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.
A basic chance assignment mass function (see
= TRUE: Exclude subsets with zero mass.
The degree of 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
Column 2: the degree of Plausibility
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.
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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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