Maximal similarity granular rough sets for mixed and incomplete information systems

Mixed and incomplete data is very common in several applications nowadays. Unfortunately, Rough Sets lack effective tools for handling both mixed as well as incomplete information systems. This paper introduces a novel approach for dealing with such information systems: The Generic Extended Rough Sets and the maximal similarity granular rough sets (MSGRS) as a particular case. MSGRS have single and multiple granulations, as well as optimistic and pessimistic definitions for both scenarios. The theoretical analysis carried out, as well as the proposed notation, shows that MSGRS are a generalization of some existing proposals for dealing with incomplete information systems and mixed information systems. The obtained results enrich rough Set Theory and are useful for addressing mixed as well as incomplete information systems, with single and multiple granulations.