Complexity of calculating independence number of a hypergraph
did not find a proof of complexity class harder than &quot;NP hard&quot; for this problem (ie the presumably more complex hypergraph version of the problem does not seem to have been proven harder than the graph version) however did find the following. Saket has recent research in the area. results in complexity theory in active areas of research tend to be highly specialized and in the form &quot;for limited hypergraph types [x], the following improved complexity bound [y] is shown.&quot; (ie more as approximability results, &amp; more specialized than what you request but it can be mined for nearest desirable results/refs.)
basically hypergraphs while an old mathematical concept are a more recent area of complexity theory research and there is a large active/ongoing research program of determining complexity of operations around them and how those complexities relate to corresponding graph operation complexities, and translating theorems and knowledge about graphs into their hypergraph analogs.

Hardness of Finding Independent Sets in 2-Colorable Hypergraphs and of Satisﬁable CSPs Saket (Dec 2013)

This work revisits the PCP Veriﬁers used in the works of H˚astad [H˚as01], Guruswami et al. [GHS02],
Holmerin [Hol02] and Guruswami [Gur00] for satisﬁable MAX-E3-SAT and MAX-Ek-SET-SPLITTING,
and independent set in 2-colorable 4-uniform hypergraphs. We provide simpler and more efficient PCP
Veriﬁers to prove ... improved hardness results ...


Hardness of Maximum Independent Set in Structured Hypergraphs Saket powerpoint slides overview