In this paper, we study some variations of perspectivity of modules. We investigate the relationships between variations of perspectivity of a module and almost uniqueness of direct complements of a module. We show that there exist s-perspective modules, and so almost dual perspective modules, whose direct complements are not almost unique. Also we construct almost dual perspective and D3-modules, namely s-perspective modules whose direct complements are not almost unique. Moreover, we examine the direct sums of s-perspective modules and the modules whose direct complements are almost unique by using pairwise orthogonal primitive idempotents and \(\textrm{m}\) -local components of any module M over a commutative ring. Finally, we prove some structural results over commutative Dedekind domains. Let R be a commutative Dedekind domain with quotient field Q. Let M be a non-zero injective R-module. Then direct complements of M are almost unique if and only if either M is a torsion module such that every non-zero P-primary component is isomorphic to \(R(P^\infty )\) or \(M\cong Q\) . As a consequence we obtain that direct complements of M are almost unique if and only if for every non-zero prime ideal P, there exist \(a\in \{0, 1\}\) and a non-negative integer n such that \(T_P(M)\cong (R(P^\infty ))^a\oplus (R/P^nR)\) if and only if M is a D3-module, where R is a commutative Dedekind domain and M is a non-zero torsion R-module. Let R be a discrete valuation ring with maximal ideal \(\textrm{m}=pR\) . Let M be a non-zero reduced R-module which is not torsion-free. We show that direct complements of M are almost unique if and only if \(M\cong R/\textrm{m}^n\) for some positive integer n.
