Abstract: Uncertainty measure is one of the key issues in the study of rough set theory, however, the existing studies on uncertainty measure are restricted to set-theoretic rough set model(crisp or fuzzy). This paper extends the uncertainty measure of formulae in rough logic to probabilistic environments. By employing the probability measure theory, a new notion of probabilistic rough truth degree (P-rough truth degree for short) is proposed. This notion is demonstrated to be adequate for measuring the extent to which any formula is roughly true in probabilistic environments. Then based upon the fundamental notion, the notions of P-rough similarity degree, P-accuracy degree and P-roughness degree of formulae in rough logic are also proposed. The properties of these concepts are investigated in detail. Moreover, the notion of P-rough similarity degree can also induce, in a natural way, three kinds of pseudo-metrics on the set of rough formulae, which can be used to develop a kind of approximate reasoning in rough logic.
