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The existing expert weight determination method for multi-attribute decision making based on the Pythagorean fuzzy number approach does not make sufficient use of the hesitation involved with the decision information, which may cause biased weight assignment. Therefore, to address the issue of unknown expert weights and attribute evaluation based on Pythagorean fuzzy numbers in multi-attribute group decision-making problems, a weight determination method is proposed that improves the treatment of hesitation in Pythagorean fuzzy sets. Firstly, the proximity of experts and similarity of the modified ones are determined according to the evaluation matrix. Then, the expert weights are integrated from the aspects of proximity and corrected similarity to obtain an assembled comprehensive evaluation matrix. Finally, the alternatives are ranked using the PF-TOPSIS method. The results of expert weight analysis and data verification demonstrate that the proposed method fully utilizes expert decision-making information, leading to a significant improvement in the rationality and accuracy of multi-attribute group decision-making problems.

Additional file 1: Table S1. The comparison of demographic and clinical variables between training group and validation group of male and female patients. Table S2. The comparison of demographic variables in PSD with and without antidepressant use of male and female patients. Table S3. Tolerance of collinearity diagnosis between independent variables entered into binary logistic regression analyses for males. Table S4. Tolerance of collinearity diagnosis between independent variables entered into binary logistic regression analyses for female. Table S5. The association between BI score and PSD at 3 months in males according to stroke severity. Figure S1. A: The number of male random forest trees; B: The number of female random forest trees.

Additional file 1: Supplemental Table I. Image Acquisition Protocols. Supplemental Figure I. Z-score standardized values of closeness, betweenness and strength for all nodes.Closeness centrality refers to the inverse sum of the lengths of the shortest paths from a node to all other nodes. Betweenness centrality is the number of times a node lies on the shortest path between two other nodes. Strength centrality is the sum of all absolute values of edges connected to a node. Betweenness and closeness have demonstrated poor reliability in psychopathology network studies. Expected influence considers both positive and negative edges and may be more reliable and interpretable than strength. DepMood indicates depressed mood; Guilt, guilt feelings; Suic, suicidality; Insomn, insomnia; Workact, loss of interest in work and activities; Retard, retardation; Agit, agitation; PsyAnx, psychiatric anxiety; SomAnx, somatic anxiety; GISom, gastrointestinal somatic symptoms; GenSom, general somatic symptoms; Hypochon, hypochondriasis; WtLoss, weight loss. Supplemental Figure II. Stability of betweenness, closeness and strength in 1,000 case-dropping bootstraps. CS-C for betweenness: 0.672; CS-C for closeness: 0.75; CS-C for strength: 0.75. Supplemental Figure III. Bootstrap edge weights difference test between non-zero estimated edge-weights in the network. Bootstrapped difference tests (α = 0.05) between edge-weights that were non-zero in the network. Significant differences between two edges are indicated by black boxes, non-significant differences are indicated by grey boxes. The color of the boxes (ranging from white to blue) corresponds to the thickness of the edge. DepMood indicates depressed mood; Guilt, guilt feelings; Suic, suicidality; Insomn, insomnia; Workact, loss of interest in work and activities; Retard, retardation; Agit, agitation; PsyAnx, psychiatric anxiety; SomAnx, somatic anxiety; GISom, gastrointestinal somatic symptoms; GenSom, general somatic symptoms; Hypochon, hypochondriasis; WtLoss, weight loss.

Additional file 1.