Bivariate quasi-copulas and doubly stochastic signed measures

Authors:
Juan Fernández-Sánchez;José Antonio Rodríguez-Lallena;Manuel Úbeda-Flores
Affiliations:
Grupo de Investigación de Análisis Matemático, 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;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:
2011

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Abstract

We show that there exist bivariate proper quasi-copulas that do not induce a doubly stochastic signed measure on [0,1]^2. We construct these quasi-copulas from the so-called proper quasi-transformation square matrices.