Defining rough sets as core-support pairs of three-valued functions

TL;DR

This paper characterizes collections of three-valued functions that correspond to rough sets defined by quasiorders and provides a new algebraic representation of rough sets via three-valued { extL}ukasiewicz algebras.

Contribution

It offers a novel characterization of three-valued functions related to rough sets and introduces a new algebraic representation using three-valued { extL}ukasiewicz algebras.

Findings

Characterization of collections of three-valued functions for rough set representation

New algebraic representation of rough sets via { extL}ukasiewicz algebras

Connection between rough sets and quasiorders established

Abstract

We answer the question what properties a collection $\mathcal{F}$ of three-valued functions on a set $U$ must fulfill so that there exists a quasiorder $\leq$ on $U$ such that the rough sets determined by $\leq$ coincide with the core--support pairs of the functions in $\mathcal{F}$. Applying this characterization, we give a new representation of rough sets determined by equivalences in terms of three-valued {\L}ukasiewicz algebras of three-valued functions.