An algorithm for finding the vertices of the k-additive monotone core

Authors:
Pedro Miranda;Michel Grabisch
Affiliations:
Universidad Complutense de Madrid, Plaza de Ciencias, 3, 28040 Madrid, Spain;Université Paris I-Panthéon-Sorbonne, 106-112 Bd. de l'Hôpital, 75013 Paris, France
Venue:
Discrete Applied Mathematics
Year:
2012

Citing 7
Cited 0

Two poset polytopes

Discrete & Computational Geometry
k-order additive discrete fuzzy measures and their representation

Fuzzy Sets and Systems - Special issue on fuzzy measures and integrals
Alternative representations of discrete fuzzy measures for decision making

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - Special issue on fuzzy measures and integrals in subjective evaluation
p-Symmetric fuzzy measures

International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Characterizing isometries on the order polytope with an application to the theory of fuzzy measures

Information Sciences: an International Journal
On the structure of the k-additive fuzzy measures

Fuzzy Sets and Systems
On the Structure of Some Families of Fuzzy Measures

IEEE Transactions on Fuzzy Systems

Quantified Score

Hi-index	0.04

Visualization

Abstract

Given a capacity, the set of dominating k-additive capacities is a convex polytope called the k-additive monotone core; 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 n-additive monotone core and we explore the possible translations for the k-additive case.