Combination of Upper and Lower Probabilities
This work addresses theoretical challenges in probabilistic reasoning for researchers in uncertainty modeling, but appears incremental as it builds on existing frameworks like Possibility Theory.
The paper tackles the problem of combining different types of information in incomplete probabilistic systems, distinguishing between a priori and evidential information, and proposes specific combination methods for each, including conditioning as a heterogeneous combination.
In this paper, we consider several types of information and methods of combination associated with incomplete probabilistic systems. We discriminate between 'a priori' and evidential information. The former one is a description of the whole population, the latest is a restriction based on observations for a particular case. Then, we propose different combination methods for each one of them. We also consider conditioning as the heterogeneous combination of 'a priori' and evidential information. The evidential information is represented as a convex set of likelihood functions. These will have an associated possibility distribution with behavior according to classical Possibility Theory.