Granularity, Multi-valued Logic, Bayes’ Theorem and Rough Sets

  • Zdzisław Pawlak
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 95)


Granularity of knowledge attracted attention of many researchers recently. This paper concerns this issue from the rough set perspective. Granularity is inherently connected with foundation of rough set theory. The concept of the rough set hinges on classification of objects of interest into similarity classes, which form elementary building blocks (atoms, granules) of knowledge. These granules are employed to define basic concepts of the theory. In the paper basic concepts of rough set theory will be defined and their granular structure will be pointed out. Next the consequences of granularity of knowledge for reasoning about imprecise concepts will be discussed. In particular the relationship between some ideas of Lukasiewicz’s multi-valued logic, Bayes’ Theorem and rough sets will be pointed out.


Decision Rule Granular Structure Information Granulation Fuzzy Graph Certainty Factor 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Zdzisław Pawlak
    • 1
  1. 1.Institute for Theoretical and Applied InformaticsPolish Academy of SciencesGliwicePoland

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