[adjective] / [verb] + 性
[noun] + 性 + 的 + [noun]
性 after a word makes an abstract noun for a quality: 重要 "important" becomes 重要性 "importance". It works like English "-ness" and "-ity", and belongs to written and formal Chinese.
The noun that has the quality comes first, with 的: 这个问题的复杂性 "the complexity of this problem". The 性 noun then works with verbs such as 有, 提高, 增加, 认识到.
With 的, a 性 word can also describe a noun, saying what type or scale it is: 全国性的比赛 "a nationwide competition", 暂时性的问题 "a temporary problem".
A 性 word is a noun. It doesn't take 很 directly the way the plain adjective does.
性 doesn't attach to just any adjective: there is no 漂亮性 or 高兴性. The common ones are a fixed list worth learning as words – 重要性, 可能性, 必要性, 安全性, 积极性, 复杂性.