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

Abstract

<p>We answer the question what properties a collection F of three-valued functions on a set U must fulfil so that there exists a quasiorder <= on U such that the rough sets determined by <= coincide with the core-support pairs of the functions in F. Applying this characterization, we give a new representation of rough sets determined by equivalences in terms of three-valued Lukasiewicz algebras of three-valued functions. </p>