Approximation properties in fuzzy normed spaces

The paper is concerned with approximation properties which are defined in fuzzy normed spaces. First, we introduce the approximation property and the bounded approximation property. Next, we provide two main examples: First example is a fuzzy normed space that does not have the approximation property and second example is a fuzzy normed space with the approximation property that does not have the bounded approximation property. Finally, we provide characterizations of approximation properties in fuzzy normed spaces.