i think bodzan pointed out the key thing here.
a radio group allows only 1 thing to be selected. because of this, there is no need to pass the selected value as an array to php anyway, because its always going to be a single value. in html, you can only select a single option from a radio group.
if you want multiple selections possible, use checkboxes like weedpacket showed you.
i think your trying to use the wrong html tool to get the job done.
once you name the radio group like so:
<input type="radio" name="history">
<input type="radio" name="history">
<input type="radio" name="history">
then validating w/ js will be simple just like validating other form fields. just check if history has been selected or has a value etc...theres no need to check each of them, because they are the same in a sense, just different values.
if you ever did need to pass an array to php without using [] in the form names, it can still be done. access the post data via $http_raw_post_data and parse it yourself.