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 language | English |
|---|---|
| Pages (from-to) | 641-654 |
| Number of pages | 14 |
| Journal | International Journal of General Systems |
| Volume | 35 |
| Issue number | 6 |
| DOIs | |
| State | Published - Dec 1 2006 |
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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 journal › Article
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TY - JOUR
T1 - Information entropy, rough entropy and knowledge granulation in incomplete information systems
AU - Liang, J.
AU - Shi, Z.
AU - Li, D.
AU - Wierman, M. J.
PY - 2006/12/1
Y1 - 2006/12/1
N2 - 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.;.
AB - 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.;.
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U2 - 10.1080/03081070600687668
DO - 10.1080/03081070600687668
M3 - Article
VL - 35
SP - 641
EP - 654
JO - International Journal of General Systems
JF - International Journal of General Systems
SN - 0308-1079
IS - 6
ER -