Towards an Algebraic Approach for Cover Based Rough Semantics and Combinations of Approximation Spaces

We introduce the concept of a synchronal approximation space (SA) and a AUAI-multiple approximation space and show that they are essentially equivalent; to an AUAI rough system. Through this we have estabilished connections between general cover based systems, dynamic spaces and generalized approximation spaces (APS) for easier algebraic semantics. AUAI-rough set theory (RST) is also extended to accommodate local determination of universes. The results obtained are also significant in the representation theory of general granular RST, for the problems of multi source RST and Ramsey-type combinatorics.