We introduce a new notion of fuzzy
r-interior which is an extension of Chang's fuzzy
interior. Using fuzzy r-interior, we define fuzzy
r-semiopen sets and fuzzy
r-semicontinuous maps which are generalizations of
fuzzy semiopen sets and fuzzy semicontinuous maps in Chang's fuzzy
topology, respectively. Some basic properties of fuzzy
r-semiopen sets and fuzzy
r-semicontinuous maps are investigated.