Rough sets with strict and weak indiscernibility relations

Rough sets theory is a tool for vague data analysis. The idea of the rough set consists in approximation of a set by a pair of sets called the lower and upper approximation of the set. The definition of the approximations follows from an indiscernibility relation between elements of the set, called objects. Objects are described by attributes of a qualitative or quantitative nature. In the case of quantitative attributes, the indiscernibility relation has been originally defined after partition of the real scale into a finite number of intervals. The bounds of the intervals are more or less arbitrary and may influence the result of the rough sets analysis. To capture this influence, the author introduces a strict and a weak indiscernibility relation and, according to them, the lower and upper approximations and the measures of vagueness are generalized