The paper investigates fuzziness of quantales by means of quasi-coincidence of fuzzy points with two parameters based on $L$-sets and developes two more generalized fuzzy structures, called $(\in_g,\in_g\vee q_h)$-$L$-subquantale and $(\in_g,\in_g\vee q_h)$-$L$-filter. Some intrinsic connections between $(\in_g,\in_g\vee q_h)$-$L$-subquantales and crisp subquantales are established, and relationships between $(\in_g,\in_g\vee q_h)$-$L$-filters of quantales and their extensions (especially the essential connections between $(\in_g,\in_g\vee q_h)$-$L$-subquantales and $(\in_g,\in_g\vee q_h)$-$L$-filters of quantales) are studied by employing the new characterizations of $(\in_g,\in_g\vee q_h)$-$L$-filters of quantales. Also, sufficient conditions for the extension of an $(\in_g,\in_g\vee q_h)$-$L$-filter to be an $(\in_g,\in_g\vee q_h)$-$L$-filter of a quantale are also offered. In particular, it is proved that the category extbf{GLFquant} (resp., extbf{GFFQant}) of $(\in_g,\in_g\vee q_h)$-$L$-subquantales (resp., $L$-filters) is of a topological construct on extbf{Quant} and posses equalizers and pullbacks.