Rule induction based on rough sets from information tables having continuous domains

Abstract

Information tables having continuous domains are handled by neighborhood rough sets. Two approximations in complete information tables are extended to handle incomplete information. Consequently, four approximations are obtained: certain and possible lower ones and certain and possible upper ones without computational complexity. These extended approximations create the same results as the ones from possible world semantics by using possible indiscernibility relations. Therefore, the extension is justified. In complete information tables two types of single rules that an object supports are obtained: consistent and inconsistent ones. The single rule has low applicability. To increase applicability, a series of single rules are brought into one combined rule with an interval value. In incomplete information tables four kinds of single rules are obtained. From them, four kinds of combined rules are obtained: certain and consistent, possible and consistent, certain and inconsistent, and possible inconsistent ones. A combined rule has higher applicability than the single rules from which it is assembled.