Using the notion of ``belongingness ($\in$)'' and ``quasi-coincidence (q)'' of fuzzy points with fuzzy sets, the concept of $(\alpha, \beta)$-fuzzy subalgebra where $\alpha, \, \beta$ are any two of $\{\in, {\rm q}, \in \!\vee \, {\rm q}, \in \!\wedge \, {\rm q}\}$ with $\alpha \ne \, \in \!\wedge \, {\rm q}$ is introduced, and related properties are investigated.