Geometry of Cores of Submodular Coherent Upper Probabilities and Possibility Measures
نویسنده
چکیده
We study and review geometrical properties of the set of the probabilities dominated by a submodular coherent upper probability (a possibility measure, in particular) on a finite set. We mention that there exists a polynomial algorithm for vertex enumeration. A new upper bound for the number of vertices in case of possibility measures is derived.
منابع مشابه
Stochastic independence with respect to upper and lower conditional probabilities deined by Hausdorff outer and inner measures
A new model of coherent upper conditional prevision is proposed in a metric space. It is defined by the Choquet integral with respect to the s-dimensional Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its dimension s. Otherwise if the conditioning event has Hausdorff outer measure in its dimension equal to zero or infinity it is defined by ...
متن کاملSupremum Preserving Upper Probabilities
We study the relation between possibility measures and the theory of imprecise probabilities, and argue that possibility measures have an important part in this theory. It is shown that a possibility measure is a coherent upper probability if and only if it is normal. A detailed comparison is given between the possibilistic and natural extension of an upper probability, both in the general case...
متن کاملIntegration in Possibility Theory
The paper discusses integration in possibility theory, both in an ordinal and in a numerical (behavioral) context. It is shown that in an ordinal context, the fuzzy integral has an important part in at least three areas: the extension of possibility measures to larger domains, the construction of product measures from marginals and the definition of conditional possibilities. In a numerical (be...
متن کاملOn the coherence of supremum preserving upper previsions
We study the relation between possibility measures and the theory of imprecise probabilities. It is shown that a possibility measure is a coherent upper probability iff it is normal. We also prove that a possibility measure is the restriction to events of the natural extension of a special kind of upper probability, defined on a class of nested sets. Next, we go from upper probabilities to uppe...
متن کاملA geometric and game-theoretic study of the conjunction of possibility measures
In this paper, we study the conjunction of possibility measures when they are interpreted as coherent upper probabilities, that is, as upper bounds for some set of probability measures. We identify conditions under which the minimum of two possibility measures remains a possibility measure. We provide graphical way to check these conditions, by means of a zero-sum game formulation of the proble...
متن کامل