Description Usage Arguments Details Value Author(s) References Examples

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.

1 |

`x` |
A basic chance assignment mass function (see |

`remove` |
= TRUE: Exclude subsets with zero mass. |

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))*.

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

Claude Boivin, Stat.ASSQ

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.

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)
``` |

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