The fusion procedure is implemented for the dilute AL lattice models a
nd a fusion hierarchy of functional equations with an su(3) structure
is derived for the fused transfer matrices, We also present the Bethe
ansatz equations for the dilute Ar, lattice models and discuss their c
onnection with the fusion hierarchy, The solution of the fusion hierar
chy for the eigenvalue spectra of the dilute Ar. lattice models will b
e presented in a subsequent paper.