اولویت‌بندی مراحل مختلف رشد چغندرقند برای مدیریت پایدار منابع آب با استفاده از تئوری تصمیم-گیری چندمعیاره

Introduction
Efficient irrigation management is one of the most important challenges in sugar beet production, particularly under conditions of increasing water scarcity. Since the sensitivity of sugar beet to water deficit varies throughout its growth cycle, identifying the critical growth stages for water allocation can substantially improve water productivity while maintaining crop performance. Conventional irrigation scheduling generally treats all growth stages similarly and therefore may not maximize the efficiency of limited water resources. Multi-criteria decision-making (MCDM) techniques provide an effective framework for integrating multiple agronomic criteria into a single decision-making process. Among these methods, the VIKOR model is capable of identifying compromise solutions by simultaneously considering group utility and individual regret. Therefore, this study aimed to prioritize sugar beet growth stages for sustainable irrigation management using the VIKOR multi-criteria decision-making method based on biomass water productivity and the relative contribution of each growth stage to plant growth.
Materials and Methods
The study was conducted using data obtained from a two-year field experiment. Two evaluation criteria, including biomass water productivity (kg m⁻³) and the relative growth share (%) of each growth stage, were used to construct the decision matrix. Four growth stages (Initial, Development, Mid-season, and Late-season) were considered as the decision alternatives. Criteria weights were determined using both equal weighting and Shannon entropy weighting approaches. The VIKOR method was then employed to rank the growth stages based on the S, R, and Q indices. The acceptable advantage and acceptable stability conditions proposed by Opricovic were evaluated to verify the validity of the compromise solution. Furthermore, sensitivity analysis based on systematic variation of criteria weights, together with Tornado analysis and Spearman rank correlation coefficient, was performed to assess the robustness and stability of the obtained rankings.
Results and discussion
The biomass accumulation pattern followed a typical sigmoid growth curve, with rapid dry matter accumulation occurring primarily during the development and mid-season stages. Mean biomass water productivity values for the Initial, Development, Mid-season, and late-season stages were 4.91, 8.66, 3.84 and 3.83 kg m⁻³, respectively for the Initial, Development, Mid and Late stages, respectively, while their corresponding relative growth shares were 7.24, 45.99, 41.77 and 5.01%, respectively. Application of the VIKOR model indicated that the Development stage consistently ranked first with Q = 0.000, followed by the Mid (Q = 0.774), Initial (Q = 0.903), and Late (Q = 1.000) stages. Both acceptable advantage (ΔQ = 0.774 > DQ = 0.333) and acceptable stability conditions were satisfied, confirming the existence of a unique compromise solution. Sensitivity analysis demonstrated that the Development stage maintained 100% ranking stability under all w eight scenarios, whereas the Mid and Initial stages exhibited 64% stability and exchanged their relative positions only within a narrow range of weight variation. The Late stage consistently remained the least preferred alternative. In addition, Spearman's rank correlation coefficient equaled 1.00 for both annual analyses and the two-year average, indicating complete agreement between rankings obtained using equal and entropy weighting methods.
Conclusion
The results demonstrated that integrating physiological growth characteristics with water productivity indicators through the VIKOR multi-criteria framework provides a reliable approach for identifying critical irrigation stages in sugar beet. Among all growth stages, the Development stage was consistently identified as the most efficient and robust stage for water allocation owing to its higher biomass water productivity, greatest contribution to biomass accumulation, and complete ranking stability under different weighting scenarios. The Mid stage represented the second priority but showed moderate sensitivity to changes in criteria weights, whereas the Initial and Late stages had comparatively lower management priority. The robustness confirmed by sensitivity analysis and Spearman correlation further supports the reliability of the proposed ranking. Therefore, prioritizing irrigation during the Development stage can improve water-use efficiency and support sustainable irrigation management of sugar beet under water-limited conditions.