Plausible reasoning and graded information: a unified approach

We propose a formal method for reasoning both under uncertainty and under vagueness in a coherent way. We deal with implicational relationships where an explicit numerical degree is used to express uncertainty. The approach relies on Dubois and Prade's Possibilistic Logic. Furthermore, we take the possible vagueness of the involved properties into account. Namely, we deal with properties of the form that some vague criterion is fulfilled to a specific degree. Thus vague properties are treated as parametrised sets of crisp properties. Finally, a rule is included to ensure smoothness of the uncertainty degree with regard to changes of the degrees to which the properties under consideration hold. The calculus is applicable wherever graded properties are subject to uncertainty. Vagueness and uncertainty are treated independently, but can optionally be interconnected in a controlled way. A specific application suggests itself in the field of medical expert systems.