Handling uncertainty is a challenge in activity recognition. Uncertainty can be due to sensor errors (e.g. run out of batteries, imprecise outputs, missing activations etc.) and communication failures. and variability in human activities. These issues may significantly influence the accuracy of activity recognition. Data-driven approaches use machine learning techniques such as Decision Tree, naïve Bayes and Support Vector Machine to develop robust activity models that extract specific features from sensor data. The advantages of learning techniques is the ability to handle uncertainty and noise. Knowledge-driven approach such as ontology exploit prior knowledge to build semantic activity model by using knowledge engineering techniques, and then reason on it with input sensor data.
Ontology is a formal and explicit way of specifying and representing domain knowledge through formal axioms and constraints. Ontology-based models have several advantages over other models .
1. Ontology allows the domain knowledge to be decoupled from the operational knowledge.
2. Ontology has strong support through standardization such as Resource Description Framework Schema (RDF) and Web Ontology Language (OWL) and hence a variety of development tools are available.
3. Rules which are tightly integrated into reasoning can be expressed via Semantic Web Rule Language (SWRL).
Despite the advantages listed above, ontology cannot deal with uncertainty. This is because, ontology can only infer an activity when all the contextual information that defines the activity is asserted. If one of the contexts is missing, ontology will not be able to infer the activity that is being carried out.
A number of approaches have been proposed for reasoning with uncertainty. Probabilistic theory is a widely used method in dealing with uncertainty. In probabilistic theory, the likelihood of an event is represented by means of a non-negative value called probability. Probabilistic theory such as Bayes theorem can model the reliability of sensor data by learning the correlation between sensor data and the activity to be detected as presented in . Although Bayesian model is capable of dealing with uncertainties due to inaccurate and contradicting sensor data, it is not capable of dealing with missing sensor data . Using Bayesian theory a missing sensor data could be represented by a proposition of inactive sensor. However, such proposition is not always true because the system might not receive the data due to communication loss. Unlike Bayesian theory where each individual proposition is assigned a non-negative value (probability), Dempster-Shafer (DS) theory distributes non-negative weights (called masses) to any combination of propositions . This means that the belief function can explicitly represent any ambiguity or ignorance about what has been observed such as missing sensor data. Using DS theory, ontological reasoning is enhanced to deal with uncertainty due to missing sensor data. It features reasoning mechanism of Description Logic and uncertainty management while combining contextual information from different sources (sensors) and provides a degree of belief of the activities, supporting the decision making process.
From ontological engineering perspective, an activity is represented as a concept in an ontology, and a concept is a specification that defines the aggregation of series of human action contexts. Such aggregation can be represented as conjunctive implication
Activity(d) = Action(xn) ∩ Action(xn-1) ∩ … ∩ Action(x1)
Activitiy(d) is the concept of activity d that defines the series of n human actions. The Action predicate is an atomic concept associated with the activity. An activity is recognized if every action concept is inferred. However uncertainty due to missing data may arise during context reasoning process. In order to accommodate such uncertainty, ontological reasoning is integrated with DS theory to support the reasoning process. Each action context x is assigned with a degree of belief. It measures the strength of the context supporting an activity. The higher the degree of belief of the context, the greater is the possibility that the activity is being performed. The concept of activity d could be represented with uncertainty component as follows.
Activity(d) = [Action(xn) with m(xn)] ∩ [Action(xn-1) with m(xn-1)] ∩ … ∩ Action(x1) with m(x1)]
where m(x) is the mass function of action x. Then, Dempster’s rule of combination can be used for fusing action contexts to calculate the degree of belief of activity d.
First the reasoning algorithm determines the state of the actions in order to assign the degree of belief. The state of an action could be active, inactive and uncertain. The active state represents that the action is occured in the environment and inactive state represents the opposite case. The uncertain state represents the ignorance about the state of the action, either active or inactive. The action states are determined by the temporal sequence of the actions and inference of the actions. The action context with active state is inferred by semantically interpreting the lower-level contextual information (which in this case the sensors). The belief of the actions is assigned by propagating the mass from the associated sensors. Readers are referred to  for details of the algorithm.
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