Belief functions on real numbers

Belief functions on real numbers

We generalize the TBM (transferable belief model) to the case where the frame of discernment is the extended set of real numbersR = [−∞,∞], under the assumptions that ‘masses’ can only be given to intervals. Masses become densities, belief functions, plausibility functions and commonality functions become integrals of these densities and pignistic probabilities become pignistic densities. The m...

Complexity theory on real numbers and functions

Belief Functions for Real-Time Script Processing

Real-time situation understanding is a d i f f i c u l t problem, in that decisions must be made on a continuous basis with continuously changing data. An attract ive approach to the problem is to match the current data set to a memory of scr ip t l ike structures. Part ial matching to scripts enables powerful understanding and prediction, but requires robust uncertainty mechanisms to overcome ...

Extending stochastic ordering to belief functions on the real line

In this paper, the concept of stochastic ordering is extended to belief functions on the real line defined by random closed intervals. In this context, the usual stochastic ordering is shown to break down into four distinct ordering relations, called credal orderings, which correspond to the four basic ordering structures between intervals. These orderings are characterized in terms of lower an...

On Error Sum Functions Formed by Convergents of Real Numbers

Let pm/qm denote the m-th convergent (m ≥ 0) from the continued fraction expansion of some real number α. We continue our work on error sum functions defined by E(α) := ∑m≥0 |qmα − pm| and E∗(α) := ∑ m≥0(qmα − pm) by proving a new density result for the values of E and E∗. Moreover, we study the function E with respect to continuity and compute the integral ∫ 1 0 E(α) dα. We also consider gener...