Miranda Menéndez, PedroGrabisch, MichelCarvalho, J.P.Dubois, D.Kaymak, U.Sousa, J.M.C.2023-06-202023-06-202009978-989-95079-6-8https://hdl.handle.net/20.500.14352/53168Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009.Given a capacity, the set of dominating k-additive capacities is a convex polytope; thus, it is defined by its vertices. In this paper we deal with the problem of deriving a procedure to obtain such vertices in the line of the results of Shapley and Ichiishi for the additive case. We propose an algorithm to determine the vertices of the k-additive monotone core. Then, we characterize the vertices of the n-additive core and finally, we explore the possible translations for the k-additive caseengbook parthttp://www.eusflat.org/proceedings/IFSA-EUSFLAT_2009/pdf/tema_0076.pdfhttp://www.eusflat.orgrestricted access514.113Keywords—Capacitiesk-additivitydominancecoreTopología1210 Topología