Rough sets, decision algorithms and Bayes' theorem

Rough set-based data analysis starts from a data table, called an information system. The information system contains data about objects of interest characterized in terms of some attributes. Often we distinguish in the information system condition and decision attributes. Such information system is called a decision table. The decision table describes decisions in terms of conditions that must be satisfied in order to carry out the decision specified in the decision table. With every decision table a set of decision rules, called a decision algorithm, can be associated. It is shown that every decision algorithm reveals some well-known probabilistic properties, in particular it satisfies the total probability theorem and Bayes' theorem. These properties give a new method of drawing conclusions from data, without referring to prior and posterior probabilities, inherently associated with Bayesian reasoning.