Often included are methods of combining and propagating uncertain information within a mathematically rigorous structure.
In heterogeneous reasoning environments, whether they exist as a distributed multi-agent system or a hybrid reasoning framework as presented here, there is a need to exchange uncertain information between independently developed software elements, which may be based on processing technologies that utilize different models and representations for uncertainty. The ideal situation would use a single universally capable and accepted uncertainty model. Unfortunately, such a model does not currently exist and is unlikely to be developed any time soon. Some of the more common approaches to representing uncertainty used by various reasoning systems today are based on Bayesian probability theory, certainty factors, Dempster-Shafer theory, imprecise probabilities, possibility theory , and fuzzy logic. As with the reasoning technologies they are typically associated with, each approach has various strengths and characteristics regarding its representational capabilities. Each has different representational characteristics and propagation models.
Much of the early work regarding uncertainty was based on Pearl 's causal models , which relate each variable to a relatively small number of immediate causes and represents uncertainty as probabilities. Other early techniques such as certainty factors used in expert systems such as MYCIN have shown initial promise but not proven sufficiently general for application to a wider range of reasoning technologies. Valuation based models using fuzzy-logic are somewhat more general but still not universal handling of uncertainty. Similarly, variations that combine Dempster-Shafer belief potentials with probabilistic argumentation at least attempt to address translation and interaction between different uncertainty models, but only between two such systems. One aspect that most uncertainty management schemes agree on is that single point values of risk are worse than representing both variability and uncertainty. Common ways to more adequately express uncertainty are: 1) to represent the level of uncertainty by modifying the probability for propositions; 2) to treat it as a separate entity that is affixed to each probability; and 3) to represent it as a range of opinions. Opinion pooling is particularly effective at assessing the usefulness of information produced by human experts. , , When applied in a hierarchical model, it can provide a natural and flexible way to incorporate dependencies among experts while acknowledging that they may justifiably disagree. In these models, uncertainty in a probabilistic value is represented by a collection of estimates of the quantity and the degree of certainty or uncertainty is measured by means of the distribution of values in the collection of estimates.
Part of the reason there are so many approaches to modeling uncertainty is that the very nature of the uncertainty is so broad. Imperfect data, imprecision and uncertainty have sufficiently different characteristics that no single model currently addresses them effectively. Complicating matters for the purposes of addressing problems related to counter-terrorism intelligence fusion is that human analysis does not typically take a probabilistic form. Most people do not naturally tend to think in terms of probabilities and therefore they are not recommended for elicitation. Not only is thinking in terms of probabilities difficult, but people also have a tendency to underestimate uncertainty.
A common alternative to individual models of uncertainty and the one endorsed by this proposal, is to take an eclectic approach whereby multiple uncertainty models are accommodated to allow the most appropriate one to be used in each part of the problem. Using this approach, information could retain the native representation for uncertainty and the various processing technologies capable of acting on that native model directly would be free to do so. Supplementing the accommodation of multiple native uncertainty models is a parallel unified uncertainty model. The unified model would be used to represent uncertainty information for processing technologies that do not have a particular bias toward one of the specific native representations. Additionally, it would serve as a mechanism for translating uncertain information between the native representations. Common code within the node wrappers would support the translation to and from the unified representation as necessary, freeing the processing technology to utilize whichever model is most appropriate.
As noted earlier, unified uncertainty models are a relatively immature concept and their internal representation as well as the calculi required to translate uncertainty values to and from the various other models are still evolving. However, there has been sufficient progress in this area to provide the promise that the approach is both mathematically sound and useful. The primary deficiencies of current approaches to unified uncertainty representation tend to deal with fringe cases, and issues relevant to only certain types of uncertainty models. It basically amounts to an 80/20 kind of problem. Current unified models can effectively address the great majority of uncertainty representation, translation and processing. For those situations where they are still
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