additive closedness in subsets of $mathbb{z}_n$

The r-value in subsets of finite abelian groups serves as a metric for evaluating the degree of closedness within these subsets. the notion of the r-value is intricately linked to other mathematical constructs such as sum-free sets, sidon sets, and schur triples. we extend the definition of r-value of a subset in a finite abelian group and investigate the r-values of subsets of z_n, by constructing a formula for r-values of intervals consist of consecutive residue classes modulo n.