Limiting the range of numbers Suppose that I have the following data set: 
{0.1, 0.2, 0.5, -0.1, 0.5, 1.1, 0.8}

I would like to limit the range of these data to be within the range of [0,1].
So the new vector is:
{0.1, 0.2, 0.5, 0, 0.5, 1, 0.8}

Note that the 4th and 6th elements are changed.
Is there a term for such a transaction?
'Winsorization' and 'truncation' came across my mind, but winsorizing use percentiles as lower and upper limit and truncation (in survival analysis context) should remove the outlying elements.
 A: This might either be called censoring or Winsorizing. 
While the term Winsorizing is usually used when values are taken to specific quantiles, like truncation/trimming it wouldn't necessarily have to be to quantiles - the name could reasonably be applied to censoring to specific values, as long as you made it clear what you were doing.
So I'd suggest either "censored to the unit interval" or perhaps "Winsorized to the unit interval".
A: I would say that you are applying a 'hard' threshold for your upper and lower bound. The word 'hard' refers to the fact that any relative magnitude between two value above the threshold is discarded after applying the threshold. 
This is opposed to 'soft' thresholding in which this distance would be preserved. In your case soft thresholding would just be normalising between 0 and 1. 
This term is often used in wavelet de-noising applications, so hence it may sound unfamiliar with you, but the concept is the same. 
A: As you said, 'truncation' could be misleading: it may refer to the limitation of the number's precision or the removal of extreme values. 
I propose 'saturation', often used in signal and image processing. At the output of an electronic device, it 'imposes upper and lower limits on an input signal'.
The term, for instance used in chemistry, has diverse meanings, based on 'reaching a maximum capacity'. It has a Latin origin, saturare, meaning 'to fill full'.
