  In the context of fuzzy logic, ordinal sums provide a method for constructing
new functions from existing functions, which can be triangular norms,
triangular conorms, fuzzy negations, copulas, overlaps, uninorms, fuzzy
implications, among others. As our main contribution, we establish conditions
for the ordinal sum of a family of fuzzy negations to be a fuzzy negation of a
specific class, such as strong, strict, continuous, invertible and frontier.
Also, we relate the natural negation of the ordinal sum on families of t-norms,
t-conorms and fuzzy implications with the ordinal sum of the natural negations
of the respective families of t-norms, t- conorms and fuzzy implications. This
motivated us to introduces a new kind of ordinal sum for families of fuzzy
implications.
