Fusion of dilute AL lattice models

The fusion procedure is implemented for the dilute AL lattice models and 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 AL lattice models and discuss their connection with the fusion hierarchy. The solution of the fusion hierarchy for the eigenvalue spectra of the dilute AL lattice models will be presented in a subsequent paper