Structures of Opposition in Fuzzy Rough Sets

Issue title: Rough Sets and Fuzzy Sets

Article type: Research Article

Authors: Ciucci, Davide^{a; *} | Dubois, Didier^b | Prade, Henri^b

Affiliations: [a] DISCo, Università di Milano – Bicocca, Viale Sarca 336/14, 20126 Milano, Italia. ciucci@disco.unimib.it | [b] IRIT, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex 9, France. dubois@irit.fr, prade@irit.fr

Correspondence: [*] Address for correspondence: DISCo, Università di Milano – Bicocca, Viale Sarca 336/14, 20126 Milano, Italia

Abstract: The square of opposition is as old as logic. There has been a recent renewal of interest on this topic, due to the emergence of new structures (hexagonal and cubic) extending the square. They apply to a large variety of representation frameworks, all based on the notions of sets and relations. After a reminder about the structures of opposition, and an introduction to their gradual extensions (exemplified on fuzzy sets), the paper more particularly studies fuzzy rough sets and rough fuzzy sets in the setting of gradual structures of opposition.

Keywords: square of opposition, fuzzy set, fuzzy relation, rough set

DOI: 10.3233/FI-2015-1282

Journal: Fundamenta Informaticae, vol. 142, no. 1-4, pp. 1-19, 2015