An Open-Frame Theory of Incomplete Interval Probabilities
Andrea Sgarro · International Journal of Uncertainty Fuzziness and Knowledge-Based Systems · 1998
We develop a reference setting for uncertainty representation, i.e. incomplete interval probabilities, which we think may be useful not only at the formal but also at the conceptual level. The universe we choose to work on is a finite set, which is thought of as open (incomplete, not fully observable); a pre-assumption we make is acceptance of Dempster rule without the normalization coefficient as an adequate tool for pooling opinions. We make use of three comparatively old ingredients: interval probabilities, open-frame bodies of evidence and Rényi's incomplete probabilities. As for open-frame bodies of evidence, we introduce a formal novelty, seemingly of little or no consequence, which instead leads us quite naturally to the unifying approach of incomplete interval probabilities. We tackle the problem of forcing incomplete states of knowledge into completeness, as required at the operational stage of decision making.