dst (version 1.3.0)

bcaRel: Representation of a mass function in a product space

Description

This function is used to represent a mass function which establish a relation between two or more variables in their product space.

Usage

bcaRel(tt, spec, infovar, infovarnames = NULL, relnb = NULL)

Arguments

tt

A (0,1)-matrix or a boolean matrix establishing the relation between two or more variables. The matrix is constructed by placing the variables side by side, as in a truth table representation.

spec

A two-column matrix. First column: numbers given to the subsets. Second column: the mass values of the subsets. A subset number and its associated mass value are repeated to match the number of elements of the subset.

infovar

A two column matrix containing variable identification numbers and the number of elements of each variable. The identification numbers must be ordered in increasing number.

infovarnames

The names of the variables. If omitted, variables are named v1, v2, etc.

relnb

A number given to the relation. Set at 0 if omitted.

Value

An object of class bcaspec. This is a list containing the following components:

• con The measure of conflict.

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

• spec The resulting two-column matrix of specification numbers with associated mass values.

• infovar The two-column matrix of variables number and size given in the input data.

• infovaluenames A list of the names of the variables with the name of the elements of their frame of discernment.

• inforel A two-column matrix containing the relation number and the depth (number of variables) of the relation.

Examples

# NOT RUN {
# A logical implication rule
# A typical relation between two variables in the context of expert systems is the
# logical implication \code{(a -> b)}. Let us suppose
# that \code{a} stands for \code{Rain: {yes, no}} and \code{b} stands for
# \code{RoadWorks: {yes, no}}. From experience,
# I am 75 % sure that there will be RoadWorks if there is no rain.
## 1. The tt table of the logical implication
 ttrwf <- matrix(c(0,1,1,0,1,0,1,0,1,0,0,1,1,1,1,1),
 nrow=4, byrow = TRUE, 
 dimnames = list(NULL, c("rWdy", "rWdn", "Ry", "Rn")) )
 ## The mass distribution
 specrw <-  matrix(c(1,1,1,2,0.75,0.75,0.75,0.25), ncol = 2, 
 dimnames = list(NULL, c("specnb", "mass"))) 
 ## Variables numbers and sizes
 inforw <- matrix(c(4,5,2,2), ncol = 2, 
 dimnames = list(NULL, c("varnb", "size")) )
bcaRel(tt = ttrwf, spec = specrw, infovar = inforw,
 infovarnames = c("RdWorks", "Rain"), relnb = 6)
 
# }