Augmented Latin Square Designs for Imprecise Data

This paper addresses a novel approach for analyzing augmented Latin square design with uncertain observations, the so-called neutrosophic augmented Latin square design (NALSD). The contribution of our work lies in estimating the effects of rows, columns, control and new treatments, as well as formulating their sums of squares. Moreover, by determining the neutrosophic hypotheses and decision rule, the 𝐹𝑁-statistic in NANOVA table is given. The performance of the proposed design is evaluated using a numerical example and simulation study. In light of the results observed, it can find that the NALSD performs better than the classic augmented Latin square design (ALSD) in the presence of uncertainty.