Semi-quantitative data - Possibility theory Sample Clauses

Semi-quantitative data - Possibility theory. Transforming a quantitative parameter into a semi-quantitative parameter may be useful in some cases. Instead of expressing risk in terms of probabilities, formulating the results from a risk assessment into categories, for instance “low”, “medium” and “high” risk may ease communication and help decision makers prioritize and target risk mitigation measures. Another situation where categorization of quantitative parameters may be appropriate is when significant uncertainty is associated with the quantitative parameter and expressing the parameter with a precise numerical value may convey a false message of high precision. Such uncertainty may stem from incomplete knowledge and imprecision due to lack of information resulting, for example, from systematic measurement errors or expert opinions (Xxxxxxx and Xxxxxx, 2006). To transform a quantitative parameter into a semi-quantitative/categorical parameter, possibility theory can be applied. An expert commonly estimates the numerical values of a parameter using confidence intervals according to his/her experience and intuition. The interval is defined by a lower and an upper bound. In most cases, experts may provide more information by expressing preferences inside this interval. For example, “an expert is certain that the value for the model parameter is located within the interval [a, b]”. However, according to a measurements and experience, the expert may be able to judge that “the value for the model parameter is most likely to be within a narrower interval [c, d]”. To represent such information, an appropriate tool is the possibility distribution, based on the Fuzzy set theory (Zadeh 1965), which describes the more or less plausible values of some uncertain quantity (Xxxxxx and Prade 1988). The preference of the expert is modelled by a degree of possibility (i.e. likelihood) ranging from 0 to 1. In practice, the most likely interval [c, d] (referred to as the "core") is assigned a degree of possibility equal to one, whereas the “certain” interval [a, b] (referred to as the "support") is assigned a degree of possibility zero, such that values located outside this interval are considered impossible. Figure 3.1 illustrates such an approach in the field of earthquake hazard assessment.
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