Possibilistic Systems Within a General Information Theory

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 elici-tation or assessment methods. Regarding fuzzy measures as special previ-sions, 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 speciically, measurements of random intervals yield empirical fuzzy intervals. In the random set (Dempster-Shafer) context, probability and possibility 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 speciied 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 nite (Markov) processes which are also strictly analogous to the probabilistic forms. 1 Possibility Theory and Imprecise Probabilities in General Information Theory A central conern for interdisciplinary scientists is the search for properties which can be measured across systems of diierent types: if we assert that two systems actually have the same structure or organization, how can that hypothesis become well-posed and testable? Such questions are usually framed in a relational language of such concepts as order, organization, structure, variety, constraint, freedom, determinism, and complexity. A formal theory of relational concepts has rested classically on information theories, and in particular on concepts of information, such as Shannon's statistical entropy, which are deened as a reduction in or lack of uncertainty. In turn, these uncertainty-based information theories were rooted deeply within the formalism of traditional probability theory , with a corresponding emphasis on entropy measures, Monte Carlo methods, Bayes nets, Markov models, etc. This view is currently expanding in two signiicant ways. First, there has been progress towards addressing a primary criticism of information theory,