2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162046we will define a fuzzy signed measure on $σ$-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.Logic28A12, 28E10text