The function seems to modify the input string in several ways, such as capitalizing lowercase letters, shifting vowels by a certain number of positions in the alphabet, and keeping numbers and special characters unchanged.

[CODE]: 

```python
def approx_function(s):
    vowels = 'AEIOU'
    result = ''
    for char in s:
        if char.islower():
            char = char.upper()
        if char in vowels:
            char = chr(ord(char) + 4)
            if char > 'Z':
                char = chr(ord(char) - 26)
        result += char
    return result
```