A characterization of quasi-copulas
Journal of Multivariate Analysis
Aggregation operators: new trends and applications
Aggregation operators: new trends and applications
On the transitivity of a parametric family of cardinality-based similarity measures
International Journal of Approximate Reasoning
Aggregation Functions: A Guide for Practitioners
Aggregation Functions: A Guide for Practitioners
Meta-theorems on inequalities for scalar fuzzy set cardinalities
Fuzzy Sets and Systems
An Introduction to Copulas
Transitivity Bounds in Additive Fuzzy Preference Structures
IEEE Transactions on Fuzzy Systems
Piecewise linear aggregation functions based on triangulation
Information Sciences: an International Journal
Ultramodular aggregation functions
Information Sciences: an International Journal
Binary survival aggregation functions
Fuzzy Sets and Systems
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We introduce two types of transformations of random variables, called flipping and cyclic shifting. As these transformations preserve monotonicity at the level of univariate cumulative distribution functions, they can be used to develop corresponding coordinate-wise transformations of binary aggregation functions. We lay bare the admissibility of these transformations, i.e. the necessary and sufficient conditions under which they result in a binary aggregation function. We investigate which additional properties, such as the 1-Lipschitz property and 2-increasingness, entail these admissibility conditions. Moreover, we point out which of these properties are preserved under flipping and/or cyclic shifting. Interestingly, quasi-copulas remain quasi-copulas under flipping, while copulas remain copulas under flipping as well as under cyclic shifting.