  Thanks to their large angular dimension and brightness, red giants and
supergiants are privileged targets for optical long-baseline interferometers.
Sixteen red giants and supergiants have been observed with the VLTI/AMBER
facility over a two-years period, at medium spectral resolution (R=1500) in the
K band. The limb-darkened angular diameters are derived from fits of stellar
atmospheric models on the visibility and the triple product data. The angular
diameters do not show any significant temporal variation, except for one
target: TX Psc, which shows a variation of 4% using visibility data. For the
eight targets previously measured by Long-Baseline Interferometry (LBI) in the
same spectral range, the difference between our diameters and the literature
values is less than 5%, except for TX Psc, which shows a difference of 11%. For
the 8 other targets, the present angular diameters are the first measured from
LBI. Angular diameters are then used to determine several fundamental stellar
parameters, and to locate these targets in the Hertzsprung-Russell Diagram
(HRD). Except for the enigmatic Tc-poor low-mass carbon star W Ori, the
location of Tc-rich stars in the HRD matches remarkably well the
thermally-pulsating AGB, as it is predicted by the stellar-evolution models.
For pulsating stars with periods available, we compute the pulsation constant
and locate the stars along the various sequences in the Period -- Luminosity
diagram. We confirm the increase in mass along the pulsation sequences, as
predicted by the theory, except for W Ori which, despite being less massive,
appears to have a longer period than T Cet along the first-overtone sequence.
