It is known that from the purely mathematical viewpoint, fuzzy sets can be interpreted as equivalent classes of random sets. This interpretations helps to teach fuzzy techniques to statisticians and also enables us to apply results about random sets to fuzzy techniques. The problem with this interpretation is that it is too complicated: a random set is not an easy notion, and classes of random sets are even more complex. This complexity goes against the spirit of fuzzy sets, whose purpose was to be simple and intuitively clear. From this viewpoint, it is desirable to simplify this interpretation. In this paper, we show that the random-set interpretation of fuzzy techniques can indeed be simplified: namely, we can show that fuzzy sets can be interpreted not as classes, but as strongly consistent random sets (in some reasonable sense). This is not yet at the desired level of simplicity, but this new interpretation is much simpler than the original one and thus, constitutes an important step towards the desired simplicity.