Two Generalizations of Aggregated Uncertainty Measure for Evaluation of Dezert–smarandache Theory

Abstract

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.

Uncertainty evaluation for an ultrasonic data fusion based target differentiation problem using Generalized Aggregated Uncertainty measure 2

“…Accordingly, uncertainty measurement would not be accurate. Two Generalized Aggregate Uncertainty measures, which are named GAU1 and GAU2, have been developed [22]. The idea of generalizing Aggregated Uncertainty measure in GAU1 to evaluate DSmT, is disjointing the free DSm model to separated sets (Fig.…”

“…So this refinement may not work for any frame of discernment. The new uncertainty measure which has been called, Generalized Uncertainty measure 2 or GAU2 has been introduced to overcome this limitation [22]. In GAU2, despite of GAU1, clarity of the frontiers of the sets in the frame of discernment is not necessary.…”

“…Two generalized AU measures, which are named GAU1 and GAU2, have been introduced by the authors (see Ref. [22]). It is proved that the new measures have enough efficiency to evaluate the DSmT based results.…”

Quantification Classification Algorithm of Multiple Sources of Evidence

“…Moreover, the D-S evidence theory combination rule can aggregate information from multiple sources to a new belief assignment. Owing to these properties, it has been used in fault diagnosis, [13][14][15][16] reliability engineering, [17][18][19][20][21][22] classi¯cation, 23 object extraction, 24 knowledge discovery, 25 risk analysis, 26,27 and so on.…”

“…For the second question, many papers only represent the classi¯cation between two bodies of evidence. [25][26][27][28][29][30][31][32][33]36,37,39 These two bodies of evidence can be classi¯ed into two categories: con°icting and noncon°icting evidence.…”