This paper studies the problem of marginalizing convex polytopes of probabilities represented by a set of constraints. This marginalization is obtained as a special case of projection on a specific subspace. An algorithm that projects a convex polytope on any subspace has been built and the expression of the subspace, where the projection must be made for obtaining the marginalization, has been calculated.
The aim of this paper is to define global measures of uncertainty in the framework of Dempster-Shafer's Theory of Evidence. Starting from the concepts of entropy and specificity introduced by Yager, two measures are considered; the lower entropy and the upper entropy.
The monotone expectation is defined as a functional over fuzzy measures on finite sets. The functional is based on Choquet functional over capacities and its more relevant properties are proved, including the generalization of classical mathematical expectation and Dempster's upper and lower expectations of an evidence. In second place, the monotone expectation is used to define measures of fuzzy sets. Such measures are compared with the ones based on Sugeno integral. Finally, we prove a generalization...
The aim of this paper is to review the different operators defined in the Theory of Evidence. All of them are presented from the same point of view. Special attention is given to the logical operators: conjunction (Dempster's Rule), disjunction and negation (defined by Dubois and Prade), and the operators changing the level of granularity on the set of possible states (partitions, fuzzy partitions, etc.).
Page 1