Dempster's rule is a fundamental tool for combining belief functions from distinct and reliable sources. However, its intersection-based semantics imposes strong structural restrictions, which limits its flexibility in handling complex source states and diverse information fusion scenarios. To overcome this limitation, we propose a reversible transformation, derived from the isopignistic principle, between belief functions and a possibilistic structure defined on the power set. In this transformation, the relationships among subsets are explicitly characterized by a belief evolution network, which provides a more flexible representation of evidential information beyond the conventional mass function structure. On this basis, we further introduce the triangular norm family to develop a general and adaptive evidential information fusion framework. Unlike fusion methods rooted in Dempster semantics, the proposed framework supports more flexible combination behaviors and exhibits advantages in non-distinct source fusion, conflict management, parametric combination design, and heterogeneous information fusion.