# Reasoning about Confidence in Goal Satisfaction
## 4 Data Quality Tagging and Propagation Mechanism
### Propagation Method  
GRL has four main types of links: AND-decomposition, XOR/OR-decomposition, contribution, and dependency (see Figure 1). For each type, the confidence level of the satisfaction of a parent goal in a model is calculated differently from the confidence of children goals. The algorithm for calculating confidence values is adapted from the standard GRL CalculateEvaluation algorithm [4]. Confidence is computed in an integrated manner from the decomposition, contribution, and dependency relationships, in that order. It is important to note that confidence can be computed _independently_ from the satisfaction values of goals; for example, a goal could have a high satisfaction with a low confidence or a low satisfaction with a high confidence. **AND-decomposition:** the confidence of the parent goal satisfaction is equal to the _average_ of its sub-goals' confidence values. Unlike satisfaction propagation (where the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Quality Type** & **Confidence Value** & **Definition** \\ \hline _Valid_ & 100 & Data already measured and available for the design alternative, in the same context as the one under evaluation \\ _Borrowed-Valid_ & 100 & Data already measured and available for the design alternative, in a context similar to the one under evaluation \\ _Borrowed_ & 75 & Data already measured and available for the design alternative, but in a different context \\ _Estimated-Context_ & 50 & No data available, but it was estimated according to a similar design alternatives in a different context \\ _Estimated-Literature_ & 25 & No data available, but it was estimated based on the literature or previous studies \\ _Unknown_ & 0 & No data-driven evidence will be used in the evaluation \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Data quality types and corresponding confidence values, in a decision-making context related to design alternatives. minimum satisfaction is propagated to the parent goal), the average is used for confidence because:  
* The confidence of the sub-goal with minimum satisfaction value might be different from the minimum confidence among all sub-goals of the AND-decomposition. * The confidence of the sub-goal with minimum satisfaction value might be much higher or lower than the confidence of the other sub-goals. Yet, all sub-goals are taken into consideration during the propagation decision. Since the satisfaction of the parent goal is computed based on the satisfaction levels of all of its sub-goals in the AND-decomposition, taking the confidence levels of all sub-goals into consideration in an AND-decomposition context (as formalized in Equation (5)) is hence a reasonable approach. As there are no explicit weights associated with AND-decomposition links, we assume here equal weights by using an average function. Note also that the average is preferable here to the maximum and minimum functions as the maximum of the confidence values is too optimistic in an AND-decomposition context whereas the minimum is too pessimistic, especially as the actual confidence level of the propagated satisfaction value might be ignored in both these alternative functions. Additionally, only propagating the confidence level of the selected (and lowest) satisfaction values is deemed insufficient here as this solution would ignore the confidence levels of the other considered nodes, which might be much lower or higher. Figure 7 illustrates how the confidence of the satisfaction of the goal model element is computed for AND-decompositions. The average of 50 and 75 is 63, which is propagated to the top goal. Note that GRL models also include other types of values that could require some confidence assessment, for instance contribution values. However, as discussed in the previous section, several techniques already exist for reaching agreement on contribution weights [26; 27; 28; 29; 30; 31]. New data quality (DQ) and confidence (C) values are highlighted in red in the figure.