# Reasoning about Confidence in Goal Satisfaction
## 3 Related Work  
As indicated in Section 1, an important approach for managing uncertainty in goal models is proposed by [PERSON] et al. [1]. Their proposal adopts a statistical decision-theoretic technique to support decision making under uncertainty. Probability distributions are used to represent uncertainties of alternatives for a decision. In addition, the study uses Monte Carlo simulations to assess the impact of uncertainties on a goal model, as well as Pareto-based multi-objective optimization techniques to guide alternative selection. This work was extended with the RADAR modeling language that optimizes and shortens the selection of architectural design in the presence of uncertainty. It was also implemented to automate developing the decisions model and its simulation [6; 7]. Adopting a different approach, [PERSON] and [PERSON] extended the probabilistic goal/obstacle specification language to handle knowledge uncertainty [8]. Their approach provides probability-based metrics and a method to identify uncertainties about goal satisfaction and to highlight the most impacting obstacles on a goal model. Similar work was done in this area by [PERSON] et al. [9], especially in a technology qualification context. [PERSON] et al. proposed another approach that used probabilistic models and analysis to handle uncertainty in goal-driven self-optimization processes [10]. More recently, [PERSON] et al. explored extensions of the \(i^{*}\) goal modeling language (e.g., with probabilistic effects for tasks) to allow representing and reasoning about both uncertainty in the environment and preferential utility in goals [11]. Other approaches of a less probabilistic nature have been proposed to address uncertainty in goal models. [PERSON] proposed a language-independent framework called MAVO to annotate and analyze formally uncertainty, targeting incompleteness in models [12]. [PERSON] et al. developed a search-based technique (Providentia) to address environmental and system uncertainty while analyzing and choosing the optimal non-functional requirements configuration for self-adaptive systems [13]. Sources and impact of uncertainty are specified in the executable specification to guide the selection of an optimal configuration using Genetic Algorithm (GA). Similarly, [PERSON] et al. proposed AutoRELAX, which applies GA and executable specification to explore possible goal model configurations under environmental uncertainty constraints [14]. [PERSON] et al. propose the use of Markov  
Figure 5: Propagation of element satisfactions in the case of contributions. Figure 6: Propagation of element satisfactions in the case of dependencies. logic to support root cause analysis, using goal models [15]. Another interesting method to support strategic decisions about Information Technology initiatives under uncertainty is presented by [PERSON] [16], while [PERSON] et al. use quantified values between 0 and 1 associated with security requirements in a goal model to deal with uncertainty [17]. Bayesian Belief Networks (BBNs) have also been used in many methods to estimate the confidence of an argument. [PERSON] and [PERSON] reported on the power and flexibility of BBN to represent the structured argument of an assurance case, where a claim is supported with multiple evidence items characterized by different degrees of confidence [18]. In a similar context, [PERSON] et al. proposed an approach to identify and estimate confidence in a safety case [19]. The safety case is modeled using the Goal Structuring Notation and the confidence of supporting arguments of a claim is estimated quantitatively and propagated using BBNs. There exist several other proposals in the area of uncertainty and confidence reasoning in goal models, as well as other approaches such as [PERSON]'s [20], where goal modeling and data mining techniques are combined.