This paper introduces a new class of fuzzy soft structures termed binary relation–fuzzy soft points (BRFS-points), constructed through the composition of binary relation soft points and fuzzy points defined with respect to a power set. The proposed framework integrates two distinct mathematical concepts within a unified structure, combining the parameterization of binary relation soft sets with graded membership characteristics of fuzzy points. As a result, nine different types of BRFS-points are systematically derived based on different combinations of underlying fuzzy and binary relation soft point types, and each case is illustrated through representative examples. The introduced BRFS-points generalize existing notions of fuzzy soft points by providing a richer and more flexible representation of uncertainty in multi-parameter environments. In contrast to classical fuzzy soft point constructions, the proposed model captures additional structural information arising from binary relations on parameter sets, thereby enhancing the expressive power of the framework. The developed structure is applicable to binary relation–fuzzy soft topological spaces and related separation axioms, where the interaction between soft parameters and fuzzy membership degrees is essential. In particular, BRFS-points provide a mathematically consistent tool for analyzing and representing uncertainty in systems involving complex relationships between elements and parameters. Furthermore, the proposed framework is suitable for decision-making problems under uncertainty, where multiple criteria and interdependent parameters must be processed simultaneously. The model enables a structured aggregation of fuzzy and soft information, making it relevant for applied fields that require formal handling of imprecise or incomplete data.