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

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.