I have just started to learn about fuzzy sets from this website which is written in Persian. Here are some quotations,
If $U$ is a finite set, we usually denote the fuzzy set $A$ as $$ A=\left\{\frac{\mu(x_1)}{x_1},\frac{\mu(x_2)}{x_2},\frac{\mu(x_3)}{x_3}, \cdots, \frac{\mu(x_n)}{x_n}\right\}, \ x_1,x_2\cdots,x_n \in U $$ Here the fractions do not mean fraction numbers.
Sometimes we denote fuzzy sets as $$ A=\dfrac{\mu(x_1)}{x_1}+\dfrac{\mu(x_2)}{x_2}+\dfrac{\mu(x_3)}{x_3}+\cdots+\dfrac{\mu(x_n)}{x_n} =\sum_{i=1}^n \dfrac{\mu(x_i)}{x_i} $$ Here the purpose of $+$ is to separate the elements of the set.
If $U$ is an infinite set, we call the fuzzy set "infinite". In this case, we use $\int$ instead of $\sum$. for example if $x$ is between $0$ and $2$, then the fuzzy set $A$ can be denoted with respect to $\mu(x)$ as: $$A = \int_x \dfrac{\mu_A(x)}{x}$$ As you can see, we don't have $dx$ in above expression since $\int$ doesn't mean integral here.
It is very strange for me that usual mathematics notation is used here with different meaning. Can you explain why this happens in this context and how is it valid? Am I missing some basic concepts?
Edit:
Now I looked up Glossary of mathematical symbols. It seems that the usage of plus sign might be relevant in this context,
$+$
- Sometimes used instead of $\sqcup$ for a disjoint union of sets.
But not sure if it really means disjoint union of sets here.
There are simply not enough symbols available to have a different symbol for every concept in all of mathematics. It is difficult to invent a new symbol or notation when writing a document electronically (it's easier when handwriting), so in a limited context, it may be convenient to reuse a common symbol or notation with a different meaning, if it is carefully explained so that it cannot be confused (in context) with its standard meaning.