Exact neutrosophic analysis of missing value in augmented randomized complete block design

The augmented randomized complete block design (ARCBD) is widely used in plant breeding programs to screen numerous new treatments. The error variance is estimated based on the replicated control treatments run over a randomized complete block design and is used to test the new treatments that are administrated each once in the extended units of the blocks. However, one or more observations corresponding to the control treatments may be missed in experiments, making difficulties, e.g., biased estimates. An approximate common approach to deal with this problem is the imputation of the estimated value which is with some uncertainties. Moreover, in real-life experiments, there are more sources of uncertainty that cause conflict-indeterminate, vague, imprecise, and erroneous data that increases the complexity of the analysis. In this paper, an exact scheme is utilized to deal with a missing control treatment in ARCBD. To overcome the problem of indeterminacies in data, a novel neutrosophic analysis approach is proposed. Specifically, the problem of a missing value in an ARCBD for an uncertain environment is resolved analytically by considering an augmented incomplete block design in the framework of neutrosophic statistics so-called neutrosophic augmented randomized complete block design (NARCBD). In this approach, by proposing the neutrosophic model, the neutrosophic estimations as well as the mathematical neutrosophic adjusted sums of squares are derived and the analysis of variance table is provided. The new model is applied to the neutrosophic genotype data example of safflower and assessed by a simulation study. Furthermore, a code in the R software was written to analyze the data based on the proposed approach to fill the calculation gap for data analysis in NARCBD with a missing value. In light of the results observed, it can be concluded that the neutrosophic exact proposed method performs better than the classic in the presence of uncertainty.