lorenzgillner / UncertainEvidence.jl

Epistemic uncertainty handling in the Dempster-Shafer framework

UncertainEvidence.jl

This package provides methods for handling epistemic uncertainty, primarily implementing the Dempster-Shafer Theory of Evidence (DST). It is, to some extend, a port of the IPP toolbox to the Julia language.

This package is still in an early development phase, but the basic principles of the Dempster-Shafer framework are already present.

Usage

Let's consider a simple introductory example. Two experts, $X_1$ and $X_2$, state their opinions on the possible causes (focal elements; $A$, $B$ and $C$) of a situation. Using UncertainEvidence.jl,

using UncertainEvidence

these opinions can be formulated in the following way:

# expert one
X1 = BPA(
    'A' => 0.5,
    'B' => 0.3,
    'C' => 0.2
)

# expert two
X2 = BPA(
    'A' => 0.6,
    'B' => 0.1,
    'C' => 0.3
)

The basic probability assessment (BPA) is the fundamental data structure for computations. To generate a general assessment of the situation, BPAs can be combined with Dempster's rule of combination (more combination rules coming soon):

X12 = combine_dempster(X1, X2)

Based on this combined structure, the lower (belief) and upper bound (plausibility) of the likelihood of a cause can be queried:

# lower bound
bel('A', X12)

# upper bound
pls('A', X12)

The masses of a BPA should always sum up to 1. To ensure this, use the method bpa instead:

X = bpa(
    Set('A') => 0.1,
    Set('B') => 0.2,
    Set('C') => 0.3
)

# Dict{Set{Char}, Float64} with 4 entries:
#   Set(['C', 'A', 'B']) => 0.4
#   Set(['B'])           => 0.2
#   Set(['A'])           => 0.1
#   Set(['C'])           => 0.3

Note the use of Sets in this example; if the sum of masses is lower than 1, the remaining mass is automatically assigned to $\Omega$, the set of all focal elements. This would fail, if all other focal elements would be of type Char.