Summary: A zig-zag order is like a directed path, only with alternating directions. A generating set of minimal size for the semigroup of all full transformations on a finite set preserving the zig-zag order was determined by V. H. Fernandes et al. in 2019 [Bull. Malays. Math. Sci. Soc. (2) 42, No. 5, 2191–2211 (2019; Zbl 1454.20110)]. This paper deals with generating sets of the semigroup \(F_{\mathbb{N}}\) of all full transformations on the set of all natural numbers preserving the zig-zag order. We prove that \(F_{\mathbb{N}}\) has no minimal generating sets and present two particular infinite decreasing chains of generating sets of \(F_{\mathbb{N}}\).