Abstract
We survey possibilistic systems theory and place it in the context of Imprecise Probabilities and General Information Theory (\git). In particular, we argue that possibilistic systems hold a distinct position within a broadly conceived, synthetic \git. Our focus is on systems and applications which are semantically grounded by empirical measurement methods (statistical counting), rather than epistemic or subjective knowledge elicitation or assessment methods. Regarding fuzzy measures as special previsions, and evidence measures (belief and plausibility measures) as special fuzzy measures, thereby we can measure imprecise probabilities directly and empirically from set-valued frequencies (random set measurement). More specifically, measurements of random intervals yield empirical fuzzy intervals. In the random set (Dempster-Shafer) context, probability and \pos\ measures stand as special plausibility measures in that their ``distributionality'' (decomposability) maps directly to an ``aggregable'' structure of the focal classes of their random sets. Further, possibility measures share with imprecise probabilities the ability to better handle ``open world'' problems where the universe of discourse is not specified in advance. In addition to empirically grounded measurement methods, possibility theory also provides another crucial component of a full systems theory, namely prediction methods in the form of finite (Markov) processes which are also strictly analogous to the probabilistic forms.
Keywords. Possibility Theory, random sets, fuzzy measures, imprecise probabilities, general information theory, possibilistic processes.
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Authors addresses:MS B265
E-mail addresses:
| Cliff Joslyn | joslyn@lanl.gov |