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"built on the basis" is correct and perfectly usable in written English.
You can use it to describe a situation that is established or constructed using a specific foundation or principle. For example, you might say, "This new government policy was built on the basis of fairness and equality."
Exact(59)
A Storm topology is built on the basis of the topology plan.
The team was built on the basis of one of the most successful British racing teams in the lower categories.
Our group has previously described neonatal seizure detectors that have been built on the basis of linear, quadratic and regularised discriminants (Greene et al., 2008a).
They also now that big achievements are built on the basis of very small ones attained on daily basis.
PID controllers being commonly used in buildings engineering, the proposed control scheme is built on the basis of a PID controller.
They were all built on the basis of a 60-year payback period.
Towns will be built on the basis of market research rather than architectural whimsy.
"Our society is built on the basis of property rights," she added.
The dynamic model is built on the basis of measurements from Inertial Measurement Unit.
The metal semiconductor diodes later built on the basis of this theory are called Schottky barrier diodes.
Similar(1)
However, the theory which has been built on the basis of these scattering experiments, QFT, turns out to have considerable problems to account for the observed 'particle trajectories'.
More suggestions(19)
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built on the success
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built on the assumption
built on the notion
built on the policy
built on the information
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com