Rough set approximations VS. measurable spaces
Wei-Zhi Wu, Wen‐Xiu Zhang · 2006
In this paper relationships between rough set ap- proximations and measurable spaces are examined. It is proved that the family of all definable sets in a serial crisp (fuzzy, respectively) rough set algebra forms a crisp (fuzzy respectively) algebra. For any crisp measurable space there must exist a crisp rough set algebra such that the family of all definable sets is the given crisp algebra. Also, for a fuzzy algebra generated by a crisp algebra there must exist a fuzzy rough set algebra such that the family of all definable sets is just the given fuzzy algebra.