A Calculus on Granules from Rough Inclusions in Information Systems

Indiscernibility relations induced in information systems in the sense of Pawlak,define granules of knowledge as unions of their equivalence classes,leading to regular structures like Boolean algebras.Apart from Boolean operations on granules, under a fixed set of attributes, that induce the partition topology on their collection,one may search for more flexible schemes that would induce in collections of granules some non-trivial topologies and in particular quasi-metrics on granules,allowing for richer structures.A way of realization of this program has been proposed as the paradigm of rough mereology;although abstract,stemming from an alternative set theory,yet it offers a calculus based on kind of quasi-metrics that allows for discussing granules from the point of view of their closeness.In this work, we would like to present the ideas of this approach and basic results with short discussion of applications.