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... 33] or based on local computations [28] or to adapt the algorithms to particulars mass functions [27, 3]. Second we can try to reduce the number of focal elements by approximating the mass functions =-=[37, 36, 4, 9, 16, 17]-=-, that could be particularly important for dynamic fusion. In practical applications the mass functions contain at first only few focal elements [7, 1]. Hence it seems interesting to only work with th...

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...odel (TBM), Burger and Cuzzolin proposed two types of ...

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...nts defined on 2Θ, onto 2Θ. Therefore the complexity of this task can be very important. This is the reason why we can reduce the number of focal elements (i.e. elements with a non null basic belief) =-=[22, 21, 2, 5]-=-. Finally, the belief functions are generally used to take a decision. In the most of applications, the decision is taken on one element of Θ and not 2Θ, by the credibility, plausibility functions or ...

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...ting a function of n mass functions using (36) grows exponentially with n, which may lead to serious problems when both the number of steps in the computations and the size of focal sets become large =-=[13]-=-. A natural way to decrease this complexity is therefore to decrease the number of focal sets by grouping similar or unimportant ones. This strategy is at the basis of the summarization method [30], i...

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...ting a function of n mass functions using (36) grows exponentially with n, which may lead to serious problems when both the number of steps in the computations and the size of focal sets become large =-=[13]-=-. A natural way to decrease this complexity is therefore to decrease the number of focal sets by grouping similar or unimportant ones. This strategy is at the basis of the summarization method [30], i...

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...ecially to manage the conflict between the sources [23, 9, 11, 19, 13]. Another common mean to manage the conflict is the use of a discounting procedure. This process consist in decreasing the basic beliefs on precise focal elements and increase the basic beliefs on imprecise focal elements such as the total ignorance Θ. The task of combination can be seen as a mapping from s basic belief assignments defined on 2Θ, onto 2Θ. Therefore the complexity of this task can be very important. This is the reason why we can reduce the number of focal elements (i.e. elements with a non null basic belief) [22, 21, 2, 5]. Finally, the belief functions are generally used to take a decision. In the most of applications, the decision is taken on one element of Θ and not 2Θ, by the credibility, plausibility functions or by the pignistic probability [4, 18]. However, the decision can also be taken on all 2Θ [1, 14]. Hence, the decision process is a mapping from 2Θ onto Θ or 2Θ. In a belief application, the definition of the basic belief assignments and all these previous tasks (reduction of focal elements number, discounting, combination and decision) must be thought in the same time. Moreover these tasks can be s...

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...ments in the combined bba is too high to be explored, a first way to proceed is to select only the partitions associated with the highest masses or use a simplification algorithm such as described in =-=[5]-=-. We propose another approach which consists in building a matrix Q = (qij) whose elements are the commonalities associated to each atom of the lattice of partitions. This approach amounts computing, ...

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... 33] or based on local computations [28] or to adapt the algorithms to particulars mass functions [27, 3]. Second we can try to reduce the number of focal elements by approximating the mass functions =-=[37, 36, 4, 9, 16, 17]-=-, that could be particularly important for dynamic fusion. In practical applications the mass functions contain at first only few focal elements [7, 1]. Hence it seems interesting to only work with th...

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...(TBM) [13], Burger and Cuzzolin proposed two types of 푘-additive belief functions [14]. Denœux uses hierarchical clustering strategy to implement the inner and outer approximation of belief functions =-=[15]-=-. In our recent research, a hierarchical proportional redistribution (HPR) approach is proposed to approximate bba [16]. In this paper, we focus on the bba approximation approach to reduce the computa...