Abstract
Probabilistic and survival implications are two kinds of fuzzy implication functions that combine the imprecision modelled by fuzzy concepts and the imprecision modelled by the probability theory. Both kinds of fuzzy implication functions are derived from copulas through two different construction methods, and since their introduction in 2011 and 2012 respectively, they have been deeply studied. In this paper an axiomatic characterization of both families is given and it is proved that both families coincide. The mentioned characterizations are obtained by reversing these construction methods in order to obtain copulas from fuzzy implication functions. As it is expected the so-called 2-increasingness property on fuzzy implication functions plays an important role in the characterization theorems.
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