A characterization of quasi-copulas
Journal of Multivariate Analysis
Quasi-copulas and copulas on a discrete scale
Soft Computing - A Fusion of Foundations, Methodologies and Applications
On a family of copulas constructed from the diagonal section
Soft Computing - A Fusion of Foundations, Methodologies and Applications
An Introduction to Copulas (Springer Series in Statistics)
An Introduction to Copulas (Springer Series in Statistics)
Solution of an open problem for associative copulas
Fuzzy Sets and Systems
Copula-Like Operations on Finite Settings
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Sklar's Theorem in Finite Settings
IEEE Transactions on Fuzzy Systems
Representation of discrete quasi-copulas through non-square matrices
Proceedings of the 2008 conference on Artificial Intelligence Research and Development: Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence
Smooth aggregation functions on finite scales
IPMU'10 Proceedings of the Computational intelligence for knowledge-based systems design, and 13th international conference on Information processing and management of uncertainty
Smooth t-subnorms on finite scales
Fuzzy Sets and Systems
Matrix representation of meet-irreducible discrete copulas
Fuzzy Sets and Systems
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In this paper discrete quasi-copulas (defined on a square grid I"n^2 of [0,1]^2) are studied and it is proved that they can be represented by means of a special class of matrices with entries in [-1,1]. Special considerations are made for the case of irreducible discrete quasi-copulas (those with range I"n), showing that they can be represented through alternating-sign matrices and that they generate all discrete quasi-copulas through convex sums. In the process, the number of irreducible quasi-copulas on I"n is given and those functions @d for which there exists a unique copula with @d as its diagonal section are characterized.