Continuity of multivalued mappings is characterized by two types of se
mi-continuity: lower and upper semi-continuity. In this paper, differe
nt equivalent ways in which these concepts can be expressed are invest
igated and then used to define lower and upper semi-continuous fuzzy m
ultivalued mappings. Some shortcomings in existing definitions of uppe
r semi-continuous multivalued mappings are addressed. Several relation
ships between the lower semi-continuity of fuzzy multivalued mappings
and the classical lower semi-continuity of their cuts, or the lower se
mi-continuity w.r.t. the level topologies are established in the setti
ng of stratified fuzzy topological spaces. Two different types of uppe
r semi-continuity of fuzzy multivalued mappings are introduced, inspir
ed by the two equivalent ones in the crisp case. The relationships bet
ween these two types are studied completely. Many interesting properti
es of lower and upper semi-continuous fuzzy multivalued mappings are p
resented, including the composition and union of lower and upper semi-
continuous fuzzy multivalued mappings and the compactness preserving p
roperty of upper semi-continuous and compact-valued fuzzy multivalued
mappings. (C) 1998 Elsevier Science B.V.