Categorical properties of M-indiscernibility spaces
This paper discusses categorical aspect of the Pawlak rough set theory. It is proved that the category of all M-indiscernibility spaces and M-equivalence relation-preserving mappings between them is both a topological construct and a topos. As an application of these results, the notions of product M-indiscernibility space, sum M-indiscernibility space, quotient M-indiscernibility space, M-indiscernibility subspace, quotient mapping, and isomorphism mapping are defined, and structures of these M-indiscernibility spaces and mappings are also given. (C) 2011 Elsevier B.V. All rights reserved.
m-indiscernibility space rough set category m-equivalence relation-preserving mapping topological construct topos product m-indiscernibility space sum m-indiscernibility space quotient m-indiscernibility space m-indiscernibility subspace quotient mapping isomorphism mapping multi-agent/multi-source approximation space m-equivalence relation natural computation