For a partially ordered set $\mathcal A$, we denote by $\mathcal A_o$ the family of all elements $D\in\mathcal A$ such that $A\wedge D=\inf\{A,D\}$ exists for all $A\in\mathcal A$. We investigate all those functions $F$ that map various subsets $\mathcal{D_F}$ of $\mathcal A_o$ into $\mathcal A$ so that $F(D)\wedge\ E=F(E)\wedge D$ for all $D,E\in\mathcal{D_F}$. The results obtained naturally extend and complement some former statements of G. Szász, J. Szendrei, M. Kolibiar, W. H. Cornish and J. Schmid on multipliers of lattices. Moreover, they are also closely related to the works of R. E. Johnson, Y. Utumi, G. D. Findlay and J. Lambek on generalized rings of quotients.