Combining belief functions based on distance of evidence

Probabilistic Combination of Multiple Evidence

“…In order to show the useful behavior of our method, we carried out experiments with two different data sets used in the previous published methods: (a) the data set in [11] (Data A) and (b) the data set in [10] (Data B). We compared our proposed method to their methods proposed in each paper.…”

“…In this paper, we focus on an averaging method for the combination rule as proposed in [9][10][11]. We use the fact that multiple bodies of evidence give a probability distribution, and the probability of each piece of evidence on this distribution can serve as a weight for that evidence.…”

“…Likewise, if one evidence is in high conflict, it can be considered less important. So, instead of a simple averaging rule, some other researchers have tried a weighted sum of evidence bodies [11,10]. Although their methods can not be easily summarized in a few equations, generally speaking, they use distances between evidence bodies for different weights, which can be interpreted as a second statistics of the evidence.…”

“…Basically, as in [9] and [11,10], we calculate a weighted sum of evidence bodies for the representative value for each hypothesis from all the evidence. However, it is natural to assume that evidence bodies make a structure as in other data sets (see manifold learning methods [14][15][16]) and this structure can be described by a probability distribution.…”

“…After the initial introduction of ET by Dempster [5], it has been improved [6,9,7] because in some cases the original ET's combination rule is against our intuitive reasoning. Many researchers have proposed different rules to address this issue, and recently, some effective averaging rules have emerged, and in these rules, how to assign the weights becomes an important issue [9][10][11]. These extensions of ET have been applied to many pattern recognition problems [12,13].…”