Definite reducts in ordered decision information systems

In ordered decision information systems, by taking the interval as basic knowledge granules, lower and upper approximations of unions of decision classes can be defined, and interval decision rules can be induced. Definite interval decision rules with univocal decision, induced by intervals in lower approximations of every decision class, can be used in classification for ordinal data. To the end of optimizing all the definite interval decision rules, definite positive region is defined and the concept of definite reduct is proposed. Discernibility function is constructed and used to compute definite reducts by Boolean reasoning technique.