I don't really know where to ask this one... In fact, I am not sure I can define it properly.
Here goes...
Let's say I take measurements.
In order to "normalize" these measurements, I divide their values by a reference measurement.
So, if my reference measurement has value 100
, and one measurement has value 150
, I rescale it as follows: 150 / 100 = 1.5
. That particular measurement's value is 1.5
time the reference value.
So far, trivial.
Now, time for a picture:
The triangles are measurement values. A
and B
are reference values.
The domain the measurements are taken in indicates that the closer a measurement value is to A
, the more A
should be the reference value to rescale it. Similarly, the closer a measurement value is to B
, the more B should be the reference value to rescale it.
So, values 1
and 2
should be restated in terms of A
, while values 4
and 5
should be restated in terms of B
.
But, in general, all values should probably be restated in function of A
and B
. This is particular true for value 3
in the picture, as it is almost equidistant from A
and B
.
In other words, there must be a function f(x){A, B}
, that will allow to order all measurements.
What do you call that type of problem? Any reference or pointer I could use to restate what I mean?
--
Update 1:
Here is a metaphor that just came to me... Let's say I must define a scale that measure the total cost of moving an object at a certain speed.
A
and B
become two reference "cost per unit of speed"s. For speeds close to B
, the total cost can be accurately estimated in terms of B
. For speeds close to A
, the total cost can be accurately estimated in terms of A
.
For speeds in between A
and B
, the total cost must be a function of A
and B
.
The farther away a speed is from A
/B
, the less A
/B
is a factor in the cost of moving the object at that speed.