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The phrase "nebulous definition" is correct and usable in written English.
You can use this phrase when referring to an idea, concept, or definition that is unclear or difficult to understand. For example, "This article presents a nebulous definition of success."
Exact(5)
Others would tolerate a more nebulous definition of sovereignty for their region.
Transmedia, by any nebulous definition, takes the big-screen experience in some other direction.
He reminded me of the half-smoke's nebulous definition.
Over the past decade, "sustainability" has become a popular corporate buzzword with a nebulous definition.
Yet it is arguable that the failure to adopt the goal of universal health coverage is attributable at least in part to its nebulous definition.
Similar(55)
In a 2016 New York Times Magazine article called "When Everyone Can Be 'Queer,' Is Anyone?", writer Jenna Wortham detangled the nebulous definitions and political connotations surrounding the term, explaining how it came to be reclaimed by the LGBTQ community from a pejorative to its current status as a self-applied term of empowerment.
Diagnostic barriers were the frequent combination of explained and unexplained symptoms, and the nebulous definitions of MUS.
Fatally nebulous in definition, it would nonetheless be – physically and metaphorically – above parliament and the houses for the prime minister and the governor general, so the people might watch over their head of state and chief executive.
(I will return to the contentious question of what exactly the non-genre of nonfiction really is. That, of course, is where the trouble starts. Fiction is a genre. Nonfiction is a library convention; its definition is nebulous. Perhaps by the time this list is complete we'll have a better idea about its constituent elements).
Moreover, grounds upon which bills may be excluded such as "public safety" and "peace", have been described as "nebulous" with potentially wide definitions that are open to abuse by the government in power.
Answer – no formal definition exists (although a nebulous generic definition certainly does (see below)).
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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