Let the set $A=(a_{1},a_{2},a_{3},a_{4})$ . If the sum of elements in every 3-element subset of $A$ makes up the set $B=(-1,5,3,8)$ , then find the set $A$.
1. Denote the elements of set \( A \) as \( a = a_1, b = a_2, c = a_3, d = a_4 \). We are given that the sum of elements in every 3-element subset of \( A \) makes up the set \( B = \{-1, 5, 3, 8\} \).

2. Write down the equations for the sums of the 3-element subsets:
   \[
   \begin{cases}
   a + b + c = -1 \\
   a + b + d = 5 \\
   a + c + d = 3 \\
   b + c + d = 8
   \end{cases}
   \]

3. Sum all four equations:
   \[
   (a + b + c) + (a + b + d) + (a + c + d) + (b + c + d) = -1 + 5 + 3 + 8
   \]
   Simplify the left-hand side:
   \[
   3a + 3b + 3c + 3d = 15
   \]
   Divide both sides by 3:
   \[
   a + b + c + d = 5
   \]

4. Use the equation \( a + b + c + d = 5 \) to find the individual elements. Subtract each of the original equations from this sum:
   \[
   \begin{cases}
   d = (a + b + c + d) - (a + b + c) = 5 - (-1) = 6 \\
   c = (a + b + c + d) - (a + b + d) = 5 - 5 = 0 \\
   b = (a + b + c + d) - (a + c + d) = 5 - 3 = 2 \\
   a = (a + b + c + d) - (b + c + d) = 5 - 8 = -3
   \end{cases}
   \]

5. Therefore, the set \( A \) is:
   \[
   A = \{-3, 0, 2, 6\}
   \]

The final answer is \(\boxed{\{-3, 0, 2, 6\}}\)