<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>Rough sets, developed by Pawlak [6], are an important tool to describe a situation of incomplete or partially unknown information. One of the algebraic models deals with the pair of the upper and the lower approximation. Although usually the tolerance or the equivalence relation is taken into account when considering a rough set, here we rather concentrate on the model with the pair of two definable sets, hence we are close to the notion of an interval set. In this article, the lattices of rough sets and intervals are formalized. This paper, being essentially the continuation of [3], is also a step towards the formalization of the algebraic theory of rough sets, as in [4] or [9].</p></abstract>

Rough sets, developed by Pawlak [6], are an important tool to describe a situation of incomplete or partially unknown information. One of the algebraic models deals with the pair of the upper and the lower approximation. Although usually the tolerance or the equivalence relation is taken into account when considering a rough set, here we rather concentrate on the model with the pair of two definable sets, hence we are close to the notion of an interval set. In this article, the lattices of rough sets and intervals are formalized. This paper, being essentially the continuation of [3], is also a step towards the formalization of the algebraic theory of rough sets, as in [4] or [9].

On the Lattice of Intervals and Rough Sets

Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland

Formalized Mathematics

{"article-title":"On the Lattice of Intervals and Rough Sets"}

Rough sets, developed by Pawlak [6], are an important tool to describe a situation of incomplete or partially unknown information. One of the algebraic models...

On the Lattice of Intervals and Rough Sets

Published Online: Jul 08, 2010

Page range: 237 - 244

DOI: https://doi.org/10.2478/v10037-009-0030-x

This content is open access.