Thanks @yadav-sachin.
To clarify, I think we should leave the text in and add the interval notation at the end.
I added it in the first line below.

        - `"left"`: only `min_val` is included in the valid interval;  [`min_val`, `max_val`)
        - `"right"`: only `max_val` is included in the valid interval;
        - `"both"`: `min_val` and `max_val` are included in the valid interval;
        - `"neither"`: neither `min_val` nor `max_val` are included in the
          valid interval.

Here's the preview:
https://166819-843222-gh.circle-artifacts.com/0/doc/modules/generated/sklearn.utils.check_scalar.html

It's ok. Though I think the addition of [min_val, max_val) washes out the parentheses interval. Not sure what the reviewers think. I would be happy with:

        - `"left"`: only `min_val` is included in the valid interval;  [ a, b )
        - `"right"`: only `max_val` is included in the valid interval;  ( a, b ]
        - `"both"`: `min_val` and `max_val` are included in the valid interval; [ a, a ]
        - `"neither"`: neither `min_val` nor `max_val` are included in the
          valid interval.  ( a, a )

LGTM. @reshamas do you want to have a look before that I merge it?

@glemaitre Can we remove the semicolons at the end of each bullet point? It's a little distracting, and I wouldn't want users to think semicolons are related to intervals.
Otherwise, it works.

@glemaitre Can we remove the semicolons at the end of each bullet point?

I always thought that it was the formal way to write a proper bullet list: https://english.stackexchange.com/a/15134
We can as well finish each sentence by a full stop in this case as well. It might be less confusing.

@glemaitre Ok, let's go with full stop at end.

Thanks @yadav-sachin @reshamas all good to go