  By extending the algebraic description of the bosonic rank-three tensor
models, a general framework for super rank-three tensor models and
correspondence to super fuzzy spaces is proposed. The corresponding super fuzzy
spaces must satisfy a certain cyclicity condition on the algebras of functions
on them. Due to the cyclicity condition, the symmetry of the super rank-three
tensor models are represented by super n-ary transformations. The Leibnitz
rules and the fundamental identities for the super n-ary transformations are
discussed from the perspective of the symmetry of the algebra of a fuzzy space.
It is shown that the super n-ary transformations of finite orders which
conserve the algebra of a fuzzy space form a finite closed n-ary super Lie
algebra. Super rank-three tensor models would be of physical interest as
background independent models for dynamical generation of supersymmetric fuzzy
spaces, in which quantum corrections are under control.
