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Miranda Menéndez, Pedro García Segador, Pedro 2023-06-16T14:25:38Z 2023-06-16T14:25:38Z 2021-11-08 Miranda P, García-Segador P. Pointed order polytopes: Studying geometrical aspects of the polytope of bi-capacities. Fuzzy Sets and Systems 2022; 444: 182–205. [DOI: 10.1016/j.fss.2021.11.001] 0165-0114 10.1016/j.fss.2021.11.001 https://hdl.handle.net/20.500.14352/5003 https://doi.org/10.1016/j.fss.2021.11.001 In this paper we study some geometrical questions about the polytope of bi-capacities. For this, we introduce the concept of pointed order polytope, a natural generalization of order polytopes. Basically, a pointed order polytope is a polytope that takes advantage of the order relation of a partially ordered set and such that there is a relevant element in the structure. We study which are the set of vertices of pointed order polytopes and sort out a simple way to determine whether two vertices are adjacent. We also study the general form of its faces. Next, we show that the set of bi-capacities is a special case of pointed order polytope. Then, we apply the results obtained for general pointed order polytopes for bi-capacities, allowing to characterize vertices and adjacency, and obtaining a bound for the diameter of this important polytope arising in Multicriteria Decision Making. eng open access Pointed order polytopes: Studying geometrical aspects of the polytope of bi-capacities journal article