The aim of the paper is mainly to introduce and study I type of strong
connectivity in L-fuzzy topological space. It preserves many good pro
perties of connected sets in general topological spaces: The sets betw
een I type of strongly connected set and its semiclosure are I type of
strongly connected. Any union of I type of strongly connected sets wi
th non-null intersection is I type of strongly connected. The images o
f irresolute order-homomorphisms of I type of strongly connected sets
are I type of strongly connected. For I type of strong connectivity th
e K. Fan's Theorem holds. (C) 1998 Elsevier Science B.V. All rights re
served.