Decision algorithms and flow graphs; a rough set approach

Abstract

This paper concerns some relationship between Bayes` theorem and rough sets. It is revealed that any decision algorithm satisfies Bayes` theorem, without referring to either prior or posterior probabilities inherently associated with classical Bayesian methodology. This leads to a new simple form of this theorem, which results in new algorithms and applications. Besides, it is shown that with every decision algorithm a flow graph can be associated. Bayes` theorem can be viewed as a flow conservation rule of information flow in the graph. Moreover, to every flow graph the Euclidean space can be assigned. Points of the space represent decisions specified by the decision algorithm, and distance between points depicts distance between decisions in the decision algorithm.