This question is completely irrelevant. This is the same as if I asked you whether this color is black:
while the only alternative would be white. Of course you can decide not to make such a classification, the same way you can decide not to believe in anything.
Accepting something only as either true or false means that you are applying a law of excluded middle, which, when used in relation to science - with all the uncertainty of the gathered information - could, and eventually would, lead to false conclusions.
It is also possible to use a three-valued logic, i.e. accept something as either true, false, and unknown, so that a classification of beliefs as Theism, Atheism, and Agnosticism, respectively, makes perfect sense (disregarding the original intend of the author of the term “Agnosticism”).
Using a binary logic also means that you have to select something that I would call a “threshold of certainty” - all above that threshold would be accepted as true, and all below as false. Threshold by its nature is something arbitrary, so it’s another reason not to use a binary logic.
So what alternative would be to “believing” in things? The best thing I can imagine is accepting every peace of information with certain dose of certainty. For example, I think there are minimum chances that God exist, but there are big chances that the Universe was created in Big Bang. I wouldn’t say that I believe in Big Bang, because I realize that there are other possibilities, some of which probably I have never even considered.
You probably know that I expected such an answer and you are right. So, for all I know, statement “Sun revolves around Earth” cannot be called true nor false without additional information (it has nothing to do with fuzzy logic though). Now the question is - have you assumed that some conditions are met or certain point of view must be taken, therefore accepted this statement as false, or are you just blindly repeating what you have been taught in school? Because if the latter, how different are you from people who are blindly following the Bible?