TWO GENERALIZATIONS OF AGGREGATED UNCERTAINTY MEASURE FOR EVALUATION OF DEZERT–SMARANDACHE THEORY

Generality of the model which is used in Dezert–Smarandache Theory (DSmT) rather than other fusion algorithms such as Dempster–Shafer theory and capability of DSmT for dealing with highly conflict problems are two main reasons to prefer DSmT for decision-making systems. Aggregated uncertainty measure, which is called AU measure, has been introduced for Dempster–Shafer theory as one of the best presented ways to quantify the total uncertainty or the ambiguity of a belief function. Since AU cannot be applied to DSmT, two generalized aggregated uncertainty measures for DSmT, which are called GAU1 measure and GAU2 measure, are proposed in this paper. The GAU1 measure is developed by extension of the frame of discernment with distinct sub-events. The GAU2 measure is developed by considering new conditions on probability assignments which are used in the uncertainty measure. The new conditions are the difference of this measure with AU measure. A rigorous discussion is presented to validate that the proposed uncertainty measures holds on the requirements for an uncertainty measure. Finally evaluation of uncertainty in a DSmT-based localization problem is presented to show how to apply the generalized uncertainty measures, GAU1 and GAU2.