Complex systems are now integrating many sensors, physical or logical, in order to be able to take the best decision knowing the exosystem and endosystem. These sensors are data sources, which deliver partial information, imprecise and/or uncertain, partially complementary and partially redundant. The theory of belief functions is now widely used in data fusion because it provides a formal framework for the representation of both imprecise and uncertainty information. However, even modeling the ignorance and the imprecision of the sources, the source combination usually lets appear some disagreement/conflict between sources.A disagreement between sources makes the system unstable and can impact the decision. Thus, for managing the disagreement, several authors have developed different combination rules where the “Dempster's conflict” is transferred to a set of elements. A few works have proposed to consider the conflict as a piece of information exploitable beyond the scope of the combination. In this work, we aim at decomposing the Dempster's conflict in order to better interpret it. We propose a decomposition with respect to different assumptions simple or compound of discernment space. We show the uniqueness of this decomposition and we specify the algorithm, based on the canonical decomposition of belief function. We then interpret each term of the decomposition as the contribution, to global conflict, brought by each hypothesis simple or compound. This decomposition is applied to the analysis of intra-conflict source (i.e. the conflict inherent in the source) or inter-conflict sources (i.e. the conflict appearing during the fusion of sources). We illustrate on toy examples how observing the distribution of conflict with respect to different assumptions may allow the identification of the origin of some conflicts.Three applications of our measurement have been developed to illustrate its usefulness.The first application deals with the preventive detection of fall for motorbike. Typical data sources are speed and accelerations measured on each of the two wheels. A conflict between these measures, supposed highly redundant or even correlated, should be interpreted as an early fall (sliding, shock). We show that the decomposition of conflict provides a finer and earlier indicator of fall than Dempster's conflict.The second application is the localization of the vehicle, the key issue being for autonomous exploration vehicles such as service robots. The sources are outputs of algorithms estimating the movement of the vehicle (such as odometers, visual odometry, FastSLAM). We first show that estimating the reliability of sources dynamically improves fusion. We then show that the decomposition of conflict allows a more refined measure of the fusion reliability than Dempster's conflict. Now, when conflict is detected, the estimation of the reliability of each source is based on the verification (or not) of an assumption of temporal regularity, verification itself based on a distance measure local to the discernment space hypotheses.The third application is the generalization of the hybrid combination [Dubois and Prade, 1988] to the case of N sources. Our measure calculates the partial conflicts associated with each subset of hypotheses. Following the hybrid combination [Dubois and Prade, 1988] principle, we redistribute the mass associated to a partial conflict on the disjunction of the hypotheses involving this partial conflict. In this redistribution, our decomposition of the conflict is essential since it allows identifying uniquely the various sub-sets of hypotheses involving partial conflicts.In conclusion, this work has shown that the information derived from the conflict measurement, and its decomposition could (should) be considered a full information, particularly for the management of sources and beliefs to combine.
