Mass of Belief

Mass of Belief

Shafer's belief theory considers a domain of reference $\Omega$ , assumed finite for the sake of simplicity, over which belief coefficients are determined. These coefficients are obtained by distributing a global mass of belief equal to 1 between all the possible events, and by assigning a degree m(A) to each one. This degree shows how much a group of observers believes in the occurrence of the event.

A basic belief assignment on $\Omega$ , also called a mass of belief is any function m that assigns a coefficient between 0 and 1 to the different parts of $\Omega$ such that:

$\displaystyle \sum_{A \in \mathcal{P}(\Omega)} m(A) = 1$

(77)

$\displaystyle m(\varnothing) = 0$

(78)

m(A) is also called the mass of A and represents the exact belief in the event represented by A. Therefore, if m(A)=1 and $\forall B \neq A, B \in \mathcal{P}(\Omega), m(B)=0$ , then A is certain in the sense that one of the elements of A is the sought value.

However, we do not know which element of A is concerned, except if A is a singleton. In addition, if $A = \Omega$ , then information m(A)=1 does not teach us anything, except that we are in a situation of total ignorance.

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