Maintenance of Reductsin the Variable Precision Rough Sets

Deenitions of a reduct for a single object, decision class and all objects of decision table for the variable precision rough sets model are introduced. The deenitions have a property that the set of prime implicants of minimal disjunctive normal form of a discernibility function is equal to the set of reducts. Thus the problem of reducts maintenance in dynamically extended information systems is equivalent to the problem of discernibility function maintenance. We prove that the problem can be stated in the form of a Boolean equation: g ^ h = f ^ k, where f, h and k are given monotonic Boolean functions and g is a function to be determined in minimal disjunctive normal form. An incremental algorithm nding the solution of the above equation is proposed.