  Multi-fan is an analogous notion of fan. As a fan is associated to a toric
variety a multi-fan is associated to a torus orbifold. Orbifold elliptic class
and orbifold elliptic genus are defined for a triple of a multi-fan, a set of
generating integral vectors of one dimensional cones and a $\mathbb{Q}$
divisor. They are shown to behave functorially with respect to birational
morphisms between these triples. The result may be considered as a
combinatorial or topological analogue of the main result of Borisov and
Libgober, McKay correspondence for elliptic genera, Ann. of Math., 161 (2005).
