Balanced Lattice Designs under Uncertain Environment

Balanced lattice designs are vital in numerous fields, especially in experimental design, where controlling variability among experimental units is crucial. In practical experiments, various sources of uncertainty can lead to ambiguous, vague, and imprecise data, complicating the analysis process. To address these indeterminacies, a novel approach using neutrosophic analysis within a balanced lattice design framework is proposed, termed the neutrosophic balanced lattice design (NBLD). This innovative method employs neutrosophic statistics to derive mathematical neutrosophic sums of squares and construct a neutrosophic analysis of variance (NANOVA) table. The effectiveness of the proposed NBLD is demonstrated through a numerical example, showing that it outperforms traditional methods in handling uncertainty.