arXiv subjects
Publications and source records attributed to Luisa Iturrioz.
In recent years, many papers have been published showing relationships between rough sets and some lattice theoretical structures. We present here some strong relations between rough sets and three-valued Łukasiewicz algebras.
Inspired by the fundamental results obtained by P. Halmos and A. Monteiro, concerning equivalence relations and monadic Boolean algebras, we recall the `concrete' Rauszer Boolean algebra pointed out by C. Rauszer (1971), via un preorder R. On this algebra we can consider one of the several binary operations defined, in an abstract way, by A. Monteiro (1971). The Heyting-Brouwer subalgebra of constants (fixpoints), allows us to give a general framework to find representations of several special algebraic structures related to logic.
The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset $T$ of two agents, which are partially ordered by the capabilities available in the system. We build up a formal system and we elaborate suitable semantic models in order to derive information from the poset. The system is related to three-valued Heyting algebras with Boolean operators.
The results here presented are a continuation of the algebraic research line which attempts to find properties of multiple-valued systems based on a poset of two agents. The aim of this paper is to exhibit two relationships between some three-valued structures and binary relations. The established connections are so narrow that two representation theorems are obtained.