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1. base on (active 主動) 基於; 根據

-Climatologists always base their predictions about climate change on computer simulations.

There is no such phrase as “on the base of” or “basing on”.

另外，沒有“on the base of” 或是“basing on”這種用法。

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3. on the basis of 以……的基礎

-On the basis of the documentation you sent us, we believe your claim is true.

Difference between “based on" and “on the basis of":

“based on" modifies a noun
“on the basis of" modifies a verb

Something can be based on something else–that is, “based on" is adjectival; it modifies a noun:

-Discrimination (n.) based on disability (adjectival phrase) is illegal as well as unjust.

-These guidelines (n.) are based on our experience (adjectival phrase).

-The movie (n.) is based on a novel (adjectival phrase).

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In contrast, we do something on the basis of something else–that is, “on the basis of" is adverbial; it modifies a verb:

-He was denied permission (verb phrase) on the basis of his criminal record (adverbial phrase).

-Rates are adjusted annually (verb phrase) on the basis of the market index (adverbial phrase).

-They have been ranked (verb phrase) on the basis of their performance (adverbial phrase).

Mini Quiz:
Fill in the blanks with “based on," “base on," or “on the basis of."

1. He was hired __________ his experience.
2. The plan was decided __________ our budget.
3. Stop discrimination __________ sex.
4. He always __________ his opinions on facts.

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Sources:
http://news.koolearn.com/bec/20120411/625177.html
http://forum.wordreference.com/showthread.php?t=2496023
http://www.englishforums.com/English/BasedOnOnTheBasisOf/wgrqv/post.htm
http://www.thefreedictionary.com/basis
http://oald8.oxfordlearnersdictionaries.com/dictionary/base_2