Discovering Patterns in Numerical Sequences Using Rough Set Theory

摘要

The patterns of numerical sequences are studied via fuzzy and rough set theories. Patterns are interpreted as formulas. If data are perfect (have no noise), then one can show, somewhat surprisingly, that any finite numerical sequence has a "simplest" pattern. That is the sequence can be defined by a recurrence polynomial of the least degree and lowest dimension. One should note that however, in general, the patterns could be arbitrary.