RT Journal Article
T1 Combinatorial Structure of the Polytope of 2-Additive Measures
A1 Miranda Menéndez, Pedro
A1 García Segador, Pedro
AB In this paper we study the polytope of 2-additive measures, an important subpolytope of theIn this paper we study the polytope of 2-additive measures, an important subpolytope of the polytope of fuzzy measures. For this polytope, we obtain its combinatorial structure, namely the adjacency structure and the structure of 2-dimensional faces, 3-dimensional faces, and so on. Basing on this information, we build a triangulation of this polytope satisfying that all simplices in the triangulation have the same volume. As a consequence, this allows a very simple and appealing way to generate points in a random way in this polytope, an interesting problema arising in the practical identi_cation of 2-additive measures. Finally, we also derive the volume, the centroid, and some properties concerning the adjacency graph of this polytope. polytope of fuzzy measures. For this polytope, we obtain its combinatorial structure, namely the adjacency structure and the structure of 2-dimensional faces, 3-dimensional faces, and so on. Basing on this information, we build a triangulation of this polytope satisfying that all simplices in the triangulation have the same volume. As a consequence, this allows a very simple and appealing way to generate points in a random way in this polytope, an interesting problema arising in the practical identi_cation of 2-additive measures. Finally, we also derive the volume, the centroid, and some properties concerning the adjacency graph of this polytope.
PB Institute of Electrical and Electronics Engineers
SN 1063-6706
YR 2020
FD 2020-11
LK https://hdl.handle.net/20.500.14352/7574
UL https://hdl.handle.net/20.500.14352/7574
LA eng
NO Miranda P, Garcia-Segador P. Combinatorial Structure of the Polytope of 2-Additive Measures. IEEE Trans Fuzzy Syst 2020; 28: 2864–2874. [DOI: 10.1109/TFUZZ.2019.2945243]
DS Docta Complutense
RD 13 abr 2025