bca: Basic chance assignment mass function

In dst: Using the Theory of Belief Functions

Basic chance assignment mass function

Description

Function bca is used to define subsets of a finite set \Theta of possible values and to assign their corresponding mass value.
The set \Theta is called the frame of discernment. Each subset A of Theta with a positive mass value is called a focal element or a proposition. The associated mass value is a number of the (0,1] interval, called "basic chance assignment" (the basic probability assignment of Shafer's book). All other subsets that have not received a positive mass value are assumed to have a mass value of zero.

Usage

bca(
  tt,
  m,
  cnames = NULL,
  con = NULL,
  idvar = NULL,
  infovar = NULL,
  varnames = NULL,
  valuenames = NULL,
  inforel = NULL,
  f,
  varnb,
  infovarnames
)

Arguments

tt	A (0,1)-matrix or a boolean matrix. The number of columns must match the number of elements (values) of the frame of discernment \Theta. Each row is a subset of \Theta. The last row is the frame \Theta, represented by a vector of 1's.
m	A numeric vector of length equal to the number of rows of the matrix tt. Values of m must lie in the interval (0,1] and must add to one. The mass m(k) represents the chance value allotted to the proposition represented by the row k of the matrix tt.
cnames	A character vector containing the names of the elements of the frame of discernment \Theta. The length must be equal to the number of elements of \Theta. The names are first searched in the valuenames parameter. If NULL, column names of the matrix tt are taken if present. Otherwise, names are generated.
con	The measure of conflict can be provided. 0 by default.
idvar	The number given to the variable. A number is necessary to manage relations between variables and make computations on a graph. 0 if omitted.
infovar	A two-column matrix containing variable identification numbers and the number of elements of the variable. Generated if omitted.
varnames	The name of the variable. Generated if omitted.
valuenames	A list of the names of the variables with the name of the elements of their frame of discernment.
inforel	Not used here. Defined within function bcaRel.
f	Deprecated. Old name for tt matrix.
varnb	Deprecated. Old name for idvar.
infovarnames	Deprecated. Old name for varnames.

Value

y An object of class bcaspec called a bca for "basic chance assignment":

• tt The table of focal elements. Rownames of the matrix of focal elements are generated from the column names of the elements of the frame. See nameRows for details.

• spec A two column matrix. First column contains numbers given to the subsets, 1 to nrow(tt). Second column contains the mass values of the subsets.

• con The measure of conflict.

• infovar The number of the variable and the size of the frame of discernment.

• varnames The name of the variable.

• valuenames A list of length 1 consisting of the name of the variable with the names of the elements of the frame of discernment (the column names of the tt matrix).

• inforel Set at 0. used in function bcaRel.

Author(s)

Claude Boivin

References

• Shafer, G., (1976). A Mathematical Theory of Evidence. Princeton University Press, Princeton, New Jersey, p. 38: Basic probability assignment.

• Guan, J. W. and Bell, D. A., (1991). Evidence Theory and its Applications. Elsevier Science Publishing company inc., New York, N.Y., p. 29: Mass functions and belief functions

Examples

tt<- t(matrix(c(1,0,1,1),ncol = 2))
m<- c(.9,.1)
cnames <- c("yes","no")
bca(tt, m)
bca(tt, m, cnames)
bca(tt, m, cnames, idvar = 1)
tt1<- t(matrix(c(1,0,1,1),ncol = 2))
colnames(tt1) <- c("yes", "no")
m <- c(.9, .1)
bca(tt=tt1, m, idvar = 1)
x <- 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"), idvar = 1)
y <- 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 = "y", idvar = 1)
vacuous <- bca(matrix(c(1,1,1), nrow = 1), m = 1, cnames = c("a","b","c"))

dst documentation built on Nov. 16, 2023, 5:08 p.m.