Narrow Results

In this paper we study some properties of the polytope of belief functions on a finite referential. These properties can be used in the problem of identification of a belief function from sample data. More concretely, we study the set of isometries, the set of invariant measures and the adjacency structure. From these results, we prove that the polytope of belief functions is not an order polytope if the referential has more than two elements. Similar results are obtained for plausibility functions.

In this paper we study some geometrical properties of the polytope of 3-tolerant fuzzy measures. To achieve this task, we profit that this polytope is an order polytope and hence many properties can be extracted from the subjacent poset. The main result in the paper is a straightforward procedure for obtaining a random 3-tolerant fuzzy measure. We also compute the volume and obtain some other properties of this polytope. These results can be also applied by duality to the polytope of 3-intolerant measures and they can also be easily extended to other subfamilies of fuzzy measures.