For most adjectives, a basic ground form to derive the rest in a paradigm seems to be that of Masculine Singular and they therefore can be divided into -ый, -ой and -ий-types.
Historically and stylistically, the shortened adjectives seem to be more archaic and related to a higher / poetic style. This comprises both relative and qualitative adjectives (although not possessive ones), even the adjectives of -ой-type (though these seem to be less productive).
[The shortened forms of adjectives (especially those derived from relative 'ancestors') are then usually to be post-positioned, but now I deliberately skip this nuance for the sake of the completeness].
зéлено яблоко <=> зелёное яблоко (зелёный)
(?) сóлев холм <=> солевой холм*
(?) челюстнен скат <=> челюстной скат (= контур)
рдян ог(о)нь <=> рдяной огонь
синий кит < = > ????
I am not mentioning here the archaic and poetic combined formes, such as зелено-яблоко and рдян-огнь, because the usage of - in Russian since, say, the 17th century seems to be the other topic.
Syntaxically, the shortened forms mostly convey a meaning of perfective utterance:
Яблоко зелено. Пол стеклянен. Огонь багрян.
But what about the shortened adjectives of the -ий-types? They seem to be non-productive, but is it a later development?
For some adjectives (mainly relative) the shortened forms are imaginable, eg. мужний, братний, весенний, зимний can be imagined as *мужен, *братнен, *весенен and *зимнен (at least, as elements of compound words).
But what about the shortened forms of relative adjectives ending in -ний? Some are imaginable (e.g. those derived from давний, давнишний, давешний, вышний, внешний) but the others are not.
To mention a few;