Context awareness and activity recognition are becoming a hot research topic in ambient intelligence (AmI) and ubiquitous robotics, due to the latest advances in wireless sensor network research which provides a richer set of context data and allows a wide coverage of AmI environments. However, using raw sensor data for activity recognition is subject to different constraints and makes activity recognition inaccurate and uncertain. The Dempster-Shafer evidence theory, known as belief functions, gives a convenient mathematical framework to handle uncertainty issues in sensor information fusion and facilitates decision making for the activity recognition process. Dempster-Shafer theory is more and more applied to represent and manipulate contextual information under uncertainty in a wide range of activity-aware systems. However, using this theory needs to solve the mapping issue of sensor data into high-level activity knowledge. The present paper contributes new ways to apply the Dempster-Shafer theory using binary discrete sensor information for activity recognition under uncertainty. We propose an efficient mapping technique that allows converting and aggregating the raw data captured, using a wireless senor network, into high-level activity knowledge. In addition, we propose a conflict resolution technique to optimize decision making in the presence of conflicting activities. For the validation of our approach, we have used a real dataset captured using sensors deployed in a smart home. Our results demonstrate that the improvement of activity recognition provided by our approaches is up to of 79 %. These results demonstrate also that the accuracy of activity recognition using the Dempster-Shafer theory with the proposed mappings outperforms both na < ve Bayes classifier and J48 decision tree.