A Partitioned Maclaurin Symmetric Mean-Based Framework for Multi-Attribute Decision-Making Under Linear Diophantine Fuzzy Sets

Linear Diophantine fuzzy sets (LDFSs) enlarge the admissible representation space for uncertain information through membership and non-membership degrees together with reference parameters. Existing LDFS aggregation studies have mainly considered weighted, ordered, power-based, and parametric operators, while partitioned aggregation operators that model possible interrelationships within criterion groups remain limited. Maclaurin symmetric mean (MSM) operators capture interactions among criteria, and reducible weighted MSM operators have been developed to preserve idempotency and reducibility properties but have not been extended to a partitioned MSM operator. This study develops an MSM-based aggregation framework for LDFSs, including the linear Diophantine fuzzy MSM (LDFMSM), the linear Diophantine fuzzy partitioned MSM (LDFPMSM), a reducible weighted partitioned MSM (RWPMSM) and its extension to LDFSs, and the linear Diophantine fuzzy reducible weighted partitioned MSM (LDFRWPMSM) operators. LDFMSM performs symmetric k-subset aggregation over the complete criterion set, LDFPMSM restricts joint aggregation terms to criteria within the same predefined partition, and LDFRWPMSM incorporates criterion weights while preserving idempotency and reducibility properties. Theoretical properties and special cases are established. The framework is demonstrated through numerical examples and an illustrative multi-attribute decision-making (MADM) application for an AI-driven precision agriculture platform selection. Sensitivity analyses examine the effects of the interaction parameter, criterion weights and partition structure and reveal systematic changes in the ranking results. Comparative analysis shows that the LDFPMSM can distinguish alternatives that remain tied under globally symmetric aggregation, while the LDFRWPMSM identifies a different best alternative from the benchmark operators, reflecting its joint treatment of criterion importance and within-partition interactions.