  To achieve our main research goal, first we survey the approaches towards
dual fusion frames existing in the literature and agree on the notion of
duality for fusion frames in the sense of Kutyniok, Paternostro and Philipp
({\it Oper. Matrices} {\bf11} (2017), no. 2, 301--336). As a main result we
show that different fusion frames have different dual fusion frames. Moreover,
this duality notion leads to a new definition of Bessel fusion multipliers
which is a slightly modified version of the commonly used definitions.
Particularly, we show that with this definition in many cases Bessel fusion
multipliers behave similar to ordinary Bessel multipliers. Finally, special
attention is devoted to the study of dual fusion frames induced by an
invertible Bessel fusion multiplier.
