dst (version 1.8.0)

nzdsr: Normalization of a basic chance assignment

Description

It may occur that the result of the combination of two basic chance assignments with Dempster's Rule of combination contains a non-zero mass allocated to the empty set. The function nzdsr normalizes the result of function dsrwon by dividing the mass value of the non-empty subsets by 1 minus the mass of the empty set.

Usage

nzdsr(x, sparse = "no", comm = "no")

Value

z The normalized basic chance assignment.

Arguments

x

A basic chance assignment, i.e. a object of class bcaspec.

sparse

Put "yes" to use sparse matrix. Default = "no".

comm

Put "yes" to use commonality function. Default = "no".

Author

Claude Boivin, Peiyuan Zhu

References

Shafer, G., (1976). A Mathematical Theory of Evidence. Princeton University Press, Princeton, New Jersey, pp. 57-61: Dempster's rule of combination.

Examples

x1 <- bca(tt= matrix(c(1,0,1,1),nrow = 2, byrow = TRUE), 
m = c(0.9,0.1), cnames = c("yes", "no"),
varnames = "x", idvar = 1)
x2 <- bca(tt = matrix(c(0,1,1,1),nrow = 2, byrow = TRUE), 
m = c(0.5,0.5), cnames = c("yes", "no"), 
varnames = "x", idvar = 1)
print("combination of x1 and x2")
x1x2 <- dsrwon(x1,x2, varname = "x")
nzdsr(x1x2) 
# Test with sparse matrices
x1s=x1
x2s=x2
x1s$tt <- methods::as(x1$tt, "RsparseMatrix")
x2s$tt <- methods::as(x2$tt, "RsparseMatrix")
x1x2s <- dsrwon(x1s, x2s, use_ssnames = TRUE)
nzdsr(x1x2s)

print("normalization of a bca definition.")
y2 <- bca(tt = matrix(c(0,0,0,1,0,0,1,1,1),nrow = 3, 
byrow = TRUE), m = c(0.2,0.5,0.3), 
cnames = c("a", "b", "c"), idvar = 1)
cat("y2")
cat("\  ")
y2
nzdsr(y2)