In this paper for a given algebra $\mathcal A$, the notation of a weak partial $\mathcal L$-valued (fuzzy) congruence algebra $\overline{K_w(\mathcal A)}=\overline{(C_w(A)},\wedge,\vee,\circ,\sigma,\Delta,A^2)$, is introduced. $\overline{C_w(A)}$ is a weak $\mathcal L$-valued (fuzzy) congruence relation on an $\mathcal A$, defined in [1], $\overline{K_w(\mathcal A)}$ gives more information on $\mathcal A$ just lattice $\overline{C_w(\mathcal A)}$.