Rough sets, Bayes' theorem and flow graphs

Rough set theory is a new approach to vagueness and uncertainty. The theory of rough sets has an overlap with many other theories. Specially interesting is the relationship to fuzzy set theory and the theory of evidence. Recently, it turned out that the theory has very interesting connections with Bayes' theorem. The look on Bayes' theorem offered by rough set theory reveals that any data set (decision table) satisfies total probability theorem and Bayes' theorem. These properties can be used directly to draw conclusions from objective data without referring to subjective prior knowledge and its revision if new evidence is available. Thus the rough set view on Bayes' theorem is rather objective in contrast to subjective "classical" interpretation of the theorem. Besides, it is revealed that Bayes' theorem can be interpreted as a flow conservation equation in a flow graph. However the flow graphs considered here are different from those introduced by Ford and Fulkerson. This property gives new perspective for applications of Bayes' theorem. Thus the paper brings two new interpretation of Bayes' theorem, without referring to its classical probabilistic interpretation: as properties of data tables and properties of flow graphs.