Quasi-copulas and signed measures

Authors:
Roger B. Nelsen;José Juan Quesada-Molina;José Antonio Rodríguez-Lallena;Manuel Úbeda-Flores
Affiliations:
Department of Mathematical Sciences, Lewis & Clark College, Portland, OR 97219, USA;Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain;Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Carretera de Sacramento s/n, 04120 La Caòada de San Urbano, Almería, Spain;Departamento de Estadística y Matemática Aplicada, Universidad de Almería, Carretera de Sacramento s/n, 04120 La Caòada de San Urbano, Almería, Spain
Venue:
Fuzzy Sets and Systems
Year:
2010

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Abstract

We study the relationship between multivariate quasi-copulas and measures that they may or may not induce on [0,1]^n. We first study the mass distribution of the pointwise best possible lower bound for the set of n-quasi-copulas for n=3. As a consequence, we show that not every n-quasi-copula induces a signed measure on [0,1]^n.