The relation between the belief function and the probability function when decisions must be made is derived and justified.
As noted in the previous section, the belief function, bel(r k ), plays an important part in any BIN, and we have used four different belief functions here.
The belief function measures the amount of belief in the hypothesis on the basis of observed evidence.
Specifically, we address the issue of handling uncertainty and information fusion for an efficient WSNs deployment by exploiting the belief functions reasoning framework.
Based on the belief functions theory, we established a general influence measure for a given user by information fusion of the different relations.
It may occur in practice that some model input variables and parameters can be represented by probability distributions (due to observed variability and sufficient statistics), while others are better represented by possibility distributions (due to imprecision), or by the Dempster Shafer belief functions (due to partial observed variability and partial ignorance).
The theory of evidence can then be utilized in the following situations where the use of conventional HMCs poses difficulties: (1) When the prior distribution p(x) is not known with precision (for instance, when p ( x n | x n − 1 ) depends on n), it can be replaced by a belief function obtained from p(x) to model the uncertainty or lack of accurate knowledge of p(x).
At each time step, a distribution over states is maintained by a belief function "b" with initial belief state b 0. We adopt b(s) to indicate the probability of being in a specific state s.
In this paper, parametric regression analyses including both linear and nonlinear regressions are investigated in the case of imprecise and uncertain data, represented by a fuzzy belief function.
So the counterfactual belief function idea needs a lot of working out if it is to rescue the idea that subjectivist Bayesian belief functions can provide a viable account of the likelihoods employed by the sciences in inductive inferences.
