Generalized decision algorithms, rough inference rules, and flow graphs

Some probabilistic properties of decision algorithms composed of “if..., then...” decision rules are considered. With every decision rule three probabilities are associated: the strength, the certainty and the coverage factors of the rule. It has been shown previously that the certainty and the coverage factors are linked by Bayes’ theorem. Bayes’ theorem has also been presented in a simple form employing the strength of decision rules. In this paper, we relax some conditions on the decision algorithm, in particular, a condition on mutual exclusion of decision rules, and show that the former properties still hold. We also show how the total probability theorem is related with modus ponens and modus tollens inference rules when decision rules are true in some degree of the certainty factor. Moreover, we show that under the relaxed condition, with every decision algorithm a flow graph can be associated, giving a useful interpretation of decision algorithms.