Information entropy, rough entropy and knowledge granulation in incomplete information systems

J. Liang, Z. Shi, D. Li, M. J. Wierman

Research output: Contribution to journalArticle

190 Citations (Scopus)

Abstract

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances that are characterized by vagueness and uncertainty. Rough set theory uses a table called an information system, and knowledge is defined as classifications of an information system. In this paper, we introduce the concepts of information entropy, rough entropy, knowledge granulation and granularity measure in incomplete information systems, their important properties are given, and the relationships among these concepts are established. The relationship between the information entropy E(A) and the knowledge granulation GK(A) of knowledge A can be expressed as E(A)+GK(A)= 1, the relationship between the granularity measure G(A) and the rough entropy Er(A) of knowledge A can be expressed as G(A)+ Er(A)= log2| U |. The conclusions in Liang and Shi (2004) are special instances in this paper. Furthermore, two inequalities - log2 GK(A) G(A) and Er(A)log2;(| U |(1-E(A)) about the measures GK , G, E and Er are obtained. These results will be very helpful for understanding the essence of uncertainty measurement, the significance of an attribute, constructing the heuristic function in a heuristic reduct algorithm and measuring the quality of a decision rule in incomplete information systems.;.

Original languageEnglish
Pages (from-to)641-654
Number of pages14
JournalInternational Journal of General Systems
Volume35
Issue number6
DOIs
StatePublished - Dec 1 2006

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Incomplete Information System
Granulation
Information Entropy
Rough
Information systems
Entropy
Rough set theory
Rough Set Theory
Granularity
Information Systems
Computer applications
Heuristics
Heuristic algorithms
Computer Applications
Measurement Uncertainty
Reduct
Vagueness
Decision Rules
Table
Attribute

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Theory and Mathematics

Cite this

Information entropy, rough entropy and knowledge granulation in incomplete information systems. / Liang, J.; Shi, Z.; Li, D.; Wierman, M. J.

In: International Journal of General Systems, Vol. 35, No. 6, 01.12.2006, p. 641-654.

Research output: Contribution to journalArticle

Liang, J. ; Shi, Z. ; Li, D. ; Wierman, M. J. / Information entropy, rough entropy and knowledge granulation in incomplete information systems. In: International Journal of General Systems. 2006 ; Vol. 35, No. 6. pp. 641-654.
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