To model the relationship between reading materials in adaptive learning systems, a fuzzy partial ordering graph can be used. A practice problem is characterized as a multiset of required concepts. The standard ordering rules are:

1. Problem s1 is harder than s2 (s1 > s2) if s1 covers all required concepts of s2.
2. Problem s1 is directly harder than s2 if s1 > s2 and no intermediate problem s3 exists.
3. The partial ordering is represented as a Directed Acyclic Graph (DAG) where edges represent the "directly harder than" relation.

To address sparse hierarchical structures in domains like vocabulary knowledge, an $\alpha$-fuzzily harder relation is applied to increase density: problem s1 is $\alpha$-fuzzily harder than problem s2 if s1 covers at least a proportion $\alpha$ of s2's required concepts. The parameter $\alpha$ is tuned to balance graph density and the likelihood of student comprehension (e.g., setting $\alpha$ to 0.8).