On various criteria of optimality in probabilistic decision-making
A note on the interval-valued marginal problem and its maximum entropy solution
This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.
On possibilistic marginal problem
A possibilistic marginal problem is introduced in a way analogous to probabilistic framework, to address the question of whether or not a common extension exists for a given set of marginal distributions. Similarities and differences between possibilistic and probabilistic marginal problems will be demonstrated, concerning necessary condition and sets of all solutions. The operators of composition will be recalled and we will show how to use them for finding a -product extension. Finally, a necessary...
A comparison of evidential networks and compositional models
Several counterparts of Bayesian networks based on different paradigms have been proposed in evidence theory. Nevertheless, none of them is completely satisfactory. In this paper we will present a new one, based on a recently introduced concept of conditional independence. We define a conditioning rule for variables, and the relationship between conditional independence and irrelevance is studied with the aim of constructing a Bayesian-network-like model. Then, through a simple example, we will...
On decision-making in possibility theory
We present an alternative approach to decision-making in the framework of possibility theory, based on the idea of decision-making under uncertainty. We utilize the fact, that any possibility distribution can be viewed as an upper envelope of a set of probability distributions to which well-known minimax principle is applicable. Finally, we recall also an alternative to the minimax rule, so-called local minimax principle. Local minimax principle not only allows sequential construction of decision...
Special issue: WUPES’12
This special issue of the Kybernetika Journal arose from the 9th workshop on uncertainty processing, WUPES’12, held in Mariánské Lázně, Czech Republic, in September 2012. In the selection process for this special issue, we tried to capture the rich variety of the presented methodological approaches. The quality of the selected papers was judged by reviewers in accord with the usual practice of Kybernetika. After a careful selection, 7 papers were included in the special issue. There are, however,...
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