## 4 Evaluation Method
### Weight Calculation Method
#### 4.1.4 Order Relationship Analysis Method (G\({}_{1}\) Method)  
The G\({}_{1}\) method is a subjective weighting technique based on AHP. This method aids decision-makers when assessing an object characterized by various indicators, helping them ascertain the importance of each. It draws on the subjective assessments of decision-makers to form order relationships and relative importance ratios, making it especially fitting for situations that demand considerable involvement from decision-makers. In contrast to the AHP, the G\({}_{1}\) method does not require consistency testing, making it more suitable for scenarios where strict consistency is not critical [117]. The G\({}_{1}\) method allocates weights to various indicators according to the ordinal relationships set by decision-makers. A specific set of evaluation criteria or indicators is determined based on the evaluation objective and the subject being evaluated. The decision-maker subsequently assesses these criteria, ranking them from most to least significant, thereby establishing an ordered relationship as per their judgment. Furthermore, the decision-maker is required to present a ratio that signifies the relative importance between two adjacent criteria, typically expressed as a numerical value, \(r\). This value conveys the significance of the former criterion in comparison to the latter. By utilizing the established order relationship along with the ratios of relative importance, a particular calculation formula--such as the eigenvector method, the inverse consistency index method, or a formula specifically tailored for the G\({}_{1}\) method--is applied to determine the weight of each criterion.  
The steps involved in the G\({}_{1}\) method are straightforward and simple to comprehend and apply. When compared to the AHP method, the G\({}_{1}\) method offers a less complicated calculation process, as it does not require the creation of an intricate judgment matrix or the execution of consistency tests. This method effectively reflects the subjective evaluations of the decision-maker, which makes it ideal for situations where the decision-maker's views are crucial. Nevertheless, the G\({}_{1}\) method's dependence on the subjective judgment of the decision-maker can result in outputs that are excessively shaped by individual experiences, preferences, and other influences. Unlike objective weighting methods, such as the EWM, the G\({}_{1}\) method does not provide strong data backing and may fail to accurately convey the true significance of each indicator [111] (Figure 5).  
In real-world applications, the G\({}_{1}\) method can be combined with various techniques, including the entropy weight method (EWM) and fuzzy comprehensive evaluation (FCE), to improve the precision and dependability of assessments. The G\({}_{1}\) method, in conjunction with the EWM, is used to identify both subjective and objective weights for indicators associated with engineering geology and hydrogeological conditions in Foshan [74]. Following this, the principle of minimum discriminant information is applied to establish their aggregated weights. This strategy not only integrates expert assessments regarding the importance of the evaluation indicators but also takes into account the intrinsic properties of the data (Figure 6 and Table 1).