# DST: Combination rules In ibelief: Belief Function Implementation

## Description

Different rules to combine masses

## Usage

 `1` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```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.