belplau: Calculation of the degrees of Belief and Plausibility In dst: Using Dempster-Shafer Theory

Description

Degrees of Belief `Bel` and Plausibility `Pl` of the focal elements of a mass function are computed. The ratio of the plausibility of a focal element against the plausibility of its contrary is also computed. Subsets with zero mass can be excluded from the calculations.

Usage

 `1` ```belplau(x, remove = FALSE) ```

Arguments

 `x` A basic chance assignment mass function (see `bca`). `remove` = TRUE: Exclude subsets with zero mass.

Details

The degree Belief `Bel` is defined by:

bel(A) = Sum((m(B); B <= A))

, for every subset B of A.
The degree of plausibility `pl` is defined by:

pl(A) = Sum[(m(B); B and A not empty]

, for every subset `B` of the frame of discernment.
The plausibility ratio of a focal element `A` versus its contrary `not A` is defined by: Pl(A)/(1-Bel(A)).

Value

A matrix of `M` rows by 3 columns is returned, where `M` is the number of focal elements:

• Column 1: the degree of belief `Bel`;

• Column 2: the degree of Plausibility `Pl`;

• Column 3: the Plausibility ratio

Author(s)

Claude Boivin, Stat.ASSQ

References

• Shafer, G., (1976). A Mathematical Theory of Evidence. Princeton University Press, Princeton, New Jersey, p. 39-43.

• Williams, P., (1990). An interpretation of Shenoy and Shafer's axioms for local computation. International Journal of Approximate Reasoning 4, pp. 225-232.

Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```x <- bca(f=matrix(c(0,1,1,1,1,0,1,1,1),nrow=3, byrow = TRUE), m=c(0.2,0.5, 0.3), cnames =c("a", "b", "c"), infovarnames = "x", varnb = 1) belplau(x) y <- bca(f=matrix(c(1,0,0,1,1,1),nrow=2, byrow = TRUE), m=c(0.6, 0.4), cnames = c("a", "b", "c"), infovarnames = "y", varnb = 1) belplau(nzdsr(dsrwon(x,y))) print("compare all elementary events") xy1 <- addTobca(nzdsr(dsrwon(x,y)), matrix(c(0,1,0,0,0,1), nrow=2, byrow = TRUE)) belplau(xy1) ```

dst documentation built on April 26, 2018, 1:03 a.m.