The fuzzification of an implicative $LI$-ideal is considered 
and some of their properties are investigated. 
Characterizations of a fuzzy implicative $LI$-ideal are established. 
Conditions for a fuzzy $LI$-ideal to be a fuzzy implicative 
$LI$-ideal are provided. Extension property of a fuzzy implicative 
$LI$-ideal is built.