Pseudo-Kleene algebras determined by rough sets

We study the pseudo-Kleene algebras of the Dedekind-MacNeille completion of the ordered set of rough set determined by a reflexive relation. We characterize the cases when PBZ and PBZ*-lattices can be defined on these pseudo-Kleene algebras.Comment: 24 pages, minor update to the initial versio

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

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.Comment: This version is accepted for publication in Approximate Reasoning (May 2021

The Structure of Multigranular Rough Sets

We study multigranulation spaces of two equivalences. The lattice-theoretical properties of so-called "optimistic" and "pessimistic" multigranular approximation systems are given. We also consider the ordered sets of rough sets determined by these approximation pairs

Workshop Notes of the Sixth International Workshop "What can FCA do for Artificial Intelligence?"

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