Abstract
A number of topological and geometrical properties of the weighted Gamma matrix of order r in Nakano sequence space for fuzzy functions equipped with definite pre-modular functions are defined and investigated in this paper. We begin by defining the necessary conditions for the formation of pre-modular Banach in this space. Second, we specify the conditions under which the multiplication operator defined on this pre-modular space is bounded, approximable, invertible, Fredholm, and closed on the basis of this space.