Using the belongs to relation ($in$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of ($alpha,;eta$)-fuzzy subalgebras where $alpha,;eta$ are any two of ${{in},;q,;{in};{vee};q,;{in};{wedge};q}$ with ${alpha};{ eq};{in};{wedge};q$ was introduced, and related properties were investigated in [3]. As a continuation of the paper [3], in this paper, the notion of a fuzzy subalgebra with thresholds is introduced, and its characterizations are obtained. Relations between a fuzzy subalgebra with thresholds and an (${in},;{in};{vee};q$)-fuzzy subalgebra are provided.