How to define a MultidimensionalScale?

25 Feb. 2011, rev. 19 March 2011

Introduction

In ISO 15926-5 you can find two rather esoteric entity types, the ClassOfMultidimensionalObject and the MultidimensionalObject. These are discussed in a separate topic. In this topic I'll try to give an explanation of one of the derivatives, the MultidimensionalScale.

Part 2 defines:

A MultidimensionalScale is a Scale that is also a MultidimensionalObject.

EXAMPLE A [Celsius, seconds] scale is a MultidimensionalScale on which temperature variation over time can be plotted.

EXPRESS specification:

ENTITY multidimensional_scale  

    SUBTYPE OF (scale, multidimensional_object);  

END_ENTITY;

Discussion

Let's use the (adapted) diagram below as reference:

The adaptation, whereby the non-applicable attributes are being left out, shows that the esoteric character disappears. For details see here.

Let us first focus on the ClassOfMultidimensionalObject, attribute by attribute.

"roles" attribute

The rdf:object of this attribute is a set of instances of RoleAndDomain that indicate what the role actually is and what subtype of Thing is the object. If the multidimensional object is the input in a function (so a ClassOfFunctional Mapping), then each role is the same as its parameter name in that function.

"cardinalities" attribute

If any of the Roles could exist 0, 1, or more times for an instance of MultidimensionalObject, then that shall be expressed by a list of instances of Cardinality. If one or more such cardinalities apply, all cardinalities shall be defined. (no example comes to my mind)

and then of the MultidimensionalProperty:

"elements" attribute

Here the 1:? multidimensional properties that are part of the multidimensional property space, where that cardinality is determined by the "cardinalities" attribute of the classifying ClassOfMultidimensionalObject.

Example

Let us now focus on the MultidimensionalScale, that classifies the PropertyQuantification relationship between the multidimensional property MDP-9877 and the multidimensional number MDNR-3040 :

Q-H point quantified against a multidimensional scale

In template format this looks like this: