That doesn't make it less of a copyright infringement, at least in the United States. According to the U.S. Department of State's Focus on Intellectual Property Rights, republished in part in this glossary, there's a chance that the concept of "substantial similarity" would apply and protect my work from being rewritten.
What is substantial similarity? The glossary defines it as how similar an original copyrighted work is to the work accused of copyright violation, and notes:
Exact word-for-word or line-for-line identity does not define the limits of copyright infringement. U.S. courts have chosen the flexible phrase "substantial similarity" to define that level of similarity that will, together with proof of validity and copying, constitute copyright infringement.So if you rewrite a work or more than one works, even if you don't use the exact phrasing, even if you never copy a single sentence, it's not only considered plagiarism, but also may constitute copyright infringement.
And if that's not enough to convince you, according to Copyright.gov, you've got a violation of copyright if you reproduce, distribute, perform, publicly display, or make the original work "into a derivative work without the permission of the copyright owner."
What is a derivative work? Back to the glossary: It's a work that's "based on a preexisting work that is changed, condensed, recast, or embellished in some way."
As with everything legal, the words are open to interpretation. But if you've had your original work copied, but not with the exact words, it still may be protected by copyright law. And if you're thinking of rewriting an existing article or articles, the safest bet would be to not do that, but produce your own original creative work instead.
And one more note. This doesn't mean you can't use other peoples' articles as sources when writing your own. There's a subtle, but very real, difference between rewriting as copyright infringement and writing your own article using another article as a source. I go into more detail about sourcing in Is Rewriting the Same as Plagiarism.