Abstract
In this article, we establish the idea of falling fuzzy
k
-ideals in hemirings through the falling shadow theory and fuzzy sets. We shall express the relations between fuzzy
k
-ideals and falling fuzzy
k
-ideals in hemirings. In particular, we shall establish different characterizations of
k
-hemiregular hemirings in the perfect positive correlation and independent probability space by means of falling fuzzy
k
-ideals.