Rough graph approximations via symmetry groups: automorphisms and permutations

Abstract

Recently, rough graphs have received considerable attention for their ability to model imprecise information in graphical data. By leveraging rough set theory, rough graphs address uncertainty through approximation and classification mechanisms. In this paper, we introduce rough graphs as mathematical objects defined through graph automorphism groups, providing a symmetry-based framework for uncertainty. Concurrently, we derive an indiscernibility relation from binary relations R via the automorphism group of its graph representation G(R), where indiscernibility corresponds to orbits under the group action. This approach generalizes to define rough relations and rough graphs through an arbitrary permutation group acting on the underlying set.