Value

(1) In the technical vernacular, a value is the exact amount of some particular property, usually represented as a number.

 

(2) As generally used herein, a value is a non-empty set of points in a space associated with a topical parameter.  This notion arises because exact amounts are rarely encountered outside of theoretical constructs1.  Most exact usages are accompanied by an adjective.  “Nominal value”, “maximum value”, “expected value” and “average value” are examples of that general practice.  This website follows that approach: when an exact value is intended, it will be usually be encountered with an appropriate modifier2.  In some cases, that modifier is the word “exact”, just to make things clear.

The set may be interchangeably expressed in either of two ways:

(a) Explicitly, by directly expressing the set as shown in Table 1 .  The explicit form is the conventional, familiar method for showing values.  Many forms of set expression exist (e.g., enumeration, set builder notation).

Table 1: Value Data Elements (Explicit)
Element Name Description
*Parameter Pointer to the topical parameter being evaluated.
Set Points in the space defined by the parameter
Units Alternatively, can be a pointer to standardized units.  Must match the order of the parameter.  Significant NULL is admissible for certain applications (e.g., pointers and other types of discretely enumerated lists).

(b) Implicitly, by expressing the criteria for selection of such points as shown in Table 2, which explicitly3 relies on measures as they are defined herein.

Table 2: Value Data Elements (Implicit)
Element Name Description
*Measure Output Pointer to the measure output used to evaluate the subject parameter
Units Alternatively, can be a pointer to standardized units.  Must match the order of the parameter.  Significant NULL is admissible for certain applications (e.g., pointers and other types of discretely enumerated lists).

Note that the units might have to be recovered from the measure’s algorithm.
Input Argument Values An array of input values to the subject measure which, when the measure’s algorithm is executed, will generate an explicit value.

The implicit structure is mostly frequently encountered when dealing with stochastic variables, where the idea of “value” exists as sort of a probability cloud4.  A unifying concept, it facilitates substitution of “result” in place of “function call” in a manner analogous to that of a compile/link sequence, bearing in mind that linking can be deferred to run-time.  It is worth noting that tolerances and uncertainties are always stochastic, even though many analyses deal with limit cases only.

Aside

It should be clear that Tables 1 and 2 are not relationally normalized.  It is possible that, in the present context5, they cannot be usefully normalized without definitive6 specification of “dimensions”.

See also Upon Evaluation, and Topical Parameterization, Part III: Measures.

Footnotes
  1.   e.g., gains and filter values in a control loop[↩]
  2.   And when it isn’t, I screwed up.[↩]
  3.   See what I did, there?[↩]
  4.   At least, until we open the box.[↩]
  5. of topics, parameters, and measures[↩]
  6. possibly project-specific[↩]