On reversible triangular norms
Fuzzy Sets and Systems - Special issue on triangular norms
A characterization of quasi-copulas
Journal of Multivariate Analysis
The functional equations of Frank and Alsina for uninorms and nullnorms
Fuzzy Sets and Systems
Some new characterizations and properties of quasi-copulas
Fuzzy Sets and Systems
Flipping and cyclic shifting of binary aggregation functions
Fuzzy Sets and Systems
Self-reversibility and some other properties of binary operations
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
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We introduce a transformation that acts on binary aggregation functions and that generalizes the transformation that maps copulas, a well-studied class of binary aggregation functions with a profound probabilistic interpretation, to their associated survival copulas. The new transformation, called double flipping, is the composition of two elementary flipping transformations introduced earlier, each operating on one of the arguments of the aggregation function. We lay bare the relationships between these elementary flipping operations and double flipping. We study invariants under these transformations. Furthermore, we characterize the transformations that preserve flippability. Most importantly, we characterize different subclasses of flippable aggregation functions, in particular aggregation functions that have an absorbing element or that have a neutral element. In this investigation, the key role played by quasi-copulas and their dual operations is highlighted. These findings support the introduction of the term survival aggregation function.