\((\in, \in \vee q_{k})\)-Intuitionistic Fuzzy Soft Boolean Near-Rings

This study proposes an enriched algebraic framework through the introduction of (∈, ∈ ∨qk)-intuitionistic fuzzy soft Boolean near-rings (IFSBNs), a class of mathematical structures that generalize previous fuzzy and soft ideal systems within Boolean near-rings. Building upon established theories, we define the corresponding (∈, ∈ ∨qk)- intuitionistic fuzzy soft ideals (IFSIs) and idealistic forms (IIFSBNs), and rigorously analyze their properties using formal definitions and examples. By expanding the capacity to model uncertainty and complex relationships, this work contributes to the theoretical backbone required for developing future intelligent systems. Importantly, the abstract nature of these algebraic tools makes them highly adaptable to curriculum designs in mathematics-focused educational environments, aligning with Sustainable Development Goal 4 (Quality Education). In particular, the framework can inspire high school and university students in research-intensive programs to engage in exploratory learning and abstract reasoning. Furthermore, this contribution exemplifies how collaborative academic efforts across institutions can produce foundational knowledge that transcends disciplinary boundaries, supporting SDG 17 (Partnerships for the Goals). The cross-institutional authorship and integration of interdisciplinary concepts promote educational equity and intellectual cooperation, fostering a culture of shared research innovation globally.