  In this paper, we derive pre-anti-flexible algebras structures in term of
zero weight's Rota-Baxter operators defined on anti-flexible algebras, view
pre-anti-flexible algebras as a splitting of anti-flexible algebras, introduce
the notion of pre-anti-flexible bialgebras and establish equivalences among
matched pair of anti-flexible algebras, matched pair of pre-anti-flexible
algebras and pre-anti-flexible bialgebras. Investigation on special class of
pre-anti-flexible bialgebras leads to the establishment of the
pre-anti-flexible Yang-Baxter equation. Both dual bimodules of
pre-anti-flexible algebras and dendriform algebras have the same shape and this
induces that both pre-anti-flexible Yang-Baxter equation and
$\mathcal{D}$-equation are identical. Symmetric solution of pre-anti-flexible
Yang-Baxter equation gives a pre-anti-flexible bialgebra. Finally, we recall
and link $\mathcal{O}$-operators of anti-flexible algebras to bimodules of
pre-anti-flexible algebras and built symmetric solutions of anti-flexible
Yang-Baxter equation.
