Information interpretation of knowledge granularity

Authors:
Rui-Zhi Wang;Duo-Qian Miao;Fei-Fei Xu;Hong-Yun Zhang
Affiliations:
The Key Laboratory of “Embedded System and Service Computing”, Ministry of Education, China and Department of Computer Science and Technology, Tongji University, Shanghai, P.R. China;The Key Laboratory of “Embedded System and Service Computing”, Ministry of Education, China and Department of Computer Science and Technology, Tongji University, Shanghai, P.R. China;Shanghai University of Electronic Power, Shanghai, P.R. China;The Key Laboratory of “Embedded System and Service Computing”, Ministry of Education, China and Department of Computer Science and Technology, Tongji University, Shanghai, P.R. China
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology - Computational intelligence models for image processing and information reasoning
Year:
2013

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Abstract

The quantitative analysis of the degree of knowledge granularity poses theoretical challenges for the development of granular computing. Information-theoretic measures have been proposed to address this problem, which exhibit usefulness in complete information systems. However, mathematical analysis of relationships between these information-theoretic measures and knowledge granularity has not been done. In this paper, after introducing Shannon's entropy and mutual information into complete information systems, we prove, for the first time, that these information-theoretic measures decrease monotonously as partition becomes coarser under complete information systems. Moreover, we illustrate that their inverse relationships do not hold generally and present an additional condition under which the inverse relationships are valid. By generalizing Shannon's entropy to incomplete information systems, we further discuss the relationship between the generalized Shannon's entropy termed as rough information entropy and knowledge granularity based on covering generalized rough sets. We find that in incomplete information systems, the rough information entropy varies nonmonotonously as covering becomes coarser. An illustrative example is given to verify the above observation result.