The search for soybean genotypes more adapted to abiotic stress conditions is essential to boost the development and yield of the crop in Brazil and worldwide. In this research, we propose a new approach using the concept of distance (or similarity) in a vector space that can quantify changes in the morphological traits of soybean seedlings exposed to stressful environments. Thus, this study was conducted to select soybean genotypes exposed to stressful environments (saline or drought) using similarity based on Manhattan distance and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method. TOPSIS is a multi-criteria decision method for selecting the best alternative using the concept of distance. The use of TOPSIS is essential because the genotypes are not absolutely similar in both treatments. That is, just the distance measure is not enough to select the best genotype simultaneously in the two stress environments. Drought and saline stresses were induced by exposing seeds of 70 soybean genotypes to -0.20 MPa iso-osmotic solutions with polyethylene glycol-PEG 6000 (119.6 g L-1) or NaCl (2.36 g L-1) for 14 days at 25 °C. The germination rate, seedling length, and seedling dry matter were measured. We showed here how the genotypic stability of soybean plants could be quantified by TOPSIS when comparing drought and salinity conditions to a non-stressful environment (control) and how this method can be employed under different conditions. Based on the TOPSIS method, we can select the best soybean genotypes for environments with multiple abiotic stresses. Among the 70 tested soybean genotypes, RK 6813 RR, ST 777 IPRO, RK 7214 IPRO, TMG 2165 IPRO, 5G 830 RR, 98R35 IPRO, 98R31 IPRO, RK 8317 IPRO, CG 7464 RR, and LG 60177 IPRO are the 10 most stable genotypes under drought and saline stress conditions. Owing to high stability and gains with selection verified for these genotypes under salinity and drought conditions, they can be used as genitors in breeding programs to obtain offspring with higher resistance to antibiotic stresses.
Keywords: abiotic stress; distance measure; multi-environment; osmotic potential; vector space model.