  we will define a fuzzy signed measure on $\sigma$-algebras, as well as
positive and negative sets. Herein, we will show that the Fuzzy Hahn
Decomposition Theorem, which is a generalization of the classical Hahn
Decomposition Theorem, decompose any space X into a positive set A and a
negative set B such that A+B=X and the signed measure of $A \wedge B $ is 0.
