dsrwon: Combination of two mass functions

In dst: Using the Theory of Belief Functions

Combination of two mass functions

Description

The unnormalized Dempster's rule is used to combine two mass functions mx and my defined on the same frame of discernment and described by their respective basic chance assignments x and y. Dempster's rule of combination is applied. The normalization is not done, leaving the choice to the user to normalize the results or not (for the normalization operation, see function nzdsr).

Usage

dsrwon(
  x,
  y,
  mcores = "no",
  use_ssnames = FALSE,
  use_qq = FALSE,
  varnames = NULL,
  relnb = NULL,
  skpt_tt = FALSE,
  infovarnames
)

Arguments

x	A basic chance assignment (see bca).
y	A basic chance assignment (see bca).
mcores	Make use of multiple cores ("yes") or not ("no"). Default = "no".
use_ssnames	= TRUE to use ssnames instead of tt matrix to do the intersections. Default = FALSE
use_qq	= TRUE to use qq instead of tt matrix to do the intersections. Default = FALSE
varnames	A character string to name the resulting variable. named "z" if omitted.
relnb	Identification number of the relation. Can be omitted.
skpt_tt	Skip reconstruction of tt matrix. Default = FALSE.
infovarnames	Deprecated. Old name for varnames.

Details

The calculations make use of multiple cores available.

The two bca's x and y must be defined on the same frame of discernment for the combination to take place. The relation number of the x input is given to the output result.

Value

A basic chance assignment with these two components added:

• I12 Intersection table of subsets.

• Sort_order Sort order of subsets.

Author(s)

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

y1 <- bca(tt = 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"),  
varnames = "x", idvar = 1) 
y2 <- bca(tt = matrix(c(1,0,0,1,1,1),nrow = 2, 
byrow = TRUE), m = c(0.6, 0.4),  
cnames = c("a", "b", "c"),  
varnames = "x", idvar = 1)
dsrwon(y1,y2)
# Sparse matrices
y1s <- y1
y2s <- y2
y1s$tt <- methods::as(y1$tt, "RsparseMatrix")
y2s$tt <- methods::as(y2$tt, "RsparseMatrix")
y1y2s <- dsrwon(y1s, y2s, use_ssnames = TRUE)

# using commonalities
bma <- bca(tt=matrix(c(1,1,0,1,rep(1,4)), ncol = 4, byrow = TRUE), 
m = c(0.1, 0.9), cnames = c("a", "b", "c", "d"))
bma2 <- dsrwon(bma, bma, use_qq = TRUE)

vacuous <- bca(matrix(c(1,1,1), nrow = 1), m = 1, cnames = c("a","b","c"))
dsrwon(vacuous, vacuous)

dst documentation built on Sept. 11, 2024, 7:05 p.m.