## 4 Related Work  
In the past, the ranking of services by QoS properties has been addressed by researchers in two different ways: (1) by considering static attributes [9, 17]; and (2) by taking a snapshot of the current values of the attributes [14, 18]. The former squanders the opportunity to improve the user experience dynamically at the time the user is actually selecting the service. In our telescope example in Table 1, capturing a measure of the availability of telescope service T3 on Day 1 and using that information to evaluate the service on Day 4, when the value has changed substantially, are misrepresenting reality. Nonetheless, the work done here is still important, because it introduces the idea of using aggregation querying in the context of web service discovery. Regarding the second option, capturing instantaneous measurements of QoS properties ignores the practical issues that arise naturally when using dynamic attributes. For example, on Day 3, the latency measurement for T2 is null, but one should be lenient, because, historically, this attribute performed well. [PERSON] _et al_. [14] introduced the concept of dominance and skyline into the field of web service discovery. They examine every subset of the QoS attributes and count the number of subsets in which a given service is dominated. The services can then be ranked in ascending order of score. In this way, they combine the notions of skyline and aggregation without having to model user context. They also present several algorithms to determine the top \(k\) web services based on several scoring functions: dominated score (TKDD), dominating score (TKDg) and dominance score (TKM). They improved the performance by having boundaries for each object, consisting of the lowest and highest values of the dominating scores. Therefore, instances (_i.e._, attributes of a service) are maintained in three lists: maximum, minimum and current values of instances for a service. This approach helps with static service discovery, where values of attributes are available, but cannot support missing values. [PERSON] _et al_. [18] proposed an algorithm, Transactional and Quality-of-Service (TQoS) driven selection, that is embedded in the transactional service selection for web service composition. The algorithm is designed for local QoS optimization; that is, the selection of the qualifying services for each activity that fulfils the transactional requirements. The algorithm's input is a workflow that includes a set of activities to fulfil a request. The output is a set of the services for each activity in the workflow with similar transactional properties, but dissimilar non-functional properties. The TQoS selection uses user preferences as a weight assigned to each QoS criterion. Then, the web service is scored through a conventional scoring function to rank services and to find the one with the maximum score. If there are multiple services with the same score, one of them is chosen randomly. Similar techniques are applied to select the maximum score path for web service composition. Possibility theory is a mathematical theory for dealing with certain types of uncertainty, which has been used to tackle the issues of skyline for uncertain QoS attributes in web service discovery [19]. This work is based on a possibility distribution that contains all possible values of QoS attributes for each service. The authors propose two skyline algorithm extensions--pos-dominates and nec-dominates--to compute whether service \(s_{i}\) dominates service \(s_{j}\) in accordance with the threshold values computed from the possibility distribution. As far as we could tell, this work has not been applied to dynamic web service discovery. [PERSON] _et al_. [20, 21] proposed the QoS-aware Vienna Runtime Environment for Service-oriented Computing (VRESCO) run-time environment for dynamic binding, invocation and mediation. They describe functional attributes in their service meta-data model.