CONTINUITY OF FUZZY MULTIVALUED MAPPINGS

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.