Combinatorial Structure of the Polytope of 2-Additive Measures

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Miranda Mnéndez, Pedro and García-Segador, Pedro (2020) Combinatorial Structure of the Polytope of 2-Additive Measures. IEEE Transactions on Fuzzy Systems, 28 (11). ISSN 1063-6706

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:Transforms; Additives; Game theory; Complexity theory; Fuzzy systems; Games; 2-additive measures; combinatorial structure; fuzzy measures; random generation; triangulation
Palabras clave (otros idiomas):Teoría de los juegos; Triangulación
Subjects:Sciences > Mathematics
Sciences > Mathematics > Applied statistics
Sciences > Mathematics > Mathematical statistics
ID Code:63271
Deposited On:03 Dec 2020 09:24
Last Modified:03 Dec 2020 09:50

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