On Roles of Models in Information Systems - Intentional Perspectives on Information Systems Engineering - page 32

instance involves one man and one woman, but there is also a corresponding class
concept of “MARRIAGE”, seen as a legal entity. In mathematics, the concept of
relation is not a primitive concept along with set and member, but is defined in
terms of notions already available in set theory for defining set and set-membership.
This is done in order to keep the number of irreducible concepts in set theory to a
minimum [33] .

4.3 Data Concepts

From a conceptual point of view there is no difference, in principle, between binary
numbers and other referents. Binary numbers may be abstracted in class concepts
and related by relation concepts as may every other collection of referents mak-
ing up this Universe of Discourse. Computers deal directly with their referents (the
data), and it becomes important to distinguish between a concept and its extension.
Important concepts for data modeling are:

• data item: the specific individual linguistic concept, the term, the value;

• data record: a structured data item composed from other data items;

• variable: the generic individual linguistic concept;

• data type: a linguistic class concept, in programming languages usually called

“type”;

• data set: a set of data items, each data item being different from the others in the

set;

• data collection: a collection of data items which need not be different;

• data base: a collection of data collections.

The names given to data types may used to distinguish among quantitative con-
cepts and how they relate to other UoD concepts. Quantitative concepts are general
in the sense that they apply to large numbers of referents, e.g., every physical body
has a weight and a temperature. A generalization of the definition in the previ-
ous section provides us with the definition of a quantitative concept as a function
q:UoD D, where UoD is the set of referents, S is the set of scales, D is the

set of linguistic units (the possible values), and consequently the set of quantitative
concepts is Q

× S →

= | × →

D}.
Assume that we want to define three data sets, one to contain the weight values of
Norwegians, one for Americans and one for the British. Assume further that weight
is measured on the metric scale, but in units of kilograms with two decimals preci-
sion for Norwegians, in pounds with one decimals precision for Americans, and in
stones with three decimals precision for the British. The corresponding (informal)
definitions may look like

{q q:UoD S

W: American x (scale lbs 1 decimal) → WA l b s 1

W: British x (scale stone 3 decimals) → WBstone3

W: Norwegian x (scale kg 2 decimals) → WNkg2