Press A Comparative Study of Some Generalized Rough Approximations ´ Anna Gomolinska Department of Mathematics University of Białystok ul. Akademicka 2, 15-267 Białystok, Poland anna.gom@math.uwb.edu.pl Abstract. In this paper we focus upon a comparison of some generalized rough approximations of sets, where the classical indiscernibility relation is generalized to any binary reflexive relation. We aim at finding the best of several candidates for generalized rough approximation mappings, where both definability of sets by elementary granules of information as well as the issue of distinction among positive, negative, and border regions of a set are taken into account. Keywords: granulation of information, approximation space, rough approximation To Grzegorz and Joanna 1. Introduction Until now the question of generalization of Pawlak’s rough approximation of sets has gained quite much interest in the rough-set community [3, 4, 8, 10, 11, 13, 14, 15, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 39, 38]. What a motivation might be then to discuss this problem again? Doing a work on modelling of some concepts of granular nature, I was stuck when trying to represent the modelled concepts by their lower and upper approximations. It was simply because several competitive approximation mappings
Many thanks to Andrzej Skowron, Peter Starke, and Marcin Wolski for insightful comments on an earlier version of this paper [7], presented at the International Workshop Concurrency, Specification and Programming (CS P’2001), Warsaw, Poland, 2001, October, 3-5th. Thanks al