dst (version 1.3.0)

bca: 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 of zero value.

Usage

bca(f, m, cnames = NULL, infovaluenames = NULL, con = NULL,
  varnb = NULL, infovar = NULL, infovarnames = NULL,
  inforel = NULL)

Arguments

f

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 vector of masses of length equal to the number of rows of the matrix f. The 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 f.

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 searched in the infovaluenames parameter first. If NULL, column names of the matrix f are taken if present. Otherwise, names are generated.

infovaluenames

Name and value names of the variable. See bcaRel.

con

The measure of conflict. 0 by default.

varnb

The number given to the variable. 0 if omitted.

infovar

A two-column matrix containing variable identification numbers and the number of elements of the variable. Generated if omitted.

infovarnames

The name of the variable. Generated if omitted.

inforel

Not used. Defined within function bcaRel.

Value

An object of class bcaspec:

• tt The table of focal elements f. 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: numbers given to the subsets, 1 to nrow(f). Second column: 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.

• infovaluenames The names of the elements of the frame of discernment of the variable (the column names of the tt matrix).

• inforel Set at 0. used in function bcaRel.

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

# NOT RUN {
f<- t(matrix(c(1,0,1,1),ncol=2))
m<- c(.9,.1)
cnames <- c("yes","no")
bca(f, m)
bca(f, m, cnames)
bca(f, m, cnames, varnb = 1)
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"), varnb = 1)
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)
frame <- bca(matrix(c(1,1,1), nrow=1), m=1, cnames = c("a","b","c"))
# }