You say "discretize" when you make a continuous number a number of discrete steps. Now I am looking at it the other way round.
I am looking for the mathemetical word that explains how I change an integer ordinal scale to ordinal scale or interval scale of decimal (1.) or continuous (2.) values.
For example, inventing some words here:
decimal:
decimalize (decimal number, limited after the comma)
This would fit perhaps if I just add more discrete steps (that is, allowing a 4.1 instead of a 4 as well, but not a 4.1234 to infinite steps after the comma).
continuous:
- continuize
- realize (to real number),
- floatize (to floating number)
I would like to say one word for the change from integers in a questionnaire into proper interval data, which is done by the Item Response Model (latent trait measurement), see How to transform ordinal data from questionnaire into proper interval data?. It might also fit to the second answer there, linking to Using ridits to assign scores to categories of ordinal scales.
For example, you have a questionnaire which has only 1 to 5 in discrete integer steps.
How would you call it, if it has to become discrete in decimals:
1, 1.1, 1.2 ... 4.9, 5
How would you call it if it has to become continuous:
1, 1.0x, 1.1x ... 4.9x, 5
with x being further numbers, up to infinite length.