International audienceThe evidence theory and its propositional conflict redistribution variant rules are mathematical formalisms used to represent uncertain as well as ambiguous data. The evidence combination rules proposed in these formalisms do not satisfy the idempotence property. However, in a variety of applications, it is desirable that the evidence combination rules satisfy this property. In response to this challenge, the present work proposes a new formalism for reasoning under uncertainty based on new consensus and conflicting of evidence concepts. This mathematical formalism is evaluated using a real world activity recognition problem in smart home environment. The results show that one rule of our formalism respects the idempotence property and improves the accuracy of activity recognition
