Let $S$ be an algebraic set generated by polynomials in $\mathbb{C}[x_1, \ldots, x_n]$. Define the "degree" of $S$ as $$ \min( \deg(f_1) + \deg(f_2) + \ldots + \deg(f_m) : f_1, f_2, \ldots, f_m \text{ generates } S ), $$ where $\deg(f_i)$ is the largest degree of a nonzero monomial in $f_i$.

Is there such a definition in algebraic geometry?