Extension of information entropy-based measures in incomplete information systems

Rough set theory1, 2], developed by professorPawlak, was conceived as a valid mathematical theoryto deal with inexact, uncertain or vague knowledge inmany applicants such as data mining, machine learningand decision support.Although rough set theory, using the concept of in-discernibility relation as its basic principle, provides aformal theoretical mechanism and a series of tools onknowledge reduction and knowledge acquisition throughset algebra, researchers realize that rough set theory isd…

Extension of information entropy-based measures in incomplete information systems

It is helpful for people to understand the essence of rough set theory to study the concepts and operations of rough set theory from its information view. In this paper we address knowledge expression and knowledge reduction in incomplete infolvnation systems from the information view of rough set theory. First, by extending information entropy-based measures in complete information systems, two new measures of incomplete entropy and incomplete conditional entropy are presented for incomplete information systems. And then, based on these measures the problem of knowledge reduction in incomplete information systems is analyzed and the reduct definitions in incomplete information system and incomplete decision table are proposed respectively. Finally, the reduct definitions based on incomplete entropy and the reduct definitions based on similarity relation are compared. Two equivalent relationships between them are proved by theorems and an in equivalent relationship between them is illustrated by an example. The work of this paper extends the research of rough set theory from information view to incomplete information systems and establishes the theoretical basis for seeking efficient algorithm of knowledge acquisition in incomplete information systems.