A morpheme is the smallest meaningful unit of a language. It the morpheme can stand by itself, it's considered a root, and is also a free morpheme. Bound morphemes have to be attached to a word, so your affixes in English are bound morphemes.
The root(base) of authorization would be author. The suffix -ize makes it a verb. The suffix -tion makes a noun out of the verb authorize, but changes the meaning from the original base noun. (Those are also known as derivational morphemes)
Ergo, three morphemes - a root/base of 'author' plus two suffixes.
While authorize is a word, it still consists of two morphemes, so it can't be the base for authorization as it can still be broken further down into meaningful units.
Also - cross posted on this forum where you got the same answer I gave you. Cross posting wastes our time. Please at least state that you're cross posting, or indicate why you're unsatisfied or are questioning the answers you got elsewhere.