dst (version 1.3.0)

belplau: Calculation of the degrees of Belief and Plausibility

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

belplau(x, remove = FALSE)

Arguments

x

A basic chance assignment mass function (see bca).

remove

= TRUE: Exclude subsets with zero mass.

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

Details

The degree of belief Bel is defined by: $$bel(A) = Sum((m(B); B \subseteq A))$$ for every subset B of A. The degree of plausibility pl is defined by: $$pl(A) = Sum[(m(B); B \cap A \neg \o]$$ 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: \(Pl(A)/(1-Bel(A))\).

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

# NOT RUN {
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) 
# }