Recently author (with A. Taouti) have introduced pseudo-valuation maps and discussed pseudo-valuation domains through these maps. In continuation we also introduced P-Krull domains with the help of defined maps as well. In this note we generalize a pseudo-valuation map $\upsilon$ in the form of almost pseudo-valuation map and a pseudo-almost valuation map $\eta$. Furthermore, we construct and discuss an almost pseudo-valuation domain and a pseudo-almost valuation domain through the defined maps. Moreover, a few relationships between both integral domains through the defined maps have been proved.