Abstract
In the present paper, closed and robust fuzzy sets on the $n$ dimensional Euclidean space $\mathbb{R}^n$ are considered. The boundedness of their fuzzy sets are not assumed. Then, it is derived that there is a one-to-one correspondence between the class of all closed fuzzy sets and the class of all monotone decreasing left-continuous set-valued mappings, and that there is a one-to-one correspondence between the class of all robust fuzzy sets and the class of all monotone decreasing continuous set-valued mappings.
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