dst (version 1.3.0)

extmin: Extension of a relation

Description

This function works on a mass function defined on a single variable or a relation defined onto a group of two variables or more. An extension of their space is made to a larger product space of a relation of reference. The mass function or relation to extend and the relation of reference must have at least one common variable for the extension to be made possible.

Usage

extmin(rel1, relRef)

Arguments

rel1

An object of class bcaspec, i.e. a mass function of one variable or a relation.

relRef

The relation of reference. It can be an existing relation, or it can be constructed as a vacuous function.

Value

R the resulting extended relation.

Details

The relRef parameter is used to extract all the information on the variables, namely their identification numbers and the number of elements of each variable, variables names and columns names of the tt matrix. The relation of reference relRef may simply be an empty relation defined on the set of variables of interest or a relation already defined.

References

G. Shafer and P. P. Shenoy. Local Computations in Hypertrees. School of Business, University of Kansas, Lawrence, KS, 1991. See p. 78, vacuous extension of a belief function.

Examples

# NOT RUN {
# Naking an empty reference relation with mass(frame) = 1 and
# extending a bca to its space.
init_tt= matrix(rep(1,10),nrow=1, 
dimnames =list(NULL, c("3", "2", "1", "0", 
 "true", "false",  "foul", "fair",  "true", "false")) )
 init_spec <- matrix(c(1,1), ncol = 2, 
 dimnames = list(NULL, c("specnb", "mass")))
 init_info <- matrix(c(3,4,7,8,4,2,2,2), ncol = 2,
  dimnames = list(NULL, c("varnb", "size")) )
 relRef <- bcaRel(tt = init_tt, spec = init_spec,
  infovar = init_info, 
  infovarnames = c("Sail", "Loading", "Weather", "Repairs"),
  relnb = 0)
 # a bcaspec defined on one variable
 l_rel <- bca(f=matrix(c(1,0,1,0,1,1), ncol=2), 
 m=c(0.3,0.5,0.2), cnames=c("true", "false"), 
 infovar=matrix(c(4,2), ncol = 2, 
 dimnames = list(NULL, c("varnb", "size"))), 
 infovarnames= c("Loading"), 
 inforel= matrix(c(7,1), ncol = 2, 
 dimnames = list(NULL, c("relnb", "depth"))))
 z <- extmin(l_rel, relRef)
 prmatrix(t(z$tt), collab = rep("", nrow(z$tt)))
 
# }