An Investigation About Rough Set Theory: Some Foundational and Mathematical Aspects

Issue title: Advances in Rough Set Theory

Article type: Research Article

Authors: Cattaneo, Gianpiero

Affiliations: Dipartimento Di Informatica, Sistemistica e Comunicazione, Università di Milano – Bicocca, Viale Sarca 336 – U14, I–20126 Milano, Italia. cattang@live.it

Note: [] Address for correspondence: University of Milano-Bicocca, via Compagnoni 34, 20129 Milano, Italy

Abstract: The approach to rough set theory is investigated from the foundational point of view, starting from the formal analysis of the mathematical structures generated by equivalence relations (the standard Pawlak approach to complete information systems) and then by tolerance or similarity relations (the approach to roughness by incomplete information systems). Making use of these approaches the “minimal” meta–theoretical principles which allow one to treat approximations in rough set theory are discussed and formulated in explicit way, in particular the conditions which can assure what can be rightly considered as lower and upper approximations of some approximable set. The hierarchy of approximation spaces generated in this way on a universe is then discussed.

DOI: 10.3233/FI-2011-420

Journal: Fundamenta Informaticae, vol. 108, no. 3-4, pp. 197-221, 2011