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The phrase "not precisely defined" is correct and can be used in written English.
You can use it to refer to something that is not clearly or exactly defined, or that is difficult to define and explain. For example: "The concept of justice is not precisely defined; it means something different to each person."
Exact(54)
Quite often during the embodiment design stage, design requirements are not precisely defined.
The boundaries of Mahopac and Mahopac Falls are not precisely defined, Putnam officials say, but are larger than the census designation.
The indigent, while not precisely defined, account for most of the 230,000 Family Court cases filed in New York City each year.
General protection goals for the environmental risk assessment (ERA) of plant protection products are stated in European legislation but specific protection goals (SPGs) are often not precisely defined.
Although it is not precisely defined, the range between macro- and microimaging i.e., from approximately 100μm to 500 μm, is usually denoted as high-resolution CT (hrCT) and MRI (hrMRI) imaging for CT and MRI.
The law permitted any Californian with a doctor's note to own up to six mature marijuana plants, or to possess up to half a pound of processed weed, which could be obtained from a patients' collective or coöperative — terms that were not precisely defined in the statute.
Similar(6)
The survey did not precisely define what constitutes a nap.
Though his book describes epidemics of all kinds of phenomena, he does not precisely define what the phenomena under discourse are.
The president and vice president did not precisely define the "middle class," a term used in conversation and politics to describe aspirations as well as income levels.
But the Country Life Commission did not precisely define what it meant by "rural".... To this day, all of the major definitions still define "rural" by defining everything that is not rural.
The Guardian has also discovered that the bonus scheme rules give managers the power to exclude a member of staff if they are considered an "unsatisfactory performer", although they do not precisely define this term and it could be subject to abuse, according to employment lawyers.
More suggestions(16)
not appropriately defined
not precisely characterised
not just defined
not accurately defined
not clearly defined
not concretely defined
not explicitly defined
not specifically defined
not rigorously defined
not properly defined
not perfectly defined
not precisely identified
not absolutely defined
not precisely examined
not precisely determined
not actually defined
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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