Extended Abstract
Introduction
Canola (Brassica napus L.) is one of the most important oilseed crops globally, but its production in arid and semi-arid regions such as Iran is severely affected by water stress, leading to significant reductions in seed yield and oil content. Biostimulants such as amino acids, humic acid, fulvic acid, and seaweed extract have emerged as effective tools to mitigate the negative effects of environmental stresses. However, their effectiveness depends strongly on environmental conditions. Selecting the best "irrigation × biostimulant" combination is a multi-criteria decision-making problem involving conflicting criteria such as seed yield, water productivity, oil percentage, and water use. In the authors' previous study, the WS × Amino acid treatment was identified as the best option using VIKOR with equal weighting. However, the robustness of this result against changes in weighting methods and ranking algorithms had not been examined—leaving open the question of whether this superiority was method-dependent or inherent in the data.
Materials and Methods
Data for this study were derived from a field experiment in which two irrigation levels (normal and water stress) and five biostimulant levels (control, amino acid, humic acid, fulvic acid, and seaweed extract) were examined in a total of 10 treatments. Four evaluation criteria water productivity (kg m⁻³), seed oil percentage (%), water use (m³ ha⁻¹), and seed yield (kg ha⁻¹) were included in the decision matrix. For comprehensive evaluation and validation of the previous finding, eight decision-making combinations were employed, formed by crossing two ranking algorithms (TOPSIS and VIKOR) with four weighting methods (equal weighting, Shannon's entropy, CRITIC, and genetic algorithm). TOPSIS operates based on Euclidean distance from the ideal solution, while VIKOR is based on compromise and consensus logic. Genetic algorithm weights were optimized using NSGA-II to maximize the separation between the best and second-best alternatives. Robustness analysis was conducted from four perspectives: agreement on the best alternative, Spearman correlation for the overall ranking structure, separate ranking of stress and normal treatments, and independence from weighting philosophy and ranking algorithm.
Results and Discussion
The results showed that all eight decision-making combinations, without exception, identified the WS × Amino acid treatment as the best option a 100% agreement that is rare in the multi-criteria decision-making literature. The Spearman correlation coefficient with a mean of 0.904 confirmed very high agreement among the methods; indeed, six of the eight methods produced completely identical rankings (ρ = 1.0). Separate analysis of irrigation conditions revealed a clear pattern. Under water stress conditions, amino acid was the best stimulant, increasing seed yield by 23% (from 3002 to 3703 kg ha⁻¹) and water productivity by 28% (from 1.40 to 1.79 kg m⁻³) compared to the control. It was followed by seaweed extract (+18%), humic acid (+14%), and fulvic acid (+14%). Under normal irrigation conditions, however, humic acid was superior, increasing seed yield by 14% (from 3369 to 3844 kg ha⁻¹) and achieving the highest oil content (43.9%), while amino acid fell to fourth place. This condition-dependent ranking shift is one of the most important agronomic findings of this study. From a methodological perspective, GA-VIKOR achieved the highest discrimination power with a separation value of 0.222 approximately five times greater than VIKOR with equal weighting (0.044) and about six times greater than VIKOR with CRITIC weighting (0.038). GA-TOPSIS was the second-best method with 0.135. These results demonstrate that optimizing weights with a genetic algorithm, while preserving the final outcome, substantially increases decision-making confidence.
Conclusion
This study produced three main achievements: First, it proved the complete robustness of the previous study's finding, demonstrating that the superiority of WS × Amino acid is an inherent, method-independent phenomenon not the result of choosing a specific analytical approach. Second, it provided conditional management recommendations: under water-limited conditions, amino acid is the best choice, while under full water availability, humic acid should be preferred. Third, it demonstrated the superiority of GA-VIKOR in enhancing discrimination power and decision-making confidence, thereby promoting the application of integrated GA-MCDM approaches in agricultural sciences. These findings have direct practical implications for farmers, water managers, and agricultural policymakers. The proposed framework can be extended to other crops, other climatic regions, and combined with multi-objective algorithms for future research. |