Let \(A\) be an algebra over a commutative ring, \(P\) be a locally finite preordered set, and \(I(P,A)\) be its incidence algebra over \(A\) (we remark that the full matrix algebras and the upper triangular matrix algebras are examples of incidence algebras). The author shows that, under certain assumptions, an algebra map of \(I(P,A)\) into \(I(P,B)\), where \(A\) is a subalgebra of \(B\), can be decomposed into simpler factors. As corollaries, automorphisms and higher derivations of \(I(P,A)\) are described.