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The phrase "a system that assigns" is correct and usable in written English.
You can use it when describing a mechanism or process that designates or allocates something, such as roles, tasks, or values.
Example: "The software implements a system that assigns tasks based on employee skill levels and availability."
Alternatives: "a mechanism that allocates" or "a framework that designates".
Exact(10)
Mr. Roth has also helped build a system that assigns kidney donation swaps.
But they weren't thinking about it the way a real-estate agent might; rather, they wanted to comment on a system that assigns a dollar amount to a slice of sea and sky.
Shienmar's organization, a nonprofit called the Mapcode Foundation, has designed a system that assigns a unique and easily remembered address to any spot on the planet, without reference to landmarks or street names.
He traffics in hard numbers, overseeing a system that assigns grades to schools based on complex and fixed formulas, in which success depends largely on how students score on a single test.
These ballots are returned to Pricewaterhouse, where each category is counted by a team of two accountants using a system that assigns more weight to first-place votes than to second-place votes, more to second than to third, and so on.
The European proposal would need the backing of a so-called qualified majority of member states to become law, a system that assigns greater voting weight to larger countries like Germany, which is said to be reluctant to back the measure.
Similar(50)
In particular, the likelihood of biochemical reactions in cellular metabolisms can be assessed in terms of a scoring system that assigns a probability of occurrence to every reaction.
New Mexico uses a classification system that assigns each inmate a number from one to six, with six being reserved for the most violent offenders; Western has inmates of all levels up to five.
A gastrointestinal pathologist assessed haematoxylin and eosin-stained ESMG images by using a scoring system that assigns individual ESMG acini to five histological types (mucous, serous, oncocytic, dilated, or ductal metaplastic).
The American Standard Code for Information Interchange, or Ascii (pronounced ASK-ee), is a coding system that assigns numbers to English-language characters.
A moratorium provision grants towns a four-year reprieve if they can document progress toward the 10 percent threshold, as calculated through a point system that assigns varying values to different housing types.
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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