  Continuing to pursue a research direction that we already explored in
connection with G\"odel-Dummett logic and Ruspini partitions, we show here that
{\L}ukasiewicz logic is able to express the notion of pseudo-triangular basis
of fuzzy sets, a mild weakening of the standard notion of triangular basis. En
route to our main result we obtain an elementary, logic-independent
characterisation of triangular bases of fuzzy sets.
