On the polytope of non-additive measures

Autor:	Pedro Miranda, Elías F. Combarro
Rok vydání:	2008
Předmět:	Discrete mathematics Linear programming Birkhoff polytope Logic Uniform k 21 polytope Combinatorics Happy ending problem Artificial Intelligence Cross-polytope Convex polytope Mathematics::Metric Geometry Ehrhart polynomial Vertex enumeration problem Mathematics
Zdroj:	Fuzzy Sets and Systems. 159:2145-2162
ISSN:	0165-0114
DOI:	10.1016/j.fss.2007.12.021
Popis:	In this paper we deal with the problem of studying the structure of the polytope of non-additive measures for finite referential sets. We give a necessary and sufficient condition for two extreme points of this polytope to be adjacent. We also show that it is possible to find out in polynomial time whether two vertices are adjacent. These results can be extended to the polytope given by the convex hull of monotone Boolean functions. We also give some results about the facets and edges of the polytope of non-additive measures; we prove that the diameter of the polytope is 3 for referentials of three elements or more. Finally, we show that the polytope is combinatorial and study the corresponding properties; more concretely, we show that the graph of non-additive measures is Hamilton connected if the cardinality of the referential set is not 2.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::5599f2999d5a83b3c78805d4d8707ae7 https://doi.org/10.1016/j.fss.2007.12.021 Zobrazit plný text záznamu Full Text from ScienceDirect