Information and Knowledge Representation in Fusion Problems - Information Fusion in Signal and Image Processing - page 55

1) a first attitude consists of eliminating imperfections as best as possible. This
involves, for example, improving sensors and increasing the number of acquisitions;
2) a second possible action is to tolerate the imprecision by producing robust algo-
rithms and programs, and by combining them with procedures for repairing failures;
3) the third possibility is to try to reason with the imperfection. In this case, it is
considered as a type of knowledge or information and taking it into account requires
modeling it, developing approximate modes of thought, and using meta-knowledge,
i.e. knowledge about these imperfections.
In this topic, we will prefer the third approach, which explicitly involves tech-
niques of information fusion and decision making.
5.3. Numerical representations of imperfect knowledge
The major numerical theories that allow us to represent imperfect knowledge and
to use them as the basis for our approach are:
- probabilities (Chapter 6);
- belief functions (Chapter 7);
- fuzzy sets and possibilities (Chapter 8).
In probabilistic representations, language is comprised of probability distributions
in a frame of reference. They allow us to rigorously take into account random or
stochastic uncertainties. It is more difficult to take into account other forms of imper-
fections, both formally and semantically. Bayesian inference, often used in fusion in
the subjects we are concerned with, serves as the basis for abductive reasoning (the
different types of inferences are presented in section 5.6).
Belief function theory (or the Dempster-Shafer theory [SHA 76]) relies on a lan-
guage defined by functions (referred to, in this context, as mass, belief and plausibility
functions) over every subset of the frame of discernment. Using representations, we
can take into account at the same time imprecision and uncertainty (including its sub-
jective form), ignorance, incompleteness and have access to conflict. Inference based
on Dempster's rule achieves conjunctive aggregation of the combined information.
In fuzzy set and possibility theories [DUB 80, DUB 88, ZAD 65, ZAD 78], lan-
guage is comprised of fuzzy subsets of the frame of reference or possibility distri-
butions over the frame of reference. It allows us to represent qualitative, imprecise,
vague information. Inference is done according to logical rules (or their equivalent in
numerical form), essentially by deductive reasoning that may be qualitative.
We will discuss these three theories again in detail in the following chapters, but
for the moment, this is what matters: