Summary: Let \(S_1\) and \(S_2\) be two \((k - 1)\)-subsets in a \(k\)-uniform hypergraph \(H\). We call \(S_1\) and \(S_2\) strongly or middle or weakly independent if \(H\) does not contain an edge \(e \in E(H)\) such that \(S_1 \cap e \neq \varnothing\) and \(S_2 \cap e \neq \varnothing\) or \(e \subseteq S_1 \cup S_2\) or \(e \supseteq S_1 \cup S_2\), respectively. In this paper, we obtain the following results concerning these three independence. (1) For any \(n \geq 2k^2 - k\) and \(k \geq 3\), there exists an \(n\)-vertex \(k\)-uniform hypergraph, which has degree sum of any two strongly independent \((k - 1)\)-sets equal to \(2n-4(k-1)\), contains no perfect matching; (2) Let \(d \geq 1\) be an integer and \(H\) be a \(k\)-uniform hypergraph of order \(n \geq kd+(k-2)k\). If the degree sum of any two middle independent \((k-1)\)-subsets is larger than \(2(d-1)\), then \(H\) contains a \(d\)-matching; (3) For all \(k \geq 3\) and sufficiently large \(n\) divisible by \(k\), we completely determine the minimum degree sum of two weakly independent \((k - 1)\)-subsets that ensures a perfect matching in a \(k\)-uniform hypergraph \(H\) of order \(n\).