Lattice Ordered N-Soft Sets and Their Applications in Decision Making

Decision-making processes heavily rely on the natural ordering structure that exists within attributes. This manuscript presents the new mathematical framework of lattice-ordered N-soft sets (LON-SS) and anti-lattice-ordered N-soft sets (A-LON-SS) that expands traditional N-soft sets (N-SSs) through attribute order relation integration. Our methodology extends the N-SS theory by resolving its limitations regarding ordered parameter handling, especially during rating and ranking situations. Further, this manuscript presents a thorough mathematical treatment and multiple examples that show how LON-SS effectively handles real-world decision problems that contain natural hierarchical parameter relationships. The examination supports that LON-SS delivers superior computational efficiency and user-friendly processing compared to traditional methods when applying the TOPSIS algorithm to decision analysis tasks. The LON-SS framework delivers substantial benefits to decision-making scenarios that need multi-valued assessments together with ordered attributes while showing potential applications in evaluation systems preference modeling and resource allocation problems. In the end, this manuscript compares the proposed concept with certain existing ones to reveal the supremacy and need of the existing theory.