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Characterizing isometries on the order polytope with an application to the theory of fuzzy measures

Combarro, Elías F. and Miranda Menéndez, Pedro (2010) Characterizing isometries on the order polytope with an application to the theory of fuzzy measures. Information Sciences, 180 (3). pp. 384-398. ISSN 0020-0255

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Abstract

In this paper we study the group of isometries over the order polytope of a poset. We provide a result that characterizes any isometry based on the order structure in the original poset. From this result we provide upper bounds for the number of isometries over the order polytope in terms of its number of connected components. Finally, as an example of application, we recover the set of isometries for the polytope of fuzzy measures and the polytope of p-symmetric measures when the indifference partition is fixed.


Item Type:Article
Uncontrolled Keywords:Order polytope; Isometries; Fuzzy measures; p-Symmetric measures
Subjects:Sciences > Mathematics > Combinatorial analysis
Sciences > Mathematics > Topology
ID Code:16936
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