Representing regular pseudocomplemented Kleene algebras by tolerance-based rough sets

TL;DR

This paper demonstrates that regular pseudocomplemented Kleene algebras on algebraic lattices can be represented as rough set Kleene algebras derived from tolerance relations induced by irredundant coverings.

Contribution

It establishes an isomorphism between regular pseudocomplemented Kleene algebras and a class of rough set Kleene algebras based on tolerance relations.

Findings

Regular pseudocomplemented Kleene algebras are isomorphic to rough set Kleene algebras.

Representation is achieved via tolerance relations induced by irredundant coverings.

Provides a new algebraic-rough set correspondence for Kleene algebras.

Abstract

We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.