Fuzzy differential inclusion is the extension of differential inclusion to fuzzy sets introduced by Lotfi A. Zadeh.
with
Suppose is a fuzzy valued continuous function on Euclidean space. Then it is the collection of all normal, upper semi-continuous, convex, compactly supported fuzzy subsets of .
The second order differential is
where , is trapezoidal fuzzy number , and is a trianglular fuzzy number (-1,0,1).
Fuzzy differential inclusion (FDI) has applications in