In this paper, we establish new definitions of smooth closure and smooth interior of a fuzzy set [3] under the name of fuzzy closure and fuzzy interior of a fuzzy set which satisfy almost all properties of the corresponding definitions in fuzzy topological spaces in Chang's sense. As a consequence of these definitions we show that the topological concepts, especially various types of compactness, can be presented in a simple way, with no additional hypotheses needed which occured in [3] and with no counterpart in [2, 4, 6].