Definitions - Information Fusion in Signal and Image Processing - page 7

1.4. Numerical/symbolic
There has been a great deal of discussion in the fusion community regarding the
duality between numerical and symbolic fusion. The objective in this section is not
to go over the details of these discussions, but rather to present the different levels on
which this question can be expressed. By cleverly describing these levels, it is often
possible to silence these debates. The three levels we will distinguish here involve the
type of data, the type of process applied to the data and the role of representations.
They are discussed in detail in the following sections.
1.4.1. Data and information
By numerical information, we mean information that is directly given in the form
of numbers. These numbers can represent physical measurements, gray levels in an
image, the intensity of a signal, the distance given by a range-finder, or the response
to a numerical processing operator. They can be either directly read inside the data we
wish to fuse or attached to the field or the contextual knowledge.
By symbolic information, we mean any information given in the form of symbols,
propositions, rules, etc. Such information can either be attached to the elements of
information we wish to fuse or to knowledge of the field (for example, proposals on
the properties of the field involved, structural information, general rules regarding the
observed phenomenon, etc.).
The classification of information and data as numerical or symbolic cannot always
be achieved in a binary way, since information can also be hybrid, and numbers can
represent the coding of information of non-numerical nature. This is typically the case
when evaluating data or a process, or when quantifying imprecision or uncertainty. In
such cases, the absolute values of the numbers are often of little importance and what
mostly counts is where they lie on a scale, or the order they are in if several quantities
are evaluated. The term “hybrid” then refers to numbers used as symbols to represent
an element of information, but with a quantization, which makes it possible to han-
dle them numerically. These numbers can be used for symbolic as well as numerical
information.
1.4.2. Processes
In the context of information processing, a numerical process refers to any calcu-
lation conducted with numbers. In information fusion, this covers all of the methods
that combine numbers using formal calculations. It is important to note that this type
of process does not necessarily formulate any hypotheses regarding the type of infor-
mation represented by numbers. At the beginning, information can be either numerical
or symbolic in nature.