Novel Distance Measure for Linear Diophantine Fuzzy Sets with CODAS-Based Decision-Making

Decision-making under uncertainty requires mathematical tools capable of capturing the complexity of real-world expert evaluations. Linear Diophantine fuzzy sets address this need by incorporating reference parameters alongside membership and non-membership degrees, offering greater flexibility than earlier fuzzy frameworks. However, existing distance measures for this setting rely entirely on component-wise differences and can fail to distinguish between two elements whenever those differences are equal. This paper proposes a new distance measure that extends the standard component-wise sum by introducing cross-interaction terms between the membership degrees and between the reference parameters of the two elements under consideration. Axiomatic validity is established through a formal proof, and the measure is compared against nine existing distance measures, revealing cases where existing measures lose discriminating power while the proposed one does not. Building on this distance, a CODAS-based multi-criteria decision-making procedure is developed for the linear Diophantine fuzzy environment and applied to a logistics specialist selection problem. Results are benchmarked against existing methods, and the consistency of the proposed approach is discussed alongside its limitations and directions for future work.