dst (version 1.8.0)

extmin: Extension of a relation

Description

This function works on a basic chance assignment (bca) x defined on a single variable or more. A relation of reference is given, and an extension of the space of x is made to the larger product space of the relation of reference. The basic chance assignment to extend and the relation of reference must have at least one common variable for the extension to occur.

Usage

extmin(rel1, relRef)

Value

the resulting extended bca.

Arguments

rel1

An object of class bcaspec, i.e. a basic chance assignment defined on 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.

Author

Claude Boivin

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 be a relation already existing or simply the the vacuous relation defined on the product set of variables of interest.

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

# Making a vacuous reference relation 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, 
  varnames = c("Sail", "Loading", "Weather", "Repairs"),
  relnb = 0)
 # a bcaspec defined on one variable
 l_rel <- bca(tt = 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"))), 
 varnames = 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)))