  Multilattices are generalisations of lattices introduced by Mihail Benado. He
replaced the existence of unique lower (resp. upper) bound by the existence of
maximal lower (resp. minimal upper) bound(s). A multilattice will be called
pure if it is not a lattice. Multilattices could be endowed with a residuation,
and therefore used as set of truth-values to evaluate elements in fuzzy
setting. In this paper we exhibit the smallest pure multilattice and show that
it is a sub-multilattice of any pure multilattice. We also prove that any
bounded residuated multilattice that is not a residuated lattice has at least
seven elements. We apply the ordinal sum construction to get more examples of
residuated multilattices that are not residuated lattices. We then use these
residuated multilattices to evaluate objects and attributes in formal concept
analysis setting, and describe the structure of the set of corresponding formal
concepts. More precisely, if $\mathcal{A}_i:
=(A_i,\le_i,\top_i,\odot_i,\to_i,\bot_i)$, $i=1,2$ are two complete residuated
multilattices, $G$ and $M$ two nonempty sets and $(\varphi, \psi)$ a Galois
connection between $A_1^G$ and $A_2^M$ that is compatible with the residuation,
then we show that
  \[\mathcal{C}: =\{(h,f)\in A_1^G\times A_2^M; \varphi(h)=f \text{ and }
\psi(f)=h \}\] can be endowed with a complete residuated multilattice
structure. This is a generalization of a result by Ruiz-Calvi{\~n}o and Medina
saying that if the (reduct of the) algebras $\mathcal{A}_i$, $i=1,2$ are
complete multilattices, then $\mathcal{C}$ is a complete multilattice.
