Can Bayesian confirmation measures be useful for rough set decision rules?

Bayesian confirmation theory considers a variety of non-equivalent confirmation measures which say in what degree a piece of evidence confirms a hypothesis. In this paper, we apply some well-known confirmation measures within the rough set approach to discovering relationships in data in terms of decision rules. Moreover, we discuss some interesting properties of these confirmation measures and we propose a new property of monotonicity that is particularly relevant within rough set approach. The main result of this paper states that only two from among confirmation measures considered in the literature have the desirable properties from the viewpoint of the rough set approach. Moreover, we clarify relationships between logical implications and decision rules, and we compare the confirmation measures to several related measures, like independence (dependence) of logical formulas, interestingness measures in data mining and Bayesian solutions of raven's paradox.

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