The Structure of Multigranular Rough Sets

Article type: Research Article

Authors: Järvinen, Jouni^a | Radeleczki, Sándor^{b; *}

Affiliations: [a] Department of Mathematics and Statistics, University of Turku, 20014 Turku, Finland. jjarvine@utu.fi | [b] Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary. matradi@uni-miskolc.hu

Correspondence: [*] The work of the second author was carried out as a part of the EFOP-3.6.1-16-00011 “Younger and Renewing University – Innovative Knowledge City” project implemented in the framework of the Széchenyi 2020 program, supported by the European Union, co-financed by the European Social Fund. Address for correspondence: Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary.

Abstract: We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called “optimistic” and “pessimistic” multigranular approximation systems are given. We also consider the ordered sets of rough sets determined by these approximation pairs.

Keywords: Equivalence relation, multigranular approximation, definable set, rough set, coherence, tolerance relation, irredundant covering, atomistic Boolean lattice, completely distributive lattice, Dedekind–MacNeille completion

DOI: 10.3233/FI-2020-1961

Journal: Fundamenta Informaticae, vol. 176, no. 1, pp. 17-41, 2020