This work introduces the concepts of fuzzy upper and lower theta star (respectively theta)- semicontinuous multifunction on fuzzy topological spaces in the Sostak sense. In L-fuzzy topological spaces, the mutual relationships of these fuzzy upper (resp. fuzzy lower) theta star (resp. theta)-semicontinuous multifunctions are established, as well as several characterizations and properties. Later, researchers looked at the composition and union of these multifunctions
