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

Dual fusion frames in the sense of Kutyniok, Paternostro and Philipp with applications to invertible Bessel fusion multipliers