Finite IUML-algebras, Finite Forests and Orthopairs

Article type: Research Article

Authors: Aguzzoli, Stefano^a | Boffa, Stefania^{b; *} | Ciucci, Davide^c | Gerla, Brunella^d

Affiliations: [a] Università di Milano, Milano, Italy. aguzzoli@di.unimi.it | [b] Università dell’Insubria, Varese, Italy. sboffa@uninsubria.it | [c] Università di Milano–Bicocca, Milano, Italy. ciucci@disco.unimib.it | [d] Università dell’Insubria, Varese, Italy. brunella.gerla@uninsubria.it

Correspondence: [*] Address for correspondence: Università dell’Insubria, Varese, Italy.

Note: [1] In this paper, we extend the results already appeared in [1] and we give the full proofs of all propositions and theorems.

Abstract: We show that finite IUML-algebras, which are residuated lattices arising from an idempotent uninorm, can be interpreted as algebras of sequences of orthopairs whose main operation is defined starting from the three-valued Sobociński operator between rough sets. Our main tool is the representation of finite IUML-algebras by means of finite forests.1

Keywords: Orthopairs, forests, IUML-algebras

DOI: 10.3233/FI-2018-1735

Journal: Fundamenta Informaticae, vol. 163, no. 2, pp. 139-163, 2018