DST: Combination rules

In ibelief: Belief Function Implementation

Description

Different rules to combine masses

Usage

DST(MassIn, criterion, TypeSSF = 0)

Arguments

MassIn	The matrix containing the masses. Each column represents a piece of mass.
criterion	The combination criterion: criterion=1 Smets criterion (conjunctive combination rule) criterion=2 Dempster-Shafer criterion (normalized) criterion=3 Yager criterion criterion=4 Disjunctive combination criterion criterion=5 Dubois criterion (normalized and disjunctive combination) criterion=6 Dubois and Prade criterion (mixt combination), only for Bayesian masses whose focal elements are singletons criterion=7 Florea criterion criterion=8 PCR6 criterion=9 Cautious Denoeux Min for functions non-dogmatics criterion=10 Cautious Denoeux Max for separable masses criterion=11 Hard Denoeux for functions sub-normal criterion=12 Mean of the bbas criterion=13 LNS rule, for separable masses criterion=131 LNSa rule, for separable masses
TypeSSF	The parameter of LNS rule (criterion = 13) and LNSa rule (criterion = 131). If TypeSSF = 0, it is not a SSF, the general case. If TypeSSF = 1, a SSF with a singleton as a focal element. If TypeSSF = 2, a SSF with any subset of Θ as a focal element.

Value

The combined mass vector. One column.

Examples

m1=c(0,0.4, 0.1, 0.2, 0.2, 0, 0, 0.1);
m2=c(0,0.2, 0.3, 0.1, 0.1, 0, 0.2, 0.1);
m3=c(0.1,0.2, 0, 0.1, 0.1, 0.1, 0, 0.3);

m3d=discounting(m3,0.95);

M_comb_Smets=DST(cbind(m1,m2,m3d),1);
M_comb_Smets
M_comb_PCR6=DST(cbind(m1,m2),8);
M_comb_PCR6
M_comb_LNS = DST(cbind(m1,m2),13);
M_comb_LNS 
M_comb_LNSa = DST(cbind(m1,m2),131);
M_comb_LNSa 

n1 = 5
ThetaSize = 3
mass_mat = matrix(0, 2^ThetaSize, n1 + 1);
mass_mat[2, 1 : n1] = c(0.12, 0.16, 0.15, 0.11, 0.14) 
mass_mat[3, n1 + 1] = 0.95;
mass_mat[8, ] = 1 - colSums(mass_mat)
mass_ssf_mat = mass_mat[c(2^(1:ThetaSize-1)+1, 8), ]
# the following three functions could produce the same results
DST(mass_mat, 13)
DST(mass_mat, 13, TypeSSF = 2)
DST(mass_ssf_mat, 13, TypeSSF = 1)

ibelief documentation built on Jan. 7, 2021, 9:07 a.m.