In rough set theory (RST), and more generally in granular computing on information tables (GRC-IT), a central tool is the Pawlak's indiscernibility relation between objects of a universe set with respect to a fixed attribute subset. Let us observe that Pawlak's relation induces in a natural way an equivalence relation ≈ on the attribute power set that identifies two attribute subsets yielding the same indiscernibility partition. We call indistinguishability relation of a given information table I the equivalence relation ≈, that can be considered as a kind of global indiscernibility. In this paper we investigate the mathematical foundations of indistinguishability relation through the introduction of two new structures that are, respectively, a complete lattice and an abstract simplicial complex. We show that these structures can be studied at both a micro granular and a macro granular level and that are naturally related to the core and the reducts of I. We first discuss the role of these structures in GrC-IT by providing some interpretations, then we prove several mathematical results concerning the fundamental properties of such structures.
Bisi, C., Chiaselotti, G., Ciucci, D., Gentile, T., & Infusino, F. (2017). Micro and macro models of granular computing induced by the indiscernibility relation. INFORMATION SCIENCES, 388-389, 247-273.
Citazione: | Bisi, C., Chiaselotti, G., Ciucci, D., Gentile, T., & Infusino, F. (2017). Micro and macro models of granular computing induced by the indiscernibility relation. INFORMATION SCIENCES, 388-389, 247-273. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Presenza di un coautore afferente ad Istituzioni straniere: | No |
Titolo: | Micro and macro models of granular computing induced by the indiscernibility relation |
Autori: | Bisi, C; Chiaselotti, G; Ciucci, D; Gentile, T; Infusino, F |
Autori: | GENTILE, TOMMASO (Penultimo) |
Data di pubblicazione: | 2017 |
Lingua: | English |
Rivista: | INFORMATION SCIENCES |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.ins.2017.01.023 |
Appare nelle tipologie: | 01 - Articolo su rivista |