Abstract 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].
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