Automated Discovery of Properties of Rough Sets

Issue title: Concurrency, Specification and Programming

Article type: Research Article

Authors: Grabowski, Adam

Affiliations: University of Białystok, Institute of Informatics, Akademicka 2, 15-267 Białystok, Poland. adam@math.uwb.edu.pl

Note: [] The article is a revised and expanded version of the paper presented at the 21st Workshop on Concurrency, Specification and Programming (CS&P 2012). Partial support for this work was provided by the Polish Ministry of Science and Higher Education grant “Managing a large repository of computer-verified mathematical knowledge” N N519 385136. Thanks go to the anonymous referees for kind remarks on the paper. Address for correspondence: University of Białystok, Institute of Informatics, Akademicka 2, 15-267 Białystok, Poland

Abstract: The computer certification of rough sets (the translation in a way understandable by machines) seems to be far beyond the test phase. To assure the feasibility of the approach, we try to encode selected problems within rough set theory and as the testbed of already developed foundations – and in the same time as a payoff of the established framework – we shed some new light on the well-known question of generalization of rough sets and the axiomatization of approximation operators in terms of (various types of) binary relations. We show how much the human work can be enhanced with the use of automatic tools, without loosing too much time for the translation. Although the syntax is understandable by the computer, it offers relative flexibility and expressive power of the formal language.

Keywords: rough sets, generalized rough approximations, formalization of mathematics

DOI: 10.3233/FI-2013-933

Journal: Fundamenta Informaticae, vol. 128, no. 1-2, pp. 65-79, 2013