Rules Induced from Rough Sets in Information Tables with Continuous Values

Rule induction based on neighborhood rough sets is described in information tables with continuous values. An indiscernible range that a value has in an attribute is determined by a threshold on that attribute. The indiscernibility relation is derived from using the indiscernible range. First, lower and upper approximations are described in complete information tables by directly using the indiscernibility relation. Rules are obtained from the approximations. To improve the applicability of rules, a series of rules is put into one rule expressed with an interval value, which is called a combined rule. Second, these are addressed in incomplete information tables. Incomplete information is expressed by a set of values or an interval value. The indiscernibility relations are constructed from two viewpoints: certainty and possibility. Consequently, we obtain four types of approximations: certain lower, certain upper, possible lower, and possible upper approximations. Using these approximations, rough sets are expressed by interval sets. From these approximations we obtain four types of combined rules: certain and consistent, certain and inconsistent, possible and consistent, and possible and inconsistent ones. These combined rules have greater applicability than single rules that individual objects support.