Betweenness, Lukasiewicz Rough Inclusions, Euclidean Representations in Information Systems, Hyper-granules, Conflict Resolution

The purpose of this note is to augment information systems with a relation of betweenness among things in the universe of the system and derive from it a geometric representation of granules of things in Euclidean spaces. Next, the notion of betweenness renders a service in introducing a new notion of a hyper– granule. An application to conflict resolution by defining coalitions of agents as granules or hyper–granules and their mixed strategies as elements of convex hulls spanned on things defining the granule is proposed. Finally, hyper–granules offer a new classifying algorithm which exploits neighborhoods of things and in a sense is an improved with respect to similarity variant of nearest neighbor classifier.