On Asymptotic Properties of Rough ― Set ― Theoretic Approximations. Fractal Dimension, Exact Sets, and Rough Inclusion in Potentially Infinite Information Systems

摘要

We look at asymptotic properties of rough set approximations exploiting them to three-fold purpose viz. to introduce a counterpart of fractal dimension in abstract information systems, to define the notion of an exact set in infinite information system to the result that so defined exact sets form a compact metric Boolean algebra of sets, and to introduce rough inclusion measures for rough mereology for infinitary concepts.