It is not safe, unless you make conventions or assumptions. The wikipedia entry for Discrete-time signal says:
A discrete signal or discrete-time signal is a time series consisting
of a sequence of quantities. In other words, it is a time series that
is a function over a domain of integers[...] the sampling rate is not
apparent in the data sequence
So first, integer indices do not imply your signal is regularly sampled. Indeed, one can distinguish two main origins:
- the sampling (possibly irregular, lacunary) of a continuous time signal
- the capture of a discrete-time process.
In the first case, without a signal model, or a sampling pattern, there a possibly infinitely many continuous signals passing through your discrete points. More precisely, you can get $s(t) = \sum_n s[n]\psi(t-t_n)$ with specific assumptions, where $t_n$ is the sampling time, and $\psi$ a specific kernel (for instance, a cardinal sine). In the second case, there are zero solutions, as nothing makes sense in the interval.
So when the set of options is either infinite or void, one can define a convention, as long as it is useful and is not contradictory with your system.
In addition to other answers, let me mention a practical cases where fractional indices are indeed useful, at the border of the two above origins.
Construct the downsampled signal $x[n]$ (by a factor of 4 here) of a regularly sampled signal $y[n]$. For instance, one writes $x[n] = y[4n]$, somehow reindexing $x$. I would not be offended to see $x[3/4] = y$ as a shorthand with obvious meaning (such improper notations sometimes appear in the filter bank literature). This is a case of two sampling systems, one being the "multiple" of the other.
I have encountered a similar situation in real-time system modeling. Some models communicate at a base rate $r$, while submodels update at a faster rate, e.g. $4r$. Here, some people index data at the communication rate $x[n]$, because it is the most natural, and index the submodel signal at rationals $y[n/4]$ without ambiguity.
The last question is: why do you want or need to define your $x[3/4]$ sample?