Relational correspondences for L-fuzzy rough approximations defined on De Morgan Heyting algebras

TL;DR

This paper explores fuzzy rough sets on De Morgan Heyting algebras, establishing a key theorem that links fuzzy rough approximations with various fuzzy relations through a unified axiom.

Contribution

It introduces a theorem that simplifies the derivation of correspondence results between fuzzy rough sets and fuzzy relations on De Morgan Heyting algebras.

Findings

Characterization of fuzzy rough approximation operators via a single axiom

Unified framework for reflexive, transitive, Euclidean, and adjoint fuzzy relations

Enhanced understanding of fuzzy rough set relations on algebraic structures

Abstract

We consider fuzzy rough sets defined on De Morgan Heyting algebras. We present a theorem that can be used to obtain several correspondence results between fuzzy rough sets and fuzzy relations defining them. We characterize fuzzy rough approximation operators corresponding to compositions of reflexive, transitive, mediate, Euclidean and adjoint fuzzy relations defined on De Morgan Heyting algebras by using only a single axiom.